2023-08-24 17:47:31 +08:00
<!doctype html>
< html lang = "zh" class = "no-js" >
< head >
< meta charset = "utf-8" >
< meta name = "viewport" content = "width=device-width,initial-scale=1" >
< meta name = "description" content = "动画图解、一键运行的数据结构与算法教程" >
< meta name = "author" content = "Krahets" >
< link rel = "canonical" href = "https://www.hello-algo.com/chapter_computational_complexity/iteration_and_recursion/" >
< link rel = "prev" href = "../performance_evaluation/" >
< link rel = "next" href = "../time_complexity/" >
< link rel = "icon" href = "../../assets/images/favicon.png" >
2023-12-14 02:56:10 +08:00
< meta name = "generator" content = "mkdocs-1.5.3, mkdocs-material-9.5.2" >
2023-08-24 17:47:31 +08:00
< title > 2.2 < / title >
2023-12-14 02:56:10 +08:00
< link rel = "stylesheet" href = "../../assets/stylesheets/main.50c56a3b.min.css" >
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
< link rel = "stylesheet" href = "../../assets/stylesheets/palette.06af60db.min.css" >
2023-08-24 17:47:31 +08:00
2023-09-24 17:12:06 +08:00
2023-08-24 17:47:31 +08:00
< link rel = "preconnect" href = "https://fonts.gstatic.com" crossorigin >
< link rel = "stylesheet" href = "https://fonts.googleapis.com/css?family=Noto+Sans+SC:300,300i,400,400i,700,700i%7CFira+Code:400,400i,700,700i&display=fallback" >
< style > : root { --md-text-font : "Noto Sans SC" ; --md-code-font : "Fira Code" } < / style >
< link rel = "stylesheet" href = "../../stylesheets/extra.css" >
< script > _ _md _scope = new URL ( "../.." , location ) , _ _md _hash = e => [ ... e ] . reduce ( ( e , _ ) => ( e << 5 ) - e + _ . charCodeAt ( 0 ) , 0 ) , _ _md _get = ( e , _ = localStorage , t = _ _md _scope ) => JSON . parse ( _ . getItem ( t . pathname + "." + e ) ) , _ _md _set = ( e , _ , t = localStorage , a = _ _md _scope ) => { try { t . setItem ( a . pathname + "." + e , JSON . stringify ( _ ) ) } catch ( e ) { } } < / script >
2023-09-22 13:08:10 +08:00
< link href = "../../assets/stylesheets/glightbox.min.css" rel = "stylesheet" / > < style >
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
< / style > < script src = "../../assets/javascripts/glightbox.min.js" > < / script > < / head >
2023-08-24 17:47:31 +08:00
< body dir = "ltr" data-md-color-scheme = "default" data-md-color-primary = "white" data-md-color-accent = "indigo" >
< input class = "md-toggle" data-md-toggle = "drawer" type = "checkbox" id = "__drawer" autocomplete = "off" >
< input class = "md-toggle" data-md-toggle = "search" type = "checkbox" id = "__search" autocomplete = "off" >
< label class = "md-overlay" for = "__drawer" > < / label >
< div data-md-component = "skip" >
< a href = "#22" class = "md-skip" >
跳转至
< / a >
< / div >
< div data-md-component = "announce" >
< / div >
< header class = "md-header md-header--shadow" data-md-component = "header" >
< nav class = "md-header__inner md-grid" aria-label = "页眉" >
< a href = "../.." title = "Hello 算法" class = "md-header__button md-logo" aria-label = "Hello 算法" data-md-component = "logo" >
2023-11-08 00:42:43 +08:00
< img src = "../../assets/images/logo.svg" alt = "logo" >
2023-08-24 17:47:31 +08:00
< / a >
< label class = "md-header__button md-icon" for = "__drawer" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z" / > < / svg >
< / label >
< div class = "md-header__title" data-md-component = "header-title" >
< div class = "md-header__ellipsis" >
< div class = "md-header__topic" >
< span class = "md-ellipsis" >
Hello 算法
< / span >
< / div >
< div class = "md-header__topic" data-md-component = "header-topic" >
< span class = "md-ellipsis" >
2.2 迭代与递归
< / span >
< / div >
< / div >
< / div >
< form class = "md-header__option" data-md-component = "palette" >
2023-09-24 17:12:06 +08:00
2023-12-07 20:12:31 +08:00
< input class = "md-option" data-md-color-media = "" data-md-color-scheme = "default" data-md-color-primary = "white" data-md-color-accent = "indigo" aria-label = "Switch to dark mode" type = "radio" name = "__palette" id = "__palette_0" >
2023-09-24 17:12:06 +08:00
2023-12-07 20:12:31 +08:00
< label class = "md-header__button md-icon" title = "Switch to dark mode" for = "__palette_1" hidden >
2023-09-24 17:12:06 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z" / > < / svg >
< / label >
2023-12-07 20:12:31 +08:00
< input class = "md-option" data-md-color-media = "" data-md-color-scheme = "slate" data-md-color-primary = "grey" data-md-color-accent = "indigo" aria-label = "Switch to light mode" type = "radio" name = "__palette" id = "__palette_1" >
2023-09-24 17:12:06 +08:00
2023-12-07 20:12:31 +08:00
< label class = "md-header__button md-icon" title = "Switch to light mode" for = "__palette_0" hidden >
2023-09-24 17:12:06 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z" / > < / svg >
< / label >
< / form >
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
< script > var media , input , key , value , palette = _ _md _get ( "__palette" ) ; if ( palette && palette . color ) { "(prefers-color-scheme)" === palette . color . media && ( media = matchMedia ( "(prefers-color-scheme: light)" ) , input = document . querySelector ( media . matches ? "[data-md-color-media='(prefers-color-scheme: light)']" : "[data-md-color-media='(prefers-color-scheme: dark)']" ) , palette . color . media = input . getAttribute ( "data-md-color-media" ) , palette . color . scheme = input . getAttribute ( "data-md-color-scheme" ) , palette . color . primary = input . getAttribute ( "data-md-color-primary" ) , palette . color . accent = input . getAttribute ( "data-md-color-accent" ) ) ; for ( [ key , value ] of Object . entries ( palette . color ) ) document . body . setAttribute ( "data-md-color-" + key , value ) } < / script >
2023-10-06 13:31:31 +08:00
< div class = "md-header__option" >
< div class = "md-select" >
< button class = "md-header__button md-icon" aria-label = "选择当前语言" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12.87 15.07-2.54-2.51.03-.03A17.52 17.52 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z" / > < / svg >
< / button >
< div class = "md-select__inner" >
< ul class = "md-select__list" >
< li class = "md-select__item" >
< a href = "/" hreflang = "zh" class = "md-select__link" >
中文
< / a >
< / li >
< / ul >
< / div >
< / div >
< / div >
2023-08-24 17:47:31 +08:00
< label class = "md-header__button md-icon" for = "__search" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z" / > < / svg >
< / label >
< div class = "md-search" data-md-component = "search" role = "dialog" >
< label class = "md-search__overlay" for = "__search" > < / label >
< div class = "md-search__inner" role = "search" >
< form class = "md-search__form" name = "search" >
< input type = "text" class = "md-search__input" name = "query" aria-label = "搜索" placeholder = "搜索" autocapitalize = "off" autocorrect = "off" autocomplete = "off" spellcheck = "false" data-md-component = "search-query" required >
< label class = "md-search__icon md-icon" for = "__search" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z" / > < / svg >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / label >
< nav class = "md-search__options" aria-label = "查找" >
< a href = "javascript:void(0)" class = "md-search__icon md-icon" title = "分享" aria-label = "分享" data-clipboard data-clipboard-text = "" data-md-component = "search-share" tabindex = "-1" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z" / > < / svg >
< / a >
< button type = "reset" class = "md-search__icon md-icon" title = "清空当前内容" aria-label = "清空当前内容" tabindex = "-1" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41Z" / > < / svg >
< / button >
< / nav >
< div class = "md-search__suggest" data-md-component = "search-suggest" > < / div >
< / form >
< div class = "md-search__output" >
< div class = "md-search__scrollwrap" data-md-scrollfix >
< div class = "md-search-result" data-md-component = "search-result" >
< div class = "md-search-result__meta" >
正在初始化搜索引擎
< / div >
< ol class = "md-search-result__list" role = "presentation" > < / ol >
< / div >
< / div >
< / div >
< / div >
< / div >
< div class = "md-header__source" >
< a href = "https://github.com/krahets/hello-algo" title = "前往仓库" class = "md-source" data-md-component = "source" >
< div class = "md-source__icon md-icon" >
2023-12-07 20:12:31 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg >
2023-08-24 17:47:31 +08:00
< / div >
< div class = "md-source__repository" >
krahets/hello-algo
< / div >
< / a >
< / div >
< / nav >
< / header >
< div class = "md-container" data-md-component = "container" >
< main class = "md-main" data-md-component = "main" >
< div class = "md-main__inner md-grid" >
< div class = "md-sidebar md-sidebar--primary" data-md-component = "sidebar" data-md-type = "navigation" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--primary" aria-label = "导航栏" data-md-level = "0" >
< label class = "md-nav__title" for = "__drawer" >
< a href = "../.." title = "Hello 算法" class = "md-nav__button md-logo" aria-label = "Hello 算法" data-md-component = "logo" >
2023-11-08 00:42:43 +08:00
< img src = "../../assets/images/logo.svg" alt = "logo" >
2023-08-24 17:47:31 +08:00
< / a >
Hello 算法
< / label >
< div class = "md-nav__source" >
< a href = "https://github.com/krahets/hello-algo" title = "前往仓库" class = "md-source" data-md-component = "source" >
< div class = "md-source__icon md-icon" >
2023-12-07 20:12:31 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg >
2023-08-24 17:47:31 +08:00
< / div >
< div class = "md-source__repository" >
krahets/hello-algo
< / div >
< / a >
< / div >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_1" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_preface/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z" / > < / svg >
< span class = "md-ellipsis" >
第 0 章 前言
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_1" id = "__nav_1_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_1_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_1" >
< span class = "md-nav__icon md-icon" > < / span >
第 0 章 前言
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/about_the_book/" class = "md-nav__link" >
< span class = "md-ellipsis" >
0.1 关于本书
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/suggestions/" class = "md-nav__link" >
< span class = "md-ellipsis" >
0.2 如何使用本书
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
0.3 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_2" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_introduction/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z" / > < / svg >
< span class = "md-ellipsis" >
第 1 章 初识算法
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_2" id = "__nav_2_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_2_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_2" >
< span class = "md-nav__icon md-icon" > < / span >
第 1 章 初识算法
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/algorithms_are_everywhere/" class = "md-nav__link" >
< span class = "md-ellipsis" >
1.1 算法无处不在
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/what_is_dsa/" class = "md-nav__link" >
< span class = "md-ellipsis" >
1.2 算法是什么
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
1.3 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--active md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_3" checked >
< div class = "md-nav__link md-nav__container" >
< a href = "../" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z" / > < / svg >
< span class = "md-ellipsis" >
2023-08-28 04:36:05 +08:00
第 2 章 复杂度分析
2023-08-24 17:47:31 +08:00
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_3" id = "__nav_3_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_3_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_3" >
< span class = "md-nav__icon md-icon" > < / span >
2023-08-28 04:36:05 +08:00
第 2 章 复杂度分析
2023-08-24 17:47:31 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../performance_evaluation/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2.1 算法效率评估
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--active" >
< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
< span class = "md-ellipsis" >
2.2 迭代与递归
< / span >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
< span class = "md-ellipsis" >
2.2 迭代与递归
< / span >
< / a >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#221" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2.2.1 迭代
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< nav class = "md-nav" aria-label = "2.2.1 >
< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#1-for" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
1. for 循环
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#2-while" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2. while 循环
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#3" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
3. 嵌套循环
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#222" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2.2.2 递归
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< nav class = "md-nav" aria-label = "2.2.2 >
< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#1" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
1. 调用栈
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#2" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2. 尾递归
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#3_1" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
3. 递归树
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< / ul >
< / nav >
2023-09-12 00:56:10 +08:00
< / li >
< li class = "md-nav__item" >
< a href = "#223" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2.2.3 两者对比
< / span >
2023-09-12 00:56:10 +08:00
< / a >
2023-08-24 17:47:31 +08:00
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../time_complexity/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2.3 时间复杂度
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../space_complexity/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2.4 空间复杂度
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2.5 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_4" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_data_structure/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z" / > < / svg >
< span class = "md-ellipsis" >
第 3 章 数据结构
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_4_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
第 3 章 数据结构
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/classification_of_data_structure/" class = "md-nav__link" >
< span class = "md-ellipsis" >
3.1 数据结构分类
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/basic_data_types/" class = "md-nav__link" >
< span class = "md-ellipsis" >
3.2 基本数据类型
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/number_encoding/" class = "md-nav__link" >
< span class = "md-ellipsis" >
3.3 数字编码 *
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/character_encoding/" class = "md-nav__link" >
< span class = "md-ellipsis" >
3.4 字符编码 *
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
3.5 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-11-26 02:06:45 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_array_and_linkedlist/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z" / > < / svg >
< span class = "md-ellipsis" >
第 4 章 数组与链表
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_5_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
第 4 章 数组与链表
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
< span class = "md-ellipsis" >
4.1 数组
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
< span class = "md-ellipsis" >
4.2 链表
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
< span class = "md-ellipsis" >
4.3 列表
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-11-26 02:06:45 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/ram_and_cache/" class = "md-nav__link" >
< span class = "md-ellipsis" >
4.4 内存与缓存 *
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2023-11-26 02:06:45 +08:00
4.5 小结
2023-08-24 17:47:31 +08:00
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_stack_and_queue/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z" / > < / svg >
< span class = "md-ellipsis" >
第 5 章 栈与队列
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_6_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
第 5 章 栈与队列
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
< span class = "md-ellipsis" >
5.1 栈
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
< span class = "md-ellipsis" >
5.2 队列
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
< span class = "md-ellipsis" >
5.3 双向队列
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
5.4 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_hashing/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z" / > < / svg >
< span class = "md-ellipsis" >
第 6 章 哈希表
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_7_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
第 6 章 哈希表
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
< span class = "md-ellipsis" >
6.1 哈希表
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
< span class = "md-ellipsis" >
6.2 哈希冲突
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_algorithm/" class = "md-nav__link" >
< span class = "md-ellipsis" >
6.3 哈希算法
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
6.4 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_tree/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z" / > < / svg >
< span class = "md-ellipsis" >
第 7 章 树
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
第 7 章 树
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.1 二叉树
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.2 二叉树遍历
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.3 二叉树数组表示
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.4 二叉搜索树
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.5 AVL 树 *
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.6 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_heap/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z" / > < / svg >
< span class = "md-ellipsis" >
第 8 章 堆
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_9_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_9" >
< span class = "md-nav__icon md-icon" > < / span >
第 8 章 堆
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
< span class = "md-ellipsis" >
8.1 堆
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
< span class = "md-ellipsis" >
8.2 建堆操作
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/top_k/" class = "md-nav__link" >
< span class = "md-ellipsis" >
8.3 Top-K 问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
8.4 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_graph/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
< span class = "md-ellipsis" >
第 9 章 图
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
第 9 章 图
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
< span class = "md-ellipsis" >
9.1 图
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
< span class = "md-ellipsis" >
9.2 图基础操作
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
< span class = "md-ellipsis" >
9.3 图的遍历
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
9.4 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_searching/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z" / > < / svg >
< span class = "md-ellipsis" >
第 10 章 搜索
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_11" id = "__nav_11_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_11_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
第 10 章 搜索
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
< span class = "md-ellipsis" >
10.1 二分查找
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_insertion/" class = "md-nav__link" >
< span class = "md-ellipsis" >
10.2 二分查找插入点
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
< span class = "md-ellipsis" >
10.3 二分查找边界
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
< span class = "md-ellipsis" >
10.4 哈希优化策略
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
< span class = "md-ellipsis" >
10.5 重识搜索算法
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
10.6 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_sorting/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z" / > < / svg >
< span class = "md-ellipsis" >
第 11 章 排序
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_12" id = "__nav_12_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_12_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
第 11 章 排序
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/sorting_algorithm/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.1 排序算法
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.2 选择排序
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.3 冒泡排序
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.4 插入排序
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.5 快速排序
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.6 归并排序
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.7 堆排序
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.8 桶排序
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.9 计数排序
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.10 基数排序
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
11.11 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z" / > < / svg >
< span class = "md-ellipsis" >
第 12 章 分治
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_13" id = "__nav_13_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
第 12 章 分治
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/divide_and_conquer/" class = "md-nav__link" >
< span class = "md-ellipsis" >
12.1 分治算法
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/binary_search_recur/" class = "md-nav__link" >
< span class = "md-ellipsis" >
12.2 分治搜索策略
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/build_binary_tree_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
12.3 构建树问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/hanota_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
12.4 汉诺塔问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
12.5 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_14" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_backtracking/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z" / > < / svg >
< span class = "md-ellipsis" >
第 13 章 回溯
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_14" id = "__nav_14_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_14_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_14" >
< span class = "md-nav__icon md-icon" > < / span >
第 13 章 回溯
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/backtracking_algorithm/" class = "md-nav__link" >
< span class = "md-ellipsis" >
13.1 回溯算法
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/permutations_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
13.2 全排列问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/subset_sum_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
13.3 子集和问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/n_queens_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
13.4 N 皇后问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
13.5 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_15" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_dynamic_programming/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z" / > < / svg >
< span class = "md-ellipsis" >
第 14 章 动态规划
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_15" id = "__nav_15_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_15_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_15" >
< span class = "md-nav__icon md-icon" > < / span >
第 14 章 动态规划
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/intro_to_dynamic_programming/" class = "md-nav__link" >
< span class = "md-ellipsis" >
14.1 初探动态规划
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/dp_problem_features/" class = "md-nav__link" >
< span class = "md-ellipsis" >
14.2 DP 问题特性
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/dp_solution_pipeline/" class = "md-nav__link" >
< span class = "md-ellipsis" >
14.3 DP 解题思路
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/knapsack_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
14.4 0-1 背包问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/unbounded_knapsack_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
14.5 完全背包问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/edit_distance_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
14.6 编辑距离问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
14.7 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_16" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_greedy/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z" / > < / svg >
< span class = "md-ellipsis" >
第 15 章 贪心
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_16" id = "__nav_16_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_16_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_16" >
< span class = "md-nav__icon md-icon" > < / span >
第 15 章 贪心
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/greedy_algorithm/" class = "md-nav__link" >
< span class = "md-ellipsis" >
15.1 贪心算法
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/fractional_knapsack_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
15.2 分数背包问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/max_capacity_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
15.3 最大容量问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/max_product_cutting_problem/" class = "md-nav__link" >
< span class = "md-ellipsis" >
15.4 最大切分乘积问题
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_greedy/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
15.5 小结
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-10-30 04:59:19 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_17" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_appendix/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z" / > < / svg >
< span class = "md-ellipsis" >
第 16 章 附录
< / span >
< / a >
2023-12-07 20:12:31 +08:00
< label class = "md-nav__link " for = "__nav_17" id = "__nav_17_label" tabindex = "0" >
2023-08-24 17:47:31 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_17_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_17" >
< span class = "md-nav__icon md-icon" > < / span >
第 16 章 附录
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/installation/" class = "md-nav__link" >
< span class = "md-ellipsis" >
16.1 编程环境安装
< / span >
< / a >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/contribution/" class = "md-nav__link" >
< span class = "md-ellipsis" >
16.2 一起参与创作
< / span >
< / a >
< / li >
2023-10-30 04:59:19 +08:00
2023-12-07 20:12:31 +08:00
2023-10-30 04:59:19 +08:00
< li class = "md-nav__item" >
2023-10-30 05:31:23 +08:00
< a href = "../../chapter_appendix/terminology/" class = "md-nav__link" >
2023-10-30 04:59:19 +08:00
< span class = "md-ellipsis" >
16.3 术语表
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
2023-08-24 17:47:31 +08:00
< / ul >
< / nav >
< / li >
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
2023-08-24 17:47:31 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_18" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_reference/" class = "md-nav__link " >
< span class = "md-ellipsis" >
参考文献
< / span >
< / a >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_18_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_18" >
< span class = "md-nav__icon md-icon" > < / span >
参考文献
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< / ul >
< / nav >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-sidebar md-sidebar--secondary" data-md-component = "sidebar" data-md-type = "toc" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#221" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2.2.1 迭代
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< nav class = "md-nav" aria-label = "2.2.1 >
< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#1-for" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
1. for 循环
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#2-while" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2. while 循环
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#3" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
3. 嵌套循环
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#222" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2.2.2 递归
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< nav class = "md-nav" aria-label = "2.2.2 >
< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#1" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
1. 调用栈
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#2" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2. 尾递归
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#3_1" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
3. 递归树
< / span >
2023-08-24 17:47:31 +08:00
< / a >
< / li >
< / ul >
< / nav >
2023-09-12 00:56:10 +08:00
< / li >
< li class = "md-nav__item" >
< a href = "#223" class = "md-nav__link" >
2023-12-07 20:12:31 +08:00
< span class = "md-ellipsis" >
2.2.3 两者对比
< / span >
2023-09-12 00:56:10 +08:00
< / a >
2023-08-24 17:47:31 +08:00
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-content" data-md-component = "content" >
< article class = "md-content__inner md-typeset" >
2023-12-06 22:28:53 +08:00
<!-- Tags -->
2023-09-21 20:44:52 +08:00
2023-12-06 22:28:53 +08:00
<!-- Actions -->
2023-09-21 20:44:52 +08:00
<!-- Actions -->
2023-08-24 17:47:31 +08:00
2023-12-06 22:28:53 +08:00
<!-- Edit button -->
2023-08-24 17:47:31 +08:00
2023-12-06 22:28:53 +08:00
< a
href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_computational_complexity/iteration_and_recursion.md"
title="编辑此页"
class="md-content__button md-icon"
>
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 512 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z" / > < / svg >
2023-08-24 17:47:31 +08:00
< / a >
2023-12-06 22:28:53 +08:00
<!-- View button -->
2023-09-21 20:44:52 +08:00
<!-- Page content -->
2023-08-24 17:47:31 +08:00
< h1 id = "22" > 2.2 迭代与递归< a class = "headerlink" href = "#22" title = "Permanent link" > ¶ < / a > < / h1 >
2023-12-14 02:53:40 +08:00
< p > 在算法中，重复执行某个任务是很常见的，它与复杂度分析息息相关。因此，在介绍时间复杂度和空间复杂度之前，我们先来了解如何在程序中实现重复执行任务，即两种基本的程序控制结构：迭代、递归。< / p >
2023-08-24 17:47:31 +08:00
< h2 id = "221" > 2.2.1 迭代< a class = "headerlink" href = "#221" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 「迭代 iteration」是一种重复执行某个任务的控制结构。在迭代中， ， < / p >
< h3 id = "1-for" > 1. for 循环< a class = "headerlink" href = "#1-for" title = "Permanent link" > ¶ < / a > < / h3 >
2023-12-02 06:24:11 +08:00
< p > < code > for< / code > 循环是最常见的迭代形式之一，< strong > 适合在预先知道迭代次数时使用< / strong > 。< / p >
< p > 以下函数基于 < code > for< / code > 循环实现了求和 < span class = "arithmatex" > \(1 + 2 + \dots + n\)< / span > ，求和结果使用变量 < code > res< / code > 记录。需要注意的是， < code > range(a, b)< / code > 对应的区间是“左闭右开”的，对应的遍历范围为 < span class = "arithmatex" > \(a, a + 1, \dots, b-1\)< / span > ： < / p >
2023-09-04 03:17:06 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:12" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_11" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_12" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Python< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Java< / label > < label for = "__tabbed_1_4" > C#< / label > < label for = "__tabbed_1_5" > Go< / label > < label for = "__tabbed_1_6" > Swift< / label > < label for = "__tabbed_1_7" > JS< / label > < label for = "__tabbed_1_8" > TS< / label > < label for = "__tabbed_1_9" > Dart< / label > < label for = "__tabbed_1_10" > Rust< / label > < label for = "__tabbed_1_11" > C< / label > < label for = "__tabbed_1_12" > Zig< / label > < / div >
2023-08-24 17:47:31 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > for_loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " for 循环" " " < / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "c1" > # 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > forLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "o" > ++< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > forLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > ForLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > forLoop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > forLoop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "mi" > 1< / span > < span class = "p" > ...< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > forLoop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-6-9" name = "__codelineno-6-9" href = "#__codelineno-6-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > forLoop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > forLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > for_loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ..=< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* for 循环 */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > forLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-25 00:05:17 +08:00
< div class = "highlight" > < span class = "filename" > iteration.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "c1" > // for 循环< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > forLoop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > usize< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > i< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nb" > @as< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "p" > }< / span > < span class = "w" > < / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-12-02 06:24:11 +08:00
< p > 图 2-1 是该求和函数的流程框图。< / p >
2023-11-09 05:13:54 +08:00
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/iteration.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "求和函数的流程框图" class = "animation-figure" src = "../iteration_and_recursion.assets/iteration.png" / > < / a > < / p >
2023-08-24 17:47:31 +08:00
< p align = "center" > 图 2-1 求和函数的流程框图 < / p >
< p > 此求和函数的操作数量与输入数据大小 < span class = "arithmatex" > \(n\)< / span > 成正比，或者说成“线性关系”。实际上，< strong > 时间复杂度描述的就是这个“线性关系”< / strong > 。相关内容将会在下一节中详细介绍。< / p >
< h3 id = "2-while" > 2. while 循环< a class = "headerlink" href = "#2-while" title = "Permanent link" > ¶ < / a > < / h3 >
2023-12-02 06:24:11 +08:00
< p > 与 < code > for< / code > 循环类似，< code > while< / code > 循环也是一种实现迭代的方法。在 < code > while< / code > 循环中，程序每轮都会先检查条件，如果条件为真，则继续执行，否则就结束循环。< / p >
< p > 下面我们用 < code > while< / code > 循环来实现求和 < span class = "arithmatex" > \(1 + 2 + \dots + n\)< / span > ： < / p >
2023-09-04 03:17:06 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:12" > < input checked = "checked" id = "__tabbed_2_1" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_2" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_3" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_4" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_5" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_6" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_7" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_8" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_9" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_10" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_11" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_12" name = "__tabbed_2" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Python< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Java< / label > < label for = "__tabbed_2_4" > C#< / label > < label for = "__tabbed_2_5" > Go< / label > < label for = "__tabbed_2_6" > Swift< / label > < label for = "__tabbed_2_7" > JS< / label > < label for = "__tabbed_2_8" > TS< / label > < label for = "__tabbed_2_9" > Dart< / label > < label for = "__tabbed_2_10" > Rust< / label > < label for = "__tabbed_2_11" > C< / label > < label for = "__tabbed_2_12" > Zig< / label > < / div >
2023-08-24 17:47:31 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > while_loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " while 循环" " " < / span >
< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "n" > i< / span > < span class = "o" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > # 初始化条件变量< / span >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "c1" > # 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "k" > while< / span > < span class = "n" > i< / span > < span class = "o" > < =< / span > < span class = "n" > n< / span > < span class = "p" > :< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span > < span class = "c1" > # 更新条件变量< / span >
< a id = "__codelineno-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-14-8" name = "__codelineno-14-8" href = "#__codelineno-14-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-10" name = "__codelineno-14-10" href = "#__codelineno-14-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > WhileLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-8" name = "__codelineno-15-8" href = "#__codelineno-15-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-15-9" name = "__codelineno-15-9" href = "#__codelineno-15-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-10" name = "__codelineno-15-10" href = "#__codelineno-15-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > whileLoop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-16-6" name = "__codelineno-16-6" href = "#__codelineno-16-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-16-7" name = "__codelineno-16-7" href = "#__codelineno-16-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-8" name = "__codelineno-16-8" href = "#__codelineno-16-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span >
< a id = "__codelineno-16-9" name = "__codelineno-16-9" href = "#__codelineno-16-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-16-10" name = "__codelineno-16-10" href = "#__codelineno-16-10" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-16-11" name = "__codelineno-16-11" href = "#__codelineno-16-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-12" name = "__codelineno-16-12" href = "#__codelineno-16-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-16-13" name = "__codelineno-16-13" href = "#__codelineno-16-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
< a id = "__codelineno-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > whileLoop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-17-4" name = "__codelineno-17-4" href = "#__codelineno-17-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > i< / span > < span class = "p" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-17-5" name = "__codelineno-17-5" href = "#__codelineno-17-5" > < / a > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-17-6" name = "__codelineno-17-6" href = "#__codelineno-17-6" > < / a > < span class = "k" > while< / span > < span class = "n" > i< / span > < span class = "o" > < =< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-17-7" name = "__codelineno-17-7" href = "#__codelineno-17-7" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-17-9" name = "__codelineno-17-9" href = "#__codelineno-17-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-10" name = "__codelineno-17-10" href = "#__codelineno-17-10" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-17-11" name = "__codelineno-17-11" href = "#__codelineno-17-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > whileLoop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > whileLoop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
< a id = "__codelineno-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > whileLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-20-5" name = "__codelineno-20-5" href = "#__codelineno-20-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-20-6" name = "__codelineno-20-6" href = "#__codelineno-20-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-8" name = "__codelineno-20-8" href = "#__codelineno-20-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-20-9" name = "__codelineno-20-9" href = "#__codelineno-20-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-10" name = "__codelineno-20-10" href = "#__codelineno-20-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-20-11" name = "__codelineno-20-11" href = "#__codelineno-20-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
< a id = "__codelineno-21-2" name = "__codelineno-21-2" href = "#__codelineno-21-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > while_loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-3" name = "__codelineno-21-3" href = "#__codelineno-21-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-21-5" name = "__codelineno-21-5" href = "#__codelineno-21-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-21-6" name = "__codelineno-21-6" href = "#__codelineno-21-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-21-7" name = "__codelineno-21-7" href = "#__codelineno-21-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-21-8" name = "__codelineno-21-8" href = "#__codelineno-21-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-21-9" name = "__codelineno-21-9" href = "#__codelineno-21-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-10" name = "__codelineno-21-10" href = "#__codelineno-21-10" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-21-11" name = "__codelineno-21-11" href = "#__codelineno-21-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "cm" > /* while 循环 */< / span >
< a id = "__codelineno-22-2" name = "__codelineno-22-2" href = "#__codelineno-22-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-3" name = "__codelineno-22-3" href = "#__codelineno-22-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-4" name = "__codelineno-22-4" href = "#__codelineno-22-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-22-5" name = "__codelineno-22-5" href = "#__codelineno-22-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-22-6" name = "__codelineno-22-6" href = "#__codelineno-22-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-7" name = "__codelineno-22-7" href = "#__codelineno-22-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-8" name = "__codelineno-22-8" href = "#__codelineno-22-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-22-9" name = "__codelineno-22-9" href = "#__codelineno-22-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-10" name = "__codelineno-22-10" href = "#__codelineno-22-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-11" name = "__codelineno-22-11" href = "#__codelineno-22-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-25 00:05:17 +08:00
< div class = "highlight" > < span class = "filename" > iteration.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / a > < span class = "c1" > // while 循环< / span >
< a id = "__codelineno-23-2" name = "__codelineno-23-2" href = "#__codelineno-23-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > whileLoop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-23-3" name = "__codelineno-23-3" href = "#__codelineno-23-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-4" name = "__codelineno-23-4" href = "#__codelineno-23-4" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-23-5" name = "__codelineno-23-5" href = "#__codelineno-23-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-23-6" name = "__codelineno-23-6" href = "#__codelineno-23-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-23-7" name = "__codelineno-23-7" href = "#__codelineno-23-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-23-8" name = "__codelineno-23-8" href = "#__codelineno-23-8" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-9" name = "__codelineno-23-9" href = "#__codelineno-23-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-23-10" name = "__codelineno-23-10" href = "#__codelineno-23-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-11" name = "__codelineno-23-11" href = "#__codelineno-23-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-12-02 06:24:11 +08:00
< p > < strong > < code > while< / code > 循环比 < code > for< / code > 循环的自由度更高< / strong > 。在 < code > while< / code > 循环中，我们可以自由地设计条件变量的初始化和更新步骤。< / p >
< p > 例如在以下代码中，条件变量 < span class = "arithmatex" > \(i\)< / span > 每轮进行两次更新，这种情况就不太方便用 < code > for< / code > 循环实现：< / p >
2023-09-04 03:17:06 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:12" > < input checked = "checked" id = "__tabbed_3_1" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_2" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_3" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_4" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_5" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_6" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_7" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_8" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_9" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_10" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_11" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_12" name = "__tabbed_3" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > Python< / label > < label for = "__tabbed_3_2" > C++< / label > < label for = "__tabbed_3_3" > Java< / label > < label for = "__tabbed_3_4" > C#< / label > < label for = "__tabbed_3_5" > Go< / label > < label for = "__tabbed_3_6" > Swift< / label > < label for = "__tabbed_3_7" > JS< / label > < label for = "__tabbed_3_8" > TS< / label > < label for = "__tabbed_3_9" > Dart< / label > < label for = "__tabbed_3_10" > Rust< / label > < label for = "__tabbed_3_11" > C< / label > < label for = "__tabbed_3_12" > Zig< / label > < / div >
2023-08-24 17:47:31 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-24-1" name = "__codelineno-24-1" href = "#__codelineno-24-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > while_loop_ii< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-24-2" name = "__codelineno-24-2" href = "#__codelineno-24-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " while 循环（两次更新）" " " < / span >
< a id = "__codelineno-24-3" name = "__codelineno-24-3" href = "#__codelineno-24-3" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-24-4" name = "__codelineno-24-4" href = "#__codelineno-24-4" > < / a > < span class = "n" > i< / span > < span class = "o" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > # 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-24-5" name = "__codelineno-24-5" href = "#__codelineno-24-5" > < / a > < span class = "c1" > # 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-24-6" name = "__codelineno-24-6" href = "#__codelineno-24-6" > < / a > < span class = "k" > while< / span > < span class = "n" > i< / span > < span class = "o" > < =< / span > < span class = "n" > n< / span > < span class = "p" > :< / span >
< a id = "__codelineno-24-7" name = "__codelineno-24-7" href = "#__codelineno-24-7" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-24-8" name = "__codelineno-24-8" href = "#__codelineno-24-8" > < / a > < span class = "c1" > # 更新条件变量< / span >
< a id = "__codelineno-24-9" name = "__codelineno-24-9" href = "#__codelineno-24-9" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-24-10" name = "__codelineno-24-10" href = "#__codelineno-24-10" > < / a > < span class = "n" > i< / span > < span class = "o" > *=< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-24-11" name = "__codelineno-24-11" href = "#__codelineno-24-11" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-25-1" name = "__codelineno-25-1" href = "#__codelineno-25-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
< a id = "__codelineno-25-2" name = "__codelineno-25-2" href = "#__codelineno-25-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoopII< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-25-3" name = "__codelineno-25-3" href = "#__codelineno-25-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-4" name = "__codelineno-25-4" href = "#__codelineno-25-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-25-5" name = "__codelineno-25-5" href = "#__codelineno-25-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-25-6" name = "__codelineno-25-6" href = "#__codelineno-25-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-25-7" name = "__codelineno-25-7" href = "#__codelineno-25-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-8" name = "__codelineno-25-8" href = "#__codelineno-25-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-25-9" name = "__codelineno-25-9" href = "#__codelineno-25-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-10" name = "__codelineno-25-10" href = "#__codelineno-25-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-11" name = "__codelineno-25-11" href = "#__codelineno-25-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-25-12" name = "__codelineno-25-12" href = "#__codelineno-25-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-25-13" name = "__codelineno-25-13" href = "#__codelineno-25-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-26-1" name = "__codelineno-26-1" href = "#__codelineno-26-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
< a id = "__codelineno-26-2" name = "__codelineno-26-2" href = "#__codelineno-26-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoopII< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-3" name = "__codelineno-26-3" href = "#__codelineno-26-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-4" name = "__codelineno-26-4" href = "#__codelineno-26-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-26-5" name = "__codelineno-26-5" href = "#__codelineno-26-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-26-6" name = "__codelineno-26-6" href = "#__codelineno-26-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-7" name = "__codelineno-26-7" href = "#__codelineno-26-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-8" name = "__codelineno-26-8" href = "#__codelineno-26-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-26-9" name = "__codelineno-26-9" href = "#__codelineno-26-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-10" name = "__codelineno-26-10" href = "#__codelineno-26-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-11" name = "__codelineno-26-11" href = "#__codelineno-26-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-26-12" name = "__codelineno-26-12" href = "#__codelineno-26-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-13" name = "__codelineno-26-13" href = "#__codelineno-26-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-27-1" name = "__codelineno-27-1" href = "#__codelineno-27-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-27-2" name = "__codelineno-27-2" href = "#__codelineno-27-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > WhileLoopII< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-27-3" name = "__codelineno-27-3" href = "#__codelineno-27-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-4" name = "__codelineno-27-4" href = "#__codelineno-27-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-27-5" name = "__codelineno-27-5" href = "#__codelineno-27-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 2, 4, 5...< / span >
< a id = "__codelineno-27-6" name = "__codelineno-27-6" href = "#__codelineno-27-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-27-7" name = "__codelineno-27-7" href = "#__codelineno-27-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-8" name = "__codelineno-27-8" href = "#__codelineno-27-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-27-9" name = "__codelineno-27-9" href = "#__codelineno-27-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span >
< a id = "__codelineno-27-10" name = "__codelineno-27-10" href = "#__codelineno-27-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-11" name = "__codelineno-27-11" href = "#__codelineno-27-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-12" name = "__codelineno-27-12" href = "#__codelineno-27-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-13" name = "__codelineno-27-13" href = "#__codelineno-27-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-28-1" name = "__codelineno-28-1" href = "#__codelineno-28-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
< a id = "__codelineno-28-2" name = "__codelineno-28-2" href = "#__codelineno-28-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > whileLoopII< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-3" name = "__codelineno-28-3" href = "#__codelineno-28-3" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-28-4" name = "__codelineno-28-4" href = "#__codelineno-28-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
< a id = "__codelineno-28-5" name = "__codelineno-28-5" href = "#__codelineno-28-5" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-28-6" name = "__codelineno-28-6" href = "#__codelineno-28-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-28-7" name = "__codelineno-28-7" href = "#__codelineno-28-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-28-8" name = "__codelineno-28-8" href = "#__codelineno-28-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span >
< a id = "__codelineno-28-9" name = "__codelineno-28-9" href = "#__codelineno-28-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-28-10" name = "__codelineno-28-10" href = "#__codelineno-28-10" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-28-11" name = "__codelineno-28-11" href = "#__codelineno-28-11" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-28-12" name = "__codelineno-28-12" href = "#__codelineno-28-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-28-13" name = "__codelineno-28-13" href = "#__codelineno-28-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-28-14" name = "__codelineno-28-14" href = "#__codelineno-28-14" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-29-1" name = "__codelineno-29-1" href = "#__codelineno-29-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
< a id = "__codelineno-29-2" name = "__codelineno-29-2" href = "#__codelineno-29-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > whileLoopII< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-3" name = "__codelineno-29-3" href = "#__codelineno-29-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-29-4" name = "__codelineno-29-4" href = "#__codelineno-29-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > i< / span > < span class = "p" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > // 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-29-5" name = "__codelineno-29-5" href = "#__codelineno-29-5" > < / a > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-29-6" name = "__codelineno-29-6" href = "#__codelineno-29-6" > < / a > < span class = "k" > while< / span > < span class = "n" > i< / span > < span class = "o" > < =< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-7" name = "__codelineno-29-7" href = "#__codelineno-29-7" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > i< / span >
< a id = "__codelineno-29-8" name = "__codelineno-29-8" href = "#__codelineno-29-8" > < / a > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-29-9" name = "__codelineno-29-9" href = "#__codelineno-29-9" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-29-10" name = "__codelineno-29-10" href = "#__codelineno-29-10" > < / a > < span class = "n" > i< / span > < span class = "o" > *=< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-29-11" name = "__codelineno-29-11" href = "#__codelineno-29-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-29-12" name = "__codelineno-29-12" href = "#__codelineno-29-12" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-29-13" name = "__codelineno-29-13" href = "#__codelineno-29-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-30-1" name = "__codelineno-30-1" href = "#__codelineno-30-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
< a id = "__codelineno-30-2" name = "__codelineno-30-2" href = "#__codelineno-30-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > whileLoopII< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-3" name = "__codelineno-30-3" href = "#__codelineno-30-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-4" name = "__codelineno-30-4" href = "#__codelineno-30-4" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-30-5" name = "__codelineno-30-5" href = "#__codelineno-30-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-30-6" name = "__codelineno-30-6" href = "#__codelineno-30-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-7" name = "__codelineno-30-7" href = "#__codelineno-30-7" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-8" name = "__codelineno-30-8" href = "#__codelineno-30-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-30-9" name = "__codelineno-30-9" href = "#__codelineno-30-9" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-10" name = "__codelineno-30-10" href = "#__codelineno-30-10" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-11" name = "__codelineno-30-11" href = "#__codelineno-30-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-12" name = "__codelineno-30-12" href = "#__codelineno-30-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-30-13" name = "__codelineno-30-13" href = "#__codelineno-30-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-31-1" name = "__codelineno-31-1" href = "#__codelineno-31-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
< a id = "__codelineno-31-2" name = "__codelineno-31-2" href = "#__codelineno-31-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > whileLoopII< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-31-3" name = "__codelineno-31-3" href = "#__codelineno-31-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-4" name = "__codelineno-31-4" href = "#__codelineno-31-4" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-31-5" name = "__codelineno-31-5" href = "#__codelineno-31-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-31-6" name = "__codelineno-31-6" href = "#__codelineno-31-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-31-7" name = "__codelineno-31-7" href = "#__codelineno-31-7" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-8" name = "__codelineno-31-8" href = "#__codelineno-31-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-31-9" name = "__codelineno-31-9" href = "#__codelineno-31-9" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-10" name = "__codelineno-31-10" href = "#__codelineno-31-10" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-11" name = "__codelineno-31-11" href = "#__codelineno-31-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-12" name = "__codelineno-31-12" href = "#__codelineno-31-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-31-13" name = "__codelineno-31-13" href = "#__codelineno-31-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-32-1" name = "__codelineno-32-1" href = "#__codelineno-32-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
< a id = "__codelineno-32-2" name = "__codelineno-32-2" href = "#__codelineno-32-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > whileLoopII< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-32-3" name = "__codelineno-32-3" href = "#__codelineno-32-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-32-4" name = "__codelineno-32-4" href = "#__codelineno-32-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-32-5" name = "__codelineno-32-5" href = "#__codelineno-32-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-32-6" name = "__codelineno-32-6" href = "#__codelineno-32-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-32-7" name = "__codelineno-32-7" href = "#__codelineno-32-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-32-8" name = "__codelineno-32-8" href = "#__codelineno-32-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-32-9" name = "__codelineno-32-9" href = "#__codelineno-32-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-32-10" name = "__codelineno-32-10" href = "#__codelineno-32-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-32-11" name = "__codelineno-32-11" href = "#__codelineno-32-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-32-12" name = "__codelineno-32-12" href = "#__codelineno-32-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-32-13" name = "__codelineno-32-13" href = "#__codelineno-32-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-33-1" name = "__codelineno-33-1" href = "#__codelineno-33-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
< a id = "__codelineno-33-2" name = "__codelineno-33-2" href = "#__codelineno-33-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > while_loop_ii< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-33-3" name = "__codelineno-33-3" href = "#__codelineno-33-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-33-4" name = "__codelineno-33-4" href = "#__codelineno-33-4" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-33-5" name = "__codelineno-33-5" href = "#__codelineno-33-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-33-6" name = "__codelineno-33-6" href = "#__codelineno-33-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-33-7" name = "__codelineno-33-7" href = "#__codelineno-33-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-33-8" name = "__codelineno-33-8" href = "#__codelineno-33-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-33-9" name = "__codelineno-33-9" href = "#__codelineno-33-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-33-10" name = "__codelineno-33-10" href = "#__codelineno-33-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-33-11" name = "__codelineno-33-11" href = "#__codelineno-33-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-12" name = "__codelineno-33-12" href = "#__codelineno-33-12" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-33-13" name = "__codelineno-33-13" href = "#__codelineno-33-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-34-1" name = "__codelineno-34-1" href = "#__codelineno-34-1" > < / a > < span class = "cm" > /* while 循环（两次更新） */< / span >
< a id = "__codelineno-34-2" name = "__codelineno-34-2" href = "#__codelineno-34-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > whileLoopII< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-34-3" name = "__codelineno-34-3" href = "#__codelineno-34-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-4" name = "__codelineno-34-4" href = "#__codelineno-34-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-34-5" name = "__codelineno-34-5" href = "#__codelineno-34-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-34-6" name = "__codelineno-34-6" href = "#__codelineno-34-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-34-7" name = "__codelineno-34-7" href = "#__codelineno-34-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-8" name = "__codelineno-34-8" href = "#__codelineno-34-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-34-9" name = "__codelineno-34-9" href = "#__codelineno-34-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-10" name = "__codelineno-34-10" href = "#__codelineno-34-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-11" name = "__codelineno-34-11" href = "#__codelineno-34-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-12" name = "__codelineno-34-12" href = "#__codelineno-34-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-13" name = "__codelineno-34-13" href = "#__codelineno-34-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-25 00:05:17 +08:00
< div class = "highlight" > < span class = "filename" > iteration.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-35-1" name = "__codelineno-35-1" href = "#__codelineno-35-1" > < / a > < span class = "c1" > // while 循环（两次更新）< / span >
< a id = "__codelineno-35-2" name = "__codelineno-35-2" href = "#__codelineno-35-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > whileLoopII< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-35-3" name = "__codelineno-35-3" href = "#__codelineno-35-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-4" name = "__codelineno-35-4" href = "#__codelineno-35-4" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 初始化条件变量< / span >
2023-12-02 06:24:11 +08:00
< a id = "__codelineno-35-5" name = "__codelineno-35-5" href = "#__codelineno-35-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环求和 1, 4, 10, ...< / span >
2023-10-25 00:05:17 +08:00
< a id = "__codelineno-35-6" name = "__codelineno-35-6" href = "#__codelineno-35-6" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-35-7" name = "__codelineno-35-7" href = "#__codelineno-35-7" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-35-8" name = "__codelineno-35-8" href = "#__codelineno-35-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 更新条件变量< / span >
< a id = "__codelineno-35-9" name = "__codelineno-35-9" href = "#__codelineno-35-9" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-10" name = "__codelineno-35-10" href = "#__codelineno-35-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-11" name = "__codelineno-35-11" href = "#__codelineno-35-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-35-12" name = "__codelineno-35-12" href = "#__codelineno-35-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-35-13" name = "__codelineno-35-13" href = "#__codelineno-35-13" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 总的来说，< strong > < code > for< / code > 循环的代码更加紧凑，< code > while< / code > 循环更加灵活< / strong > ，两者都可以实现迭代结构。选择使用哪一个应该根据特定问题的需求来决定。< / p >
< h3 id = "3" > 3. 嵌套循环< a class = "headerlink" href = "#3" title = "Permanent link" > ¶ < / a > < / h3 >
2023-12-02 06:24:11 +08:00
< p > 我们可以在一个循环结构内嵌套另一个循环结构，下面以 < code > for< / code > 循环为例：< / p >
2023-09-04 03:17:06 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "4:12" > < input checked = "checked" id = "__tabbed_4_1" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_2" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_3" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_4" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_5" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_6" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_7" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_8" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_9" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_10" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_11" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_12" name = "__tabbed_4" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_4_1" > Python< / label > < label for = "__tabbed_4_2" > C++< / label > < label for = "__tabbed_4_3" > Java< / label > < label for = "__tabbed_4_4" > C#< / label > < label for = "__tabbed_4_5" > Go< / label > < label for = "__tabbed_4_6" > Swift< / label > < label for = "__tabbed_4_7" > JS< / label > < label for = "__tabbed_4_8" > TS< / label > < label for = "__tabbed_4_9" > Dart< / label > < label for = "__tabbed_4_10" > Rust< / label > < label for = "__tabbed_4_11" > C< / label > < label for = "__tabbed_4_12" > Zig< / label > < / div >
2023-08-24 17:47:31 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-36-1" name = "__codelineno-36-1" href = "#__codelineno-36-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > nested_for_loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > str< / span > < span class = "p" > :< / span >
< a id = "__codelineno-36-2" name = "__codelineno-36-2" href = "#__codelineno-36-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 双层 for 循环" " " < / span >
< a id = "__codelineno-36-3" name = "__codelineno-36-3" href = "#__codelineno-36-3" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "s2" > " " < / span >
< a id = "__codelineno-36-4" name = "__codelineno-36-4" href = "#__codelineno-36-4" > < / a > < span class = "c1" > # 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-36-5" name = "__codelineno-36-5" href = "#__codelineno-36-5" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-36-6" name = "__codelineno-36-6" href = "#__codelineno-36-6" > < / a > < span class = "c1" > # 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-36-7" name = "__codelineno-36-7" href = "#__codelineno-36-7" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-36-8" name = "__codelineno-36-8" href = "#__codelineno-36-8" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "sa" > f< / span > < span class = "s2" > " (< / span > < span class = "si" > {< / span > < span class = "n" > i< / span > < span class = "si" > }< / span > < span class = "s2" > , < / span > < span class = "si" > {< / span > < span class = "n" > j< / span > < span class = "si" > }< / span > < span class = "s2" > ), " < / span >
< a id = "__codelineno-36-9" name = "__codelineno-36-9" href = "#__codelineno-36-9" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-37-1" name = "__codelineno-37-1" href = "#__codelineno-37-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
< a id = "__codelineno-37-2" name = "__codelineno-37-2" href = "#__codelineno-37-2" > < / a > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "nf" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-37-3" name = "__codelineno-37-3" href = "#__codelineno-37-3" > < / a > < span class = "w" > < / span > < span class = "n" > ostringstream< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-4" name = "__codelineno-37-4" href = "#__codelineno-37-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-37-5" name = "__codelineno-37-5" href = "#__codelineno-37-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "o" > ++< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-37-6" name = "__codelineno-37-6" href = "#__codelineno-37-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-37-7" name = "__codelineno-37-7" href = "#__codelineno-37-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "o" > ++< / span > < span class = "n" > j< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-37-8" name = "__codelineno-37-8" href = "#__codelineno-37-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "s" > " (" < / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "s" > " , " < / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "s" > " ), " < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-9" name = "__codelineno-37-9" href = "#__codelineno-37-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-10" name = "__codelineno-37-10" href = "#__codelineno-37-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-11" name = "__codelineno-37-11" href = "#__codelineno-37-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > str< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-37-12" name = "__codelineno-37-12" href = "#__codelineno-37-12" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-38-1" name = "__codelineno-38-1" href = "#__codelineno-38-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
< a id = "__codelineno-38-2" name = "__codelineno-38-2" href = "#__codelineno-38-2" > < / a > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "nf" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-3" name = "__codelineno-38-3" href = "#__codelineno-38-3" > < / a > < span class = "w" > < / span > < span class = "n" > StringBuilder< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > StringBuilder< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-38-4" name = "__codelineno-38-4" href = "#__codelineno-38-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-38-5" name = "__codelineno-38-5" href = "#__codelineno-38-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-6" name = "__codelineno-38-6" href = "#__codelineno-38-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-38-7" name = "__codelineno-38-7" href = "#__codelineno-38-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-8" name = "__codelineno-38-8" href = "#__codelineno-38-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > append< / span > < span class = "p" > (< / span > < span class = "s" > " (" < / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "s" > " , " < / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "s" > " ), " < / span > < span class = "p" > );< / span >
< a id = "__codelineno-38-9" name = "__codelineno-38-9" href = "#__codelineno-38-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-38-10" name = "__codelineno-38-10" href = "#__codelineno-38-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-38-11" name = "__codelineno-38-11" href = "#__codelineno-38-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > toString< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-38-12" name = "__codelineno-38-12" href = "#__codelineno-38-12" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-39-1" name = "__codelineno-39-1" href = "#__codelineno-39-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-39-2" name = "__codelineno-39-2" href = "#__codelineno-39-2" > < / a > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "nf" > NestedForLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-39-3" name = "__codelineno-39-3" href = "#__codelineno-39-3" > < / a > < span class = "w" > < / span > < span class = "n" > StringBuilder< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-39-4" name = "__codelineno-39-4" href = "#__codelineno-39-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-39-5" name = "__codelineno-39-5" href = "#__codelineno-39-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-39-6" name = "__codelineno-39-6" href = "#__codelineno-39-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-39-7" name = "__codelineno-39-7" href = "#__codelineno-39-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-39-8" name = "__codelineno-39-8" href = "#__codelineno-39-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > Append< / span > < span class = "p" > (< / span > < span class = "s" > $" ({i}, {j}), " < / span > < span class = "p" > );< / span >
< a id = "__codelineno-39-9" name = "__codelineno-39-9" href = "#__codelineno-39-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-10" name = "__codelineno-39-10" href = "#__codelineno-39-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-11" name = "__codelineno-39-11" href = "#__codelineno-39-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > ToString< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-39-12" name = "__codelineno-39-12" href = "#__codelineno-39-12" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-40-1" name = "__codelineno-40-1" href = "#__codelineno-40-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
< a id = "__codelineno-40-2" name = "__codelineno-40-2" href = "#__codelineno-40-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-40-3" name = "__codelineno-40-3" href = "#__codelineno-40-3" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "s" > " " < / span >
< a id = "__codelineno-40-4" name = "__codelineno-40-4" href = "#__codelineno-40-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-40-5" name = "__codelineno-40-5" href = "#__codelineno-40-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-40-6" name = "__codelineno-40-6" href = "#__codelineno-40-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-40-7" name = "__codelineno-40-7" href = "#__codelineno-40-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-40-8" name = "__codelineno-40-8" href = "#__codelineno-40-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > fmt< / span > < span class = "p" > .< / span > < span class = "nx" > Sprintf< / span > < span class = "p" > (< / span > < span class = "s" > " (%d, %d), " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "p" > )< / span >
< a id = "__codelineno-40-9" name = "__codelineno-40-9" href = "#__codelineno-40-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-40-10" name = "__codelineno-40-10" href = "#__codelineno-40-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-40-11" name = "__codelineno-40-11" href = "#__codelineno-40-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-40-12" name = "__codelineno-40-12" href = "#__codelineno-40-12" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-41-1" name = "__codelineno-41-1" href = "#__codelineno-41-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
< a id = "__codelineno-41-2" name = "__codelineno-41-2" href = "#__codelineno-41-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > String< / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-3" name = "__codelineno-41-3" href = "#__codelineno-41-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "s" > " " < / span >
< a id = "__codelineno-41-4" name = "__codelineno-41-4" href = "#__codelineno-41-4" > < / a > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-41-5" name = "__codelineno-41-5" href = "#__codelineno-41-5" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "mi" > 1< / span > < span class = "p" > ...< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-6" name = "__codelineno-41-6" href = "#__codelineno-41-6" > < / a > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-41-7" name = "__codelineno-41-7" href = "#__codelineno-41-7" > < / a > < span class = "k" > for< / span > < span class = "n" > j< / span > < span class = "k" > in< / span > < span class = "mi" > 1< / span > < span class = "p" > ...< / span > < span class = "n" > n< / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-8" name = "__codelineno-41-8" href = "#__codelineno-41-8" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "s" > " (< / span > < span class = "si" > \(< / span > < span class = "n" > i< / span > < span class = "si" > )< / span > < span class = "s" > , < / span > < span class = "si" > \(< / span > < span class = "n" > j< / span > < span class = "si" > )< / span > < span class = "s" > ), " < / span > < span class = "p" > )< / span >
< a id = "__codelineno-41-9" name = "__codelineno-41-9" href = "#__codelineno-41-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-41-10" name = "__codelineno-41-10" href = "#__codelineno-41-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-41-11" name = "__codelineno-41-11" href = "#__codelineno-41-11" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-41-12" name = "__codelineno-41-12" href = "#__codelineno-41-12" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-42-1" name = "__codelineno-42-1" href = "#__codelineno-42-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
< a id = "__codelineno-42-2" name = "__codelineno-42-2" href = "#__codelineno-42-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-42-3" name = "__codelineno-42-3" href = "#__codelineno-42-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' ' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-42-4" name = "__codelineno-42-4" href = "#__codelineno-42-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-42-5" name = "__codelineno-42-5" href = "#__codelineno-42-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-42-6" name = "__codelineno-42-6" href = "#__codelineno-42-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-42-7" name = "__codelineno-42-7" href = "#__codelineno-42-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-42-8" name = "__codelineno-42-8" href = "#__codelineno-42-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "sb" > `(< / span > < span class = "si" > ${< / span > < span class = "nx" > i< / span > < span class = "si" > }< / span > < span class = "sb" > , < / span > < span class = "si" > ${< / span > < span class = "nx" > j< / span > < span class = "si" > }< / span > < span class = "sb" > ), `< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-42-9" name = "__codelineno-42-9" href = "#__codelineno-42-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-42-10" name = "__codelineno-42-10" href = "#__codelineno-42-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-42-11" name = "__codelineno-42-11" href = "#__codelineno-42-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-42-12" name = "__codelineno-42-12" href = "#__codelineno-42-12" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-43-1" name = "__codelineno-43-1" href = "#__codelineno-43-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
< a id = "__codelineno-43-2" name = "__codelineno-43-2" href = "#__codelineno-43-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-43-3" name = "__codelineno-43-3" href = "#__codelineno-43-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s1" > ' ' < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-43-4" name = "__codelineno-43-4" href = "#__codelineno-43-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-43-5" name = "__codelineno-43-5" href = "#__codelineno-43-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-43-6" name = "__codelineno-43-6" href = "#__codelineno-43-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-43-7" name = "__codelineno-43-7" href = "#__codelineno-43-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-43-8" name = "__codelineno-43-8" href = "#__codelineno-43-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "sb" > `(< / span > < span class = "si" > ${< / span > < span class = "nx" > i< / span > < span class = "si" > }< / span > < span class = "sb" > , < / span > < span class = "si" > ${< / span > < span class = "nx" > j< / span > < span class = "si" > }< / span > < span class = "sb" > ), `< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-43-9" name = "__codelineno-43-9" href = "#__codelineno-43-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-10" name = "__codelineno-43-10" href = "#__codelineno-43-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-11" name = "__codelineno-43-11" href = "#__codelineno-43-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-43-12" name = "__codelineno-43-12" href = "#__codelineno-43-12" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-44-1" name = "__codelineno-44-1" href = "#__codelineno-44-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
< a id = "__codelineno-44-2" name = "__codelineno-44-2" href = "#__codelineno-44-2" > < / a > < span class = "kt" > String< / span > < span class = "w" > < / span > < span class = "n" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-44-3" name = "__codelineno-44-3" href = "#__codelineno-44-3" > < / a > < span class = "w" > < / span > < span class = "kt" > String< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s2" > " " < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-44-4" name = "__codelineno-44-4" href = "#__codelineno-44-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-44-5" name = "__codelineno-44-5" href = "#__codelineno-44-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-44-6" name = "__codelineno-44-6" href = "#__codelineno-44-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-44-7" name = "__codelineno-44-7" href = "#__codelineno-44-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-44-8" name = "__codelineno-44-8" href = "#__codelineno-44-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "s2" > " (< / span > < span class = "si" > $< / span > < span class = "n" > i< / span > < span class = "s2" > , < / span > < span class = "si" > $< / span > < span class = "n" > j< / span > < span class = "s2" > ), " < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-44-9" name = "__codelineno-44-9" href = "#__codelineno-44-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-44-10" name = "__codelineno-44-10" href = "#__codelineno-44-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-44-11" name = "__codelineno-44-11" href = "#__codelineno-44-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-44-12" name = "__codelineno-44-12" href = "#__codelineno-44-12" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-45-1" name = "__codelineno-45-1" href = "#__codelineno-45-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
< a id = "__codelineno-45-2" name = "__codelineno-45-2" href = "#__codelineno-45-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > nested_for_loop< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nb" > String< / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-3" name = "__codelineno-45-3" href = "#__codelineno-45-3" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "fm" > vec!< / span > < span class = "p" > [];< / span >
< a id = "__codelineno-45-4" name = "__codelineno-45-4" href = "#__codelineno-45-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-45-5" name = "__codelineno-45-5" href = "#__codelineno-45-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ..=< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-6" name = "__codelineno-45-6" href = "#__codelineno-45-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-45-7" name = "__codelineno-45-7" href = "#__codelineno-45-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "o" > ..=< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-8" name = "__codelineno-45-8" href = "#__codelineno-45-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "fm" > format!< / span > < span class = "p" > (< / span > < span class = "s" > " ({}, {}), " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-45-9" name = "__codelineno-45-9" href = "#__codelineno-45-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-10" name = "__codelineno-45-10" href = "#__codelineno-45-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-11" name = "__codelineno-45-11" href = "#__codelineno-45-11" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > join< / span > < span class = "p" > (< / span > < span class = "s" > " " < / span > < span class = "p" > )< / span >
< a id = "__codelineno-45-12" name = "__codelineno-45-12" href = "#__codelineno-45-12" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > iteration.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-46-1" name = "__codelineno-46-1" href = "#__codelineno-46-1" > < / a > < span class = "cm" > /* 双层 for 循环 */< / span >
< a id = "__codelineno-46-2" name = "__codelineno-46-2" href = "#__codelineno-46-2" > < / a > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-46-3" name = "__codelineno-46-3" href = "#__codelineno-46-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // n * n 为对应点数量，" (i, j), " 对应字符串长最大为 6+10*2， < / span >
< a id = "__codelineno-46-4" name = "__codelineno-46-4" href = "#__codelineno-46-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "mi" > 26< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-46-5" name = "__codelineno-46-5" href = "#__codelineno-46-5" > < / a > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-46-6" name = "__codelineno-46-6" href = "#__codelineno-46-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-46-7" name = "__codelineno-46-7" href = "#__codelineno-46-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-46-8" name = "__codelineno-46-8" href = "#__codelineno-46-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-46-9" name = "__codelineno-46-9" href = "#__codelineno-46-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-46-10" name = "__codelineno-46-10" href = "#__codelineno-46-10" > < / a > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "mi" > 26< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-46-11" name = "__codelineno-46-11" href = "#__codelineno-46-11" > < / a > < span class = "w" > < / span > < span class = "n" > snprintf< / span > < span class = "p" > (< / span > < span class = "n" > tmp< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > tmp< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "s" > " (%d, %d), " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-12" name = "__codelineno-46-12" href = "#__codelineno-46-12" > < / a > < span class = "w" > < / span > < span class = "n" > strncat< / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > strlen< / span > < span class = "p" > (< / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-46-13" name = "__codelineno-46-13" href = "#__codelineno-46-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-46-14" name = "__codelineno-46-14" href = "#__codelineno-46-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-46-15" name = "__codelineno-46-15" href = "#__codelineno-46-15" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-46-16" name = "__codelineno-46-16" href = "#__codelineno-46-16" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-25 00:05:17 +08:00
< div class = "highlight" > < span class = "filename" > iteration.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-47-1" name = "__codelineno-47-1" href = "#__codelineno-47-1" > < / a > < span class = "c1" > // 双层 for 循环< / span >
< a id = "__codelineno-47-2" name = "__codelineno-47-2" href = "#__codelineno-47-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > nestedForLoop< / span > < span class = "p" > (< / span > < span class = "n" > allocator< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > Allocator< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > usize< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "p" > []< / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "kt" > u8< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-3" name = "__codelineno-47-3" href = "#__codelineno-47-3" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > ArrayList< / span > < span class = "p" > (< / span > < span class = "kt" > u8< / span > < span class = "p" > ).< / span > < span class = "n" > init< / span > < span class = "p" > (< / span > < span class = "n" > allocator< / span > < span class = "p" > );< / span >
< a id = "__codelineno-47-4" name = "__codelineno-47-4" href = "#__codelineno-47-4" > < / a > < span class = "w" > < / span > < span class = "k" > defer< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > deinit< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-47-5" name = "__codelineno-47-5" href = "#__codelineno-47-5" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > buffer< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "mi" > 20< / span > < span class = "p" > ]< / span > < span class = "kt" > u8< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-47-6" name = "__codelineno-47-6" href = "#__codelineno-47-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 i = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-47-7" name = "__codelineno-47-7" href = "#__codelineno-47-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > i< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-8" name = "__codelineno-47-8" href = "#__codelineno-47-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 j = 1, 2, ..., n-1, n< / span >
< a id = "__codelineno-47-9" name = "__codelineno-47-9" href = "#__codelineno-47-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "p" > ..< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "n" > j< / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-10" name = "__codelineno-47-10" href = "#__codelineno-47-10" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > _str< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > fmt< / span > < span class = "p" > .< / span > < span class = "n" > bufPrint< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "n" > buffer< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " ({d}, {d}), " < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > .{< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > });< / span >
< a id = "__codelineno-47-11" name = "__codelineno-47-11" href = "#__codelineno-47-11" > < / a > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > appendSlice< / span > < span class = "p" > (< / span > < span class = "n" > _str< / span > < span class = "p" > );< / span >
< a id = "__codelineno-47-12" name = "__codelineno-47-12" href = "#__codelineno-47-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-13" name = "__codelineno-47-13" href = "#__codelineno-47-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-14" name = "__codelineno-47-14" href = "#__codelineno-47-14" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > toOwnedSlice< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-47-15" name = "__codelineno-47-15" href = "#__codelineno-47-15" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-12-02 06:24:11 +08:00
< p > 图 2-2 是该嵌套循环的流程框图。< / p >
2023-11-09 05:13:54 +08:00
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/nested_iteration.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "嵌套循环的流程框图" class = "animation-figure" src = "../iteration_and_recursion.assets/nested_iteration.png" / > < / a > < / p >
2023-08-24 17:47:31 +08:00
< p align = "center" > 图 2-2 嵌套循环的流程框图 < / p >
< p > 在这种情况下，函数的操作数量与 < span class = "arithmatex" > \(n^2\)< / span > 成正比，或者说算法运行时间和输入数据大小 < span class = "arithmatex" > \(n\)< / span > 成“平方关系”。< / p >
2023-12-02 06:24:11 +08:00
< p > 我们可以继续添加嵌套循环，每一次嵌套都是一次“升维”，将会使时间复杂度提高至“立方关系”“四次方关系”，以此类推。< / p >
2023-08-24 17:47:31 +08:00
< h2 id = "222" > 2.2.2 递归< a class = "headerlink" href = "#222" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 「递归 recursion」是一种算法策略， < / p >
< ol >
< li > < strong > 递< / strong > ：程序不断深入地调用自身，通常传入更小或更简化的参数，直到达到“终止条件”。< / li >
< li > < strong > 归< / strong > ：触发“终止条件”后，程序从最深层的递归函数开始逐层返回，汇聚每一层的结果。< / li >
< / ol >
< p > 而从实现的角度看，递归代码主要包含三个要素。< / p >
< ol >
< li > < strong > 终止条件< / strong > ：用于决定什么时候由“递”转“归”。< / li >
< li > < strong > 递归调用< / strong > ：对应“递”，函数调用自身，通常输入更小或更简化的参数。< / li >
< li > < strong > 返回结果< / strong > ：对应“归”，将当前递归层级的结果返回至上一层。< / li >
< / ol >
< p > 观察以下代码，我们只需调用函数 < code > recur(n)< / code > ，就可以完成 < span class = "arithmatex" > \(1 + 2 + \dots + n\)< / span > 的计算：< / p >
2023-09-04 03:17:06 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "5:12" > < input checked = "checked" id = "__tabbed_5_1" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_2" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_3" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_4" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_5" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_6" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_7" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_8" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_9" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_10" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_11" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_12" name = "__tabbed_5" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_5_1" > Python< / label > < label for = "__tabbed_5_2" > C++< / label > < label for = "__tabbed_5_3" > Java< / label > < label for = "__tabbed_5_4" > C#< / label > < label for = "__tabbed_5_5" > Go< / label > < label for = "__tabbed_5_6" > Swift< / label > < label for = "__tabbed_5_7" > JS< / label > < label for = "__tabbed_5_8" > TS< / label > < label for = "__tabbed_5_9" > Dart< / label > < label for = "__tabbed_5_10" > Rust< / label > < label for = "__tabbed_5_11" > C< / label > < label for = "__tabbed_5_12" > Zig< / label > < / div >
2023-08-24 17:47:31 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-48-1" name = "__codelineno-48-1" href = "#__codelineno-48-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-48-2" name = "__codelineno-48-2" href = "#__codelineno-48-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 递归" " " < / span >
< a id = "__codelineno-48-3" name = "__codelineno-48-3" href = "#__codelineno-48-3" > < / a > < span class = "c1" > # 终止条件< / span >
< a id = "__codelineno-48-4" name = "__codelineno-48-4" href = "#__codelineno-48-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span >
< a id = "__codelineno-48-5" name = "__codelineno-48-5" href = "#__codelineno-48-5" > < / a > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-48-6" name = "__codelineno-48-6" href = "#__codelineno-48-6" > < / a > < span class = "c1" > # 递：递归调用< / span >
< a id = "__codelineno-48-7" name = "__codelineno-48-7" href = "#__codelineno-48-7" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-48-8" name = "__codelineno-48-8" href = "#__codelineno-48-8" > < / a > < span class = "c1" > # 归：返回结果< / span >
< a id = "__codelineno-48-9" name = "__codelineno-48-9" href = "#__codelineno-48-9" > < / a > < span class = "k" > return< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "n" > res< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-49-1" name = "__codelineno-49-1" href = "#__codelineno-49-1" > < / a > < span class = "cm" > /* 递归 */< / span >
< a id = "__codelineno-49-2" name = "__codelineno-49-2" href = "#__codelineno-49-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-3" name = "__codelineno-49-3" href = "#__codelineno-49-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-49-4" name = "__codelineno-49-4" href = "#__codelineno-49-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-49-5" name = "__codelineno-49-5" href = "#__codelineno-49-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-6" name = "__codelineno-49-6" href = "#__codelineno-49-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-49-7" name = "__codelineno-49-7" href = "#__codelineno-49-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-8" name = "__codelineno-49-8" href = "#__codelineno-49-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-49-9" name = "__codelineno-49-9" href = "#__codelineno-49-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-10" name = "__codelineno-49-10" href = "#__codelineno-49-10" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-50-1" name = "__codelineno-50-1" href = "#__codelineno-50-1" > < / a > < span class = "cm" > /* 递归 */< / span >
< a id = "__codelineno-50-2" name = "__codelineno-50-2" href = "#__codelineno-50-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-50-3" name = "__codelineno-50-3" href = "#__codelineno-50-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-50-4" name = "__codelineno-50-4" href = "#__codelineno-50-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-50-5" name = "__codelineno-50-5" href = "#__codelineno-50-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-6" name = "__codelineno-50-6" href = "#__codelineno-50-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-50-7" name = "__codelineno-50-7" href = "#__codelineno-50-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-50-8" name = "__codelineno-50-8" href = "#__codelineno-50-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-50-9" name = "__codelineno-50-9" href = "#__codelineno-50-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-10" name = "__codelineno-50-10" href = "#__codelineno-50-10" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-51-1" name = "__codelineno-51-1" href = "#__codelineno-51-1" > < / a > < span class = "cm" > /* 递归 */< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-51-2" name = "__codelineno-51-2" href = "#__codelineno-51-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > Recur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-51-3" name = "__codelineno-51-3" href = "#__codelineno-51-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-51-4" name = "__codelineno-51-4" href = "#__codelineno-51-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-51-5" name = "__codelineno-51-5" href = "#__codelineno-51-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-51-6" name = "__codelineno-51-6" href = "#__codelineno-51-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-51-7" name = "__codelineno-51-7" href = "#__codelineno-51-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-51-8" name = "__codelineno-51-8" href = "#__codelineno-51-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-51-9" name = "__codelineno-51-9" href = "#__codelineno-51-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-51-10" name = "__codelineno-51-10" href = "#__codelineno-51-10" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-52-1" name = "__codelineno-52-1" href = "#__codelineno-52-1" > < / a > < span class = "cm" > /* 递归 */< / span >
< a id = "__codelineno-52-2" name = "__codelineno-52-2" href = "#__codelineno-52-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-3" name = "__codelineno-52-3" href = "#__codelineno-52-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-52-4" name = "__codelineno-52-4" href = "#__codelineno-52-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-5" name = "__codelineno-52-5" href = "#__codelineno-52-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-52-6" name = "__codelineno-52-6" href = "#__codelineno-52-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-52-7" name = "__codelineno-52-7" href = "#__codelineno-52-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-52-8" name = "__codelineno-52-8" href = "#__codelineno-52-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-9" name = "__codelineno-52-9" href = "#__codelineno-52-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-52-10" name = "__codelineno-52-10" href = "#__codelineno-52-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-52-11" name = "__codelineno-52-11" href = "#__codelineno-52-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-53-1" name = "__codelineno-53-1" href = "#__codelineno-53-1" > < / a > < span class = "cm" > /* 递归 */< / span >
< a id = "__codelineno-53-2" name = "__codelineno-53-2" href = "#__codelineno-53-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-53-3" name = "__codelineno-53-3" href = "#__codelineno-53-3" > < / a > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-53-4" name = "__codelineno-53-4" href = "#__codelineno-53-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "p" > ==< / span > < span class = "mi" > 1< / span > < span class = "p" > {< / span >
< a id = "__codelineno-53-5" name = "__codelineno-53-5" href = "#__codelineno-53-5" > < / a > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-53-6" name = "__codelineno-53-6" href = "#__codelineno-53-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-53-7" name = "__codelineno-53-7" href = "#__codelineno-53-7" > < / a > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-53-8" name = "__codelineno-53-8" href = "#__codelineno-53-8" > < / a > < span class = "kd" > let< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-53-9" name = "__codelineno-53-9" href = "#__codelineno-53-9" > < / a > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-53-10" name = "__codelineno-53-10" href = "#__codelineno-53-10" > < / a > < span class = "k" > return< / span > < span class = "n" > n< / span > < span class = "o" > +< / span > < span class = "n" > res< / span >
< a id = "__codelineno-53-11" name = "__codelineno-53-11" href = "#__codelineno-53-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-54-1" name = "__codelineno-54-1" href = "#__codelineno-54-1" > < / a > < span class = "cm" > /* 递归 */< / span >
< a id = "__codelineno-54-2" name = "__codelineno-54-2" href = "#__codelineno-54-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-54-3" name = "__codelineno-54-3" href = "#__codelineno-54-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-54-4" name = "__codelineno-54-4" href = "#__codelineno-54-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-54-5" name = "__codelineno-54-5" href = "#__codelineno-54-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-54-6" name = "__codelineno-54-6" href = "#__codelineno-54-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-54-7" name = "__codelineno-54-7" href = "#__codelineno-54-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-54-8" name = "__codelineno-54-8" href = "#__codelineno-54-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-54-9" name = "__codelineno-54-9" href = "#__codelineno-54-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-55-1" name = "__codelineno-55-1" href = "#__codelineno-55-1" > < / a > < span class = "cm" > /* 递归 */< / span >
< a id = "__codelineno-55-2" name = "__codelineno-55-2" href = "#__codelineno-55-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-55-3" name = "__codelineno-55-3" href = "#__codelineno-55-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-55-4" name = "__codelineno-55-4" href = "#__codelineno-55-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-55-5" name = "__codelineno-55-5" href = "#__codelineno-55-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-55-6" name = "__codelineno-55-6" href = "#__codelineno-55-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > recur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-55-7" name = "__codelineno-55-7" href = "#__codelineno-55-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-55-8" name = "__codelineno-55-8" href = "#__codelineno-55-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-55-9" name = "__codelineno-55-9" href = "#__codelineno-55-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-56-1" name = "__codelineno-56-1" href = "#__codelineno-56-1" > < / a > < span class = "cm" > /* 递归 */< / span >
< a id = "__codelineno-56-2" name = "__codelineno-56-2" href = "#__codelineno-56-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-56-3" name = "__codelineno-56-3" href = "#__codelineno-56-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-56-4" name = "__codelineno-56-4" href = "#__codelineno-56-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-56-5" name = "__codelineno-56-5" href = "#__codelineno-56-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-56-6" name = "__codelineno-56-6" href = "#__codelineno-56-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-56-7" name = "__codelineno-56-7" href = "#__codelineno-56-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-56-8" name = "__codelineno-56-8" href = "#__codelineno-56-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-56-9" name = "__codelineno-56-9" href = "#__codelineno-56-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-57-1" name = "__codelineno-57-1" href = "#__codelineno-57-1" > < / a > < span class = "cm" > /* 递归 */< / span >
< a id = "__codelineno-57-2" name = "__codelineno-57-2" href = "#__codelineno-57-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-57-3" name = "__codelineno-57-3" href = "#__codelineno-57-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-57-4" name = "__codelineno-57-4" href = "#__codelineno-57-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-57-5" name = "__codelineno-57-5" href = "#__codelineno-57-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-57-6" name = "__codelineno-57-6" href = "#__codelineno-57-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-57-7" name = "__codelineno-57-7" href = "#__codelineno-57-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-57-8" name = "__codelineno-57-8" href = "#__codelineno-57-8" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-57-9" name = "__codelineno-57-9" href = "#__codelineno-57-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-57-10" name = "__codelineno-57-10" href = "#__codelineno-57-10" > < / a > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-57-11" name = "__codelineno-57-11" href = "#__codelineno-57-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-58-1" name = "__codelineno-58-1" href = "#__codelineno-58-1" > < / a > < span class = "cm" > /* 递归 */< / span >
< a id = "__codelineno-58-2" name = "__codelineno-58-2" href = "#__codelineno-58-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > recur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-58-3" name = "__codelineno-58-3" href = "#__codelineno-58-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-58-4" name = "__codelineno-58-4" href = "#__codelineno-58-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-58-5" name = "__codelineno-58-5" href = "#__codelineno-58-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-58-6" name = "__codelineno-58-6" href = "#__codelineno-58-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-58-7" name = "__codelineno-58-7" href = "#__codelineno-58-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-58-8" name = "__codelineno-58-8" href = "#__codelineno-58-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-58-9" name = "__codelineno-58-9" href = "#__codelineno-58-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-58-10" name = "__codelineno-58-10" href = "#__codelineno-58-10" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-25 00:05:17 +08:00
< div class = "highlight" > < span class = "filename" > recursion.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-59-1" name = "__codelineno-59-1" href = "#__codelineno-59-1" > < / a > < span class = "c1" > // 递归函数< / span >
< a id = "__codelineno-59-2" name = "__codelineno-59-2" href = "#__codelineno-59-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-59-3" name = "__codelineno-59-3" href = "#__codelineno-59-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-59-4" name = "__codelineno-59-4" href = "#__codelineno-59-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-59-5" name = "__codelineno-59-5" href = "#__codelineno-59-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-59-6" name = "__codelineno-59-6" href = "#__codelineno-59-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-59-7" name = "__codelineno-59-7" href = "#__codelineno-59-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-59-8" name = "__codelineno-59-8" href = "#__codelineno-59-8" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-59-9" name = "__codelineno-59-9" href = "#__codelineno-59-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-59-10" name = "__codelineno-59-10" href = "#__codelineno-59-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-59-11" name = "__codelineno-59-11" href = "#__codelineno-59-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 图 2-3 展示了该函数的递归过程。< / p >
2023-11-09 05:13:54 +08:00
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/recursion_sum.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "求和函数的递归过程" class = "animation-figure" src = "../iteration_and_recursion.assets/recursion_sum.png" / > < / a > < / p >
2023-08-24 17:47:31 +08:00
< p align = "center" > 图 2-3 求和函数的递归过程 < / p >
< p > 虽然从计算角度看，迭代与递归可以得到相同的结果，< strong > 但它们代表了两种完全不同的思考和解决问题的范式< / strong > 。< / p >
< ul >
< li > < strong > 迭代< / strong > ：“自下而上”地解决问题。从最基础的步骤开始，然后不断重复或累加这些步骤，直到任务完成。< / li >
< li > < strong > 递归< / strong > ：“自上而下”地解决问题。将原问题分解为更小的子问题，这些子问题和原问题具有相同的形式。接下来将子问题继续分解为更小的子问题，直到基本情况时停止（基本情况的解是已知的）。< / li >
< / ul >
2023-12-02 06:24:11 +08:00
< p > 以上述求和函数为例，设问题 < span class = "arithmatex" > \(f(n) = 1 + 2 + \dots + n\)< / span > 。< / p >
2023-08-24 17:47:31 +08:00
< ul >
< li > < strong > 迭代< / strong > ：在循环中模拟求和过程，从 < span class = "arithmatex" > \(1\)< / span > 遍历到 < span class = "arithmatex" > \(n\)< / span > ，每轮执行求和操作，即可求得 < span class = "arithmatex" > \(f(n)\)< / span > 。< / li >
2023-09-24 22:52:46 +08:00
< li > < strong > 递归< / strong > ：将问题分解为子问题 < span class = "arithmatex" > \(f(n) = n + f(n-1)\)< / span > ，不断（递归地）分解下去，直至基本情况 < span class = "arithmatex" > \(f(1) = 1\)< / span > 时终止。< / li >
2023-08-24 17:47:31 +08:00
< / ul >
< h3 id = "1" > 1. 调用栈< a class = "headerlink" href = "#1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 递归函数每次调用自身时，系统都会为新开启的函数分配内存，以存储局部变量、调用地址和其他信息等。这将导致两方面的结果。< / p >
< ul >
< li > 函数的上下文数据都存储在称为“栈帧空间”的内存区域中，直至函数返回后才会被释放。因此，< strong > 递归通常比迭代更加耗费内存空间< / strong > 。< / li >
< li > 递归调用函数会产生额外的开销。< strong > 因此递归通常比循环的时间效率更低< / strong > 。< / li >
< / ul >
< p > 如图 2-4 所示，在触发终止条件前，同时存在 < span class = "arithmatex" > \(n\)< / span > 个未返回的递归函数，< strong > 递归深度为 < span class = "arithmatex" > \(n\)< / span > < / strong > 。< / p >
2023-11-09 05:13:54 +08:00
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/recursion_sum_depth.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "递归调用深度" class = "animation-figure" src = "../iteration_and_recursion.assets/recursion_sum_depth.png" / > < / a > < / p >
2023-08-24 17:47:31 +08:00
< p align = "center" > 图 2-4 递归调用深度 < / p >
2023-12-02 06:24:11 +08:00
< p > 在实际中，编程语言允许的递归深度通常是有限的，过深的递归可能导致栈溢出错误。< / p >
2023-08-24 17:47:31 +08:00
< h3 id = "2" > 2. 尾递归< a class = "headerlink" href = "#2" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 有趣的是，< strong > 如果函数在返回前的最后一步才进行递归调用< / strong > ，则该函数可以被编译器或解释器优化，使其在空间效率上与迭代相当。这种情况被称为「尾递归 tail recursion」。< / p >
< ul >
< li > < strong > 普通递归< / strong > ：当函数返回到上一层级的函数后，需要继续执行代码，因此系统需要保存上一层调用的上下文。< / li >
2023-12-02 06:24:11 +08:00
< li > < strong > 尾递归< / strong > ：递归调用是函数返回前的最后一个操作，这意味着函数返回到上一层级后，无须继续执行其他操作，因此系统无须保存上一层函数的上下文。< / li >
2023-08-24 17:47:31 +08:00
< / ul >
2023-12-02 06:24:11 +08:00
< p > 以计算 < span class = "arithmatex" > \(1 + 2 + \dots + n\)< / span > 为例，我们可以将结果变量 < code > res< / code > 设为函数参数，从而实现尾递归：< / p >
2023-09-04 03:17:06 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "6:12" > < input checked = "checked" id = "__tabbed_6_1" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_2" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_3" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_4" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_5" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_6" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_7" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_8" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_9" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_10" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_11" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_12" name = "__tabbed_6" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_6_1" > Python< / label > < label for = "__tabbed_6_2" > C++< / label > < label for = "__tabbed_6_3" > Java< / label > < label for = "__tabbed_6_4" > C#< / label > < label for = "__tabbed_6_5" > Go< / label > < label for = "__tabbed_6_6" > Swift< / label > < label for = "__tabbed_6_7" > JS< / label > < label for = "__tabbed_6_8" > TS< / label > < label for = "__tabbed_6_9" > Dart< / label > < label for = "__tabbed_6_10" > Rust< / label > < label for = "__tabbed_6_11" > C< / label > < label for = "__tabbed_6_12" > Zig< / label > < / div >
2023-08-24 17:47:31 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-60-1" name = "__codelineno-60-1" href = "#__codelineno-60-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > tail_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-60-2" name = "__codelineno-60-2" href = "#__codelineno-60-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 尾递归" " " < / span >
< a id = "__codelineno-60-3" name = "__codelineno-60-3" href = "#__codelineno-60-3" > < / a > < span class = "c1" > # 终止条件< / span >
< a id = "__codelineno-60-4" name = "__codelineno-60-4" href = "#__codelineno-60-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span >
< a id = "__codelineno-60-5" name = "__codelineno-60-5" href = "#__codelineno-60-5" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-60-6" name = "__codelineno-60-6" href = "#__codelineno-60-6" > < / a > < span class = "c1" > # 尾递归调用< / span >
< a id = "__codelineno-60-7" name = "__codelineno-60-7" href = "#__codelineno-60-7" > < / a > < span class = "k" > return< / span > < span class = "n" > tail_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "o" > +< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-61-1" name = "__codelineno-61-1" href = "#__codelineno-61-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
< a id = "__codelineno-61-2" name = "__codelineno-61-2" href = "#__codelineno-61-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > tailRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-61-3" name = "__codelineno-61-3" href = "#__codelineno-61-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-61-4" name = "__codelineno-61-4" href = "#__codelineno-61-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-61-5" name = "__codelineno-61-5" href = "#__codelineno-61-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-61-6" name = "__codelineno-61-6" href = "#__codelineno-61-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-61-7" name = "__codelineno-61-7" href = "#__codelineno-61-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-61-8" name = "__codelineno-61-8" href = "#__codelineno-61-8" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-62-1" name = "__codelineno-62-1" href = "#__codelineno-62-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
< a id = "__codelineno-62-2" name = "__codelineno-62-2" href = "#__codelineno-62-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > tailRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-62-3" name = "__codelineno-62-3" href = "#__codelineno-62-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-62-4" name = "__codelineno-62-4" href = "#__codelineno-62-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-62-5" name = "__codelineno-62-5" href = "#__codelineno-62-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-62-6" name = "__codelineno-62-6" href = "#__codelineno-62-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-62-7" name = "__codelineno-62-7" href = "#__codelineno-62-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-62-8" name = "__codelineno-62-8" href = "#__codelineno-62-8" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-63-1" name = "__codelineno-63-1" href = "#__codelineno-63-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-63-2" name = "__codelineno-63-2" href = "#__codelineno-63-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > TailRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-63-3" name = "__codelineno-63-3" href = "#__codelineno-63-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-63-4" name = "__codelineno-63-4" href = "#__codelineno-63-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-63-5" name = "__codelineno-63-5" href = "#__codelineno-63-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-63-6" name = "__codelineno-63-6" href = "#__codelineno-63-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-63-7" name = "__codelineno-63-7" href = "#__codelineno-63-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nf" > TailRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-63-8" name = "__codelineno-63-8" href = "#__codelineno-63-8" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-64-1" name = "__codelineno-64-1" href = "#__codelineno-64-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
< a id = "__codelineno-64-2" name = "__codelineno-64-2" href = "#__codelineno-64-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > tailRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-64-3" name = "__codelineno-64-3" href = "#__codelineno-64-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-64-4" name = "__codelineno-64-4" href = "#__codelineno-64-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-64-5" name = "__codelineno-64-5" href = "#__codelineno-64-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-64-6" name = "__codelineno-64-6" href = "#__codelineno-64-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-64-7" name = "__codelineno-64-7" href = "#__codelineno-64-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-64-8" name = "__codelineno-64-8" href = "#__codelineno-64-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > tailRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > +< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-64-9" name = "__codelineno-64-9" href = "#__codelineno-64-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-65-1" name = "__codelineno-65-1" href = "#__codelineno-65-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
< a id = "__codelineno-65-2" name = "__codelineno-65-2" href = "#__codelineno-65-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > tailRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-65-3" name = "__codelineno-65-3" href = "#__codelineno-65-3" > < / a > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-65-4" name = "__codelineno-65-4" href = "#__codelineno-65-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "p" > ==< / span > < span class = "mi" > 0< / span > < span class = "p" > {< / span >
< a id = "__codelineno-65-5" name = "__codelineno-65-5" href = "#__codelineno-65-5" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-65-6" name = "__codelineno-65-6" href = "#__codelineno-65-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-65-7" name = "__codelineno-65-7" href = "#__codelineno-65-7" > < / a > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-65-8" name = "__codelineno-65-8" href = "#__codelineno-65-8" > < / a > < span class = "k" > return< / span > < span class = "n" > tailRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "n" > res< / span > < span class = "o" > +< / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-65-9" name = "__codelineno-65-9" href = "#__codelineno-65-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-66-1" name = "__codelineno-66-1" href = "#__codelineno-66-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
< a id = "__codelineno-66-2" name = "__codelineno-66-2" href = "#__codelineno-66-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > tailRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-66-3" name = "__codelineno-66-3" href = "#__codelineno-66-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-66-4" name = "__codelineno-66-4" href = "#__codelineno-66-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-66-5" name = "__codelineno-66-5" href = "#__codelineno-66-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-66-6" name = "__codelineno-66-6" href = "#__codelineno-66-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > tailRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-66-7" name = "__codelineno-66-7" href = "#__codelineno-66-7" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-67-1" name = "__codelineno-67-1" href = "#__codelineno-67-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
< a id = "__codelineno-67-2" name = "__codelineno-67-2" href = "#__codelineno-67-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > tailRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-67-3" name = "__codelineno-67-3" href = "#__codelineno-67-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-67-4" name = "__codelineno-67-4" href = "#__codelineno-67-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-67-5" name = "__codelineno-67-5" href = "#__codelineno-67-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-67-6" name = "__codelineno-67-6" href = "#__codelineno-67-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > tailRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-67-7" name = "__codelineno-67-7" href = "#__codelineno-67-7" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-68-1" name = "__codelineno-68-1" href = "#__codelineno-68-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
< a id = "__codelineno-68-2" name = "__codelineno-68-2" href = "#__codelineno-68-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-68-3" name = "__codelineno-68-3" href = "#__codelineno-68-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-68-4" name = "__codelineno-68-4" href = "#__codelineno-68-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-68-5" name = "__codelineno-68-5" href = "#__codelineno-68-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-68-6" name = "__codelineno-68-6" href = "#__codelineno-68-6" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-68-7" name = "__codelineno-68-7" href = "#__codelineno-68-7" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-69-1" name = "__codelineno-69-1" href = "#__codelineno-69-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
< a id = "__codelineno-69-2" name = "__codelineno-69-2" href = "#__codelineno-69-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > tail_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > : < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-69-3" name = "__codelineno-69-3" href = "#__codelineno-69-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-69-4" name = "__codelineno-69-4" href = "#__codelineno-69-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-69-5" name = "__codelineno-69-5" href = "#__codelineno-69-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-69-6" name = "__codelineno-69-6" href = "#__codelineno-69-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-69-7" name = "__codelineno-69-7" href = "#__codelineno-69-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-69-8" name = "__codelineno-69-8" href = "#__codelineno-69-8" > < / a > < span class = "w" > < / span > < span class = "n" > tail_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-69-9" name = "__codelineno-69-9" href = "#__codelineno-69-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-70-1" name = "__codelineno-70-1" href = "#__codelineno-70-1" > < / a > < span class = "cm" > /* 尾递归 */< / span >
< a id = "__codelineno-70-2" name = "__codelineno-70-2" href = "#__codelineno-70-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > tailRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-70-3" name = "__codelineno-70-3" href = "#__codelineno-70-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-70-4" name = "__codelineno-70-4" href = "#__codelineno-70-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-70-5" name = "__codelineno-70-5" href = "#__codelineno-70-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-6" name = "__codelineno-70-6" href = "#__codelineno-70-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-70-7" name = "__codelineno-70-7" href = "#__codelineno-70-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-70-8" name = "__codelineno-70-8" href = "#__codelineno-70-8" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-25 00:05:17 +08:00
< div class = "highlight" > < span class = "filename" > recursion.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-71-1" name = "__codelineno-71-1" href = "#__codelineno-71-1" > < / a > < span class = "c1" > // 尾递归函数< / span >
< a id = "__codelineno-71-2" name = "__codelineno-71-2" href = "#__codelineno-71-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-3" name = "__codelineno-71-3" href = "#__codelineno-71-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-71-4" name = "__codelineno-71-4" href = "#__codelineno-71-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-71-5" name = "__codelineno-71-5" href = "#__codelineno-71-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-71-6" name = "__codelineno-71-6" href = "#__codelineno-71-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-71-7" name = "__codelineno-71-7" href = "#__codelineno-71-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尾递归调用< / span >
< a id = "__codelineno-71-8" name = "__codelineno-71-8" href = "#__codelineno-71-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tailRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > );< / span >
< a id = "__codelineno-71-9" name = "__codelineno-71-9" href = "#__codelineno-71-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-12-02 06:24:11 +08:00
< p > 尾递归的执行过程如图 2-5 所示。对比普通递归和尾递归，两者的求和操作的执行点是不同的。< / p >
2023-08-24 17:47:31 +08:00
< ul >
< li > < strong > 普通递归< / strong > ：求和操作是在“归”的过程中执行的，每层返回后都要再执行一次求和操作。< / li >
< li > < strong > 尾递归< / strong > ：求和操作是在“递”的过程中执行的，“归”的过程只需层层返回。< / li >
< / ul >
2023-11-09 05:13:54 +08:00
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/tail_recursion_sum.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "尾递归过程" class = "animation-figure" src = "../iteration_and_recursion.assets/tail_recursion_sum.png" / > < / a > < / p >
2023-08-24 17:47:31 +08:00
< p align = "center" > 图 2-5 尾递归过程 < / p >
2023-09-12 00:56:10 +08:00
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
2023-12-02 06:24:11 +08:00
< p > 请注意， ， < / p >
2023-09-12 00:56:10 +08:00
< / div >
2023-08-24 17:47:31 +08:00
< h3 id = "3_1" > 3. 递归树< a class = "headerlink" href = "#3_1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 当处理与“分治”相关的算法问题时，递归往往比迭代的思路更加直观、代码更加易读。以“斐波那契数列”为例。< / p >
< div class = "admonition question" >
< p class = "admonition-title" > Question< / p >
< p > 给定一个斐波那契数列 < span class = "arithmatex" > \(0, 1, 1, 2, 3, 5, 8, 13, \dots\)< / span > ，求该数列的第 < span class = "arithmatex" > \(n\)< / span > 个数字。< / p >
< / div >
< p > 设斐波那契数列的第 < span class = "arithmatex" > \(n\)< / span > 个数字为 < span class = "arithmatex" > \(f(n)\)< / span > ，易得两个结论。< / p >
< ul >
< li > 数列的前两个数字为 < span class = "arithmatex" > \(f(1) = 0\)< / span > 和 < span class = "arithmatex" > \(f(2) = 1\)< / span > 。< / li >
< li > 数列中的每个数字是前两个数字的和，即 < span class = "arithmatex" > \(f(n) = f(n - 1) + f(n - 2)\)< / span > 。< / li >
< / ul >
2023-12-02 06:24:11 +08:00
< p > 按照递推关系进行递归调用，将前两个数字作为终止条件，便可写出递归代码。调用 < code > fib(n)< / code > 即可得到斐波那契数列的第 < span class = "arithmatex" > \(n\)< / span > 个数字：< / p >
2023-09-04 03:17:06 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "7:12" > < input checked = "checked" id = "__tabbed_7_1" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_2" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_3" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_4" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_5" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_6" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_7" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_8" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_9" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_10" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_11" name = "__tabbed_7" type = "radio" / > < input id = "__tabbed_7_12" name = "__tabbed_7" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_7_1" > Python< / label > < label for = "__tabbed_7_2" > C++< / label > < label for = "__tabbed_7_3" > Java< / label > < label for = "__tabbed_7_4" > C#< / label > < label for = "__tabbed_7_5" > Go< / label > < label for = "__tabbed_7_6" > Swift< / label > < label for = "__tabbed_7_7" > JS< / label > < label for = "__tabbed_7_8" > TS< / label > < label for = "__tabbed_7_9" > Dart< / label > < label for = "__tabbed_7_10" > Rust< / label > < label for = "__tabbed_7_11" > C< / label > < label for = "__tabbed_7_12" > Zig< / label > < / div >
2023-08-24 17:47:31 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-72-1" name = "__codelineno-72-1" href = "#__codelineno-72-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-2" name = "__codelineno-72-2" href = "#__codelineno-72-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 斐波那契数列：递归" " " < / span >
< a id = "__codelineno-72-3" name = "__codelineno-72-3" href = "#__codelineno-72-3" > < / a > < span class = "c1" > # 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-72-4" name = "__codelineno-72-4" href = "#__codelineno-72-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 1< / span > < span class = "ow" > or< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 2< / span > < span class = "p" > :< / span >
< a id = "__codelineno-72-5" name = "__codelineno-72-5" href = "#__codelineno-72-5" > < / a > < span class = "k" > return< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-72-6" name = "__codelineno-72-6" href = "#__codelineno-72-6" > < / a > < span class = "c1" > # 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-72-7" name = "__codelineno-72-7" href = "#__codelineno-72-7" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "o" > +< / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-72-8" name = "__codelineno-72-8" href = "#__codelineno-72-8" > < / a > < span class = "c1" > # 返回结果 f(n)< / span >
< a id = "__codelineno-72-9" name = "__codelineno-72-9" href = "#__codelineno-72-9" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-73-1" name = "__codelineno-73-1" href = "#__codelineno-73-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
< a id = "__codelineno-73-2" name = "__codelineno-73-2" href = "#__codelineno-73-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > fib< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-73-3" name = "__codelineno-73-3" href = "#__codelineno-73-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-73-4" name = "__codelineno-73-4" href = "#__codelineno-73-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-73-5" name = "__codelineno-73-5" href = "#__codelineno-73-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-73-6" name = "__codelineno-73-6" href = "#__codelineno-73-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-73-7" name = "__codelineno-73-7" href = "#__codelineno-73-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-73-8" name = "__codelineno-73-8" href = "#__codelineno-73-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-73-9" name = "__codelineno-73-9" href = "#__codelineno-73-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-73-10" name = "__codelineno-73-10" href = "#__codelineno-73-10" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-74-1" name = "__codelineno-74-1" href = "#__codelineno-74-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
< a id = "__codelineno-74-2" name = "__codelineno-74-2" href = "#__codelineno-74-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > fib< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-74-3" name = "__codelineno-74-3" href = "#__codelineno-74-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-74-4" name = "__codelineno-74-4" href = "#__codelineno-74-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-74-5" name = "__codelineno-74-5" href = "#__codelineno-74-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-6" name = "__codelineno-74-6" href = "#__codelineno-74-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-74-7" name = "__codelineno-74-7" href = "#__codelineno-74-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-74-8" name = "__codelineno-74-8" href = "#__codelineno-74-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-74-9" name = "__codelineno-74-9" href = "#__codelineno-74-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-74-10" name = "__codelineno-74-10" href = "#__codelineno-74-10" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-75-1" name = "__codelineno-75-1" href = "#__codelineno-75-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-75-2" name = "__codelineno-75-2" href = "#__codelineno-75-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > Fib< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-75-3" name = "__codelineno-75-3" href = "#__codelineno-75-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-75-4" name = "__codelineno-75-4" href = "#__codelineno-75-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-75-5" name = "__codelineno-75-5" href = "#__codelineno-75-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-6" name = "__codelineno-75-6" href = "#__codelineno-75-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-75-7" name = "__codelineno-75-7" href = "#__codelineno-75-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > Fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > );< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-75-8" name = "__codelineno-75-8" href = "#__codelineno-75-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-75-9" name = "__codelineno-75-9" href = "#__codelineno-75-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-75-10" name = "__codelineno-75-10" href = "#__codelineno-75-10" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-76-1" name = "__codelineno-76-1" href = "#__codelineno-76-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
< a id = "__codelineno-76-2" name = "__codelineno-76-2" href = "#__codelineno-76-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-76-3" name = "__codelineno-76-3" href = "#__codelineno-76-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-76-4" name = "__codelineno-76-4" href = "#__codelineno-76-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-76-5" name = "__codelineno-76-5" href = "#__codelineno-76-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-76-6" name = "__codelineno-76-6" href = "#__codelineno-76-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-76-7" name = "__codelineno-76-7" href = "#__codelineno-76-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-76-8" name = "__codelineno-76-8" href = "#__codelineno-76-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-76-9" name = "__codelineno-76-9" href = "#__codelineno-76-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-76-10" name = "__codelineno-76-10" href = "#__codelineno-76-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-76-11" name = "__codelineno-76-11" href = "#__codelineno-76-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-77-1" name = "__codelineno-77-1" href = "#__codelineno-77-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
< a id = "__codelineno-77-2" name = "__codelineno-77-2" href = "#__codelineno-77-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-77-3" name = "__codelineno-77-3" href = "#__codelineno-77-3" > < / a > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-77-4" name = "__codelineno-77-4" href = "#__codelineno-77-4" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "p" > ==< / span > < span class = "mi" > 1< / span > < span class = "o" > ||< / span > < span class = "n" > n< / span > < span class = "p" > ==< / span > < span class = "mi" > 2< / span > < span class = "p" > {< / span >
< a id = "__codelineno-77-5" name = "__codelineno-77-5" href = "#__codelineno-77-5" > < / a > < span class = "k" > return< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-77-6" name = "__codelineno-77-6" href = "#__codelineno-77-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-77-7" name = "__codelineno-77-7" href = "#__codelineno-77-7" > < / a > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-77-8" name = "__codelineno-77-8" href = "#__codelineno-77-8" > < / a > < span class = "kd" > let< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "o" > +< / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "o" > -< / span > < span class = "mi" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-77-9" name = "__codelineno-77-9" href = "#__codelineno-77-9" > < / a > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-77-10" name = "__codelineno-77-10" href = "#__codelineno-77-10" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-77-11" name = "__codelineno-77-11" href = "#__codelineno-77-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-78-1" name = "__codelineno-78-1" href = "#__codelineno-78-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
< a id = "__codelineno-78-2" name = "__codelineno-78-2" href = "#__codelineno-78-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-78-3" name = "__codelineno-78-3" href = "#__codelineno-78-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-78-4" name = "__codelineno-78-4" href = "#__codelineno-78-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-78-5" name = "__codelineno-78-5" href = "#__codelineno-78-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-78-6" name = "__codelineno-78-6" href = "#__codelineno-78-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-78-7" name = "__codelineno-78-7" href = "#__codelineno-78-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-78-8" name = "__codelineno-78-8" href = "#__codelineno-78-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-78-9" name = "__codelineno-78-9" href = "#__codelineno-78-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-79-1" name = "__codelineno-79-1" href = "#__codelineno-79-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
< a id = "__codelineno-79-2" name = "__codelineno-79-2" href = "#__codelineno-79-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-79-3" name = "__codelineno-79-3" href = "#__codelineno-79-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-79-4" name = "__codelineno-79-4" href = "#__codelineno-79-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-5" name = "__codelineno-79-5" href = "#__codelineno-79-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-79-6" name = "__codelineno-79-6" href = "#__codelineno-79-6" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > fib< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-79-7" name = "__codelineno-79-7" href = "#__codelineno-79-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-79-8" name = "__codelineno-79-8" href = "#__codelineno-79-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-79-9" name = "__codelineno-79-9" href = "#__codelineno-79-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-80-1" name = "__codelineno-80-1" href = "#__codelineno-80-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
< a id = "__codelineno-80-2" name = "__codelineno-80-2" href = "#__codelineno-80-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-80-3" name = "__codelineno-80-3" href = "#__codelineno-80-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-80-4" name = "__codelineno-80-4" href = "#__codelineno-80-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-80-5" name = "__codelineno-80-5" href = "#__codelineno-80-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-80-6" name = "__codelineno-80-6" href = "#__codelineno-80-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-80-7" name = "__codelineno-80-7" href = "#__codelineno-80-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-80-8" name = "__codelineno-80-8" href = "#__codelineno-80-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-80-9" name = "__codelineno-80-9" href = "#__codelineno-80-9" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-81-1" name = "__codelineno-81-1" href = "#__codelineno-81-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
< a id = "__codelineno-81-2" name = "__codelineno-81-2" href = "#__codelineno-81-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-81-3" name = "__codelineno-81-3" href = "#__codelineno-81-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-81-4" name = "__codelineno-81-4" href = "#__codelineno-81-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-81-5" name = "__codelineno-81-5" href = "#__codelineno-81-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-81-6" name = "__codelineno-81-6" href = "#__codelineno-81-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-81-7" name = "__codelineno-81-7" href = "#__codelineno-81-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-81-8" name = "__codelineno-81-8" href = "#__codelineno-81-8" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-81-9" name = "__codelineno-81-9" href = "#__codelineno-81-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果< / span >
< a id = "__codelineno-81-10" name = "__codelineno-81-10" href = "#__codelineno-81-10" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-81-11" name = "__codelineno-81-11" href = "#__codelineno-81-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-82-1" name = "__codelineno-82-1" href = "#__codelineno-82-1" > < / a > < span class = "cm" > /* 斐波那契数列：递归 */< / span >
< a id = "__codelineno-82-2" name = "__codelineno-82-2" href = "#__codelineno-82-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > fib< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-82-3" name = "__codelineno-82-3" href = "#__codelineno-82-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-82-4" name = "__codelineno-82-4" href = "#__codelineno-82-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > )< / span >
< a id = "__codelineno-82-5" name = "__codelineno-82-5" href = "#__codelineno-82-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-82-6" name = "__codelineno-82-6" href = "#__codelineno-82-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-82-7" name = "__codelineno-82-7" href = "#__codelineno-82-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-82-8" name = "__codelineno-82-8" href = "#__codelineno-82-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-82-9" name = "__codelineno-82-9" href = "#__codelineno-82-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-82-10" name = "__codelineno-82-10" href = "#__codelineno-82-10" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-25 00:05:17 +08:00
< div class = "highlight" > < span class = "filename" > recursion.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-83-1" name = "__codelineno-83-1" href = "#__codelineno-83-1" > < / a > < span class = "c1" > // 斐波那契数列< / span >
< a id = "__codelineno-83-2" name = "__codelineno-83-2" href = "#__codelineno-83-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-83-3" name = "__codelineno-83-3" href = "#__codelineno-83-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件 f(1) = 0, f(2) = 1< / span >
< a id = "__codelineno-83-4" name = "__codelineno-83-4" href = "#__codelineno-83-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "k" > or< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-83-5" name = "__codelineno-83-5" href = "#__codelineno-83-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-83-6" name = "__codelineno-83-6" href = "#__codelineno-83-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-83-7" name = "__codelineno-83-7" href = "#__codelineno-83-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递归调用 f(n) = f(n-1) + f(n-2)< / span >
< a id = "__codelineno-83-8" name = "__codelineno-83-8" href = "#__codelineno-83-8" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > fib< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-83-9" name = "__codelineno-83-9" href = "#__codelineno-83-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回结果 f(n)< / span >
< a id = "__codelineno-83-10" name = "__codelineno-83-10" href = "#__codelineno-83-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-83-11" name = "__codelineno-83-11" href = "#__codelineno-83-11" > < / a > < span class = "p" > }< / span >
2023-08-24 17:47:31 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-12-02 06:24:11 +08:00
< p > 观察以上代码，我们在函数内递归调用了两个函数，< strong > 这意味着从一个调用产生了两个调用分支< / strong > 。如图 2-6 所示，这样不断递归调用下去，最终将产生一棵层数为 < span class = "arithmatex" > \(n\)< / span > 的「递归树 recursion tree」。< / p >
2023-11-09 05:13:54 +08:00
< p > < a class = "glightbox" href = "../iteration_and_recursion.assets/recursion_tree.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "斐波那契数列的递归树" class = "animation-figure" src = "../iteration_and_recursion.assets/recursion_tree.png" / > < / a > < / p >
2023-08-24 17:47:31 +08:00
< p align = "center" > 图 2-6 斐波那契数列的递归树 < / p >
2023-12-02 06:24:11 +08:00
< p > 从本质上看，递归体现了“将问题分解为更小子问题”的思维范式，这种分治策略至关重要。< / p >
2023-08-24 17:47:31 +08:00
< ul >
2023-12-02 06:24:11 +08:00
< li > 从算法角度看，搜索、排序、回溯、分治、动态规划等许多重要算法策略直接或间接地应用了这种思维方式。< / li >
2023-08-24 17:47:31 +08:00
< li > 从数据结构角度看，递归天然适合处理链表、树和图的相关问题，因为它们非常适合用分治思想进行分析。< / li >
< / ul >
2023-09-12 00:56:10 +08:00
< h2 id = "223" > 2.2.3 两者对比< a class = "headerlink" href = "#223" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 总结以上内容，如表 2-1 所示，迭代和递归在实现、性能和适用性上有所不同。< / p >
< p align = "center" > 表 2-1 迭代与递归特点对比 < / p >
< div class = "center-table" >
< table >
< thead >
< tr >
< th > < / th >
< th > 迭代< / th >
< th > 递归< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > 实现方式< / td >
< td > 循环结构< / td >
< td > 函数调用自身< / td >
< / tr >
< tr >
< td > 时间效率< / td >
< td > 效率通常较高，无函数调用开销< / td >
< td > 每次函数调用都会产生开销< / td >
< / tr >
< tr >
< td > 内存使用< / td >
< td > 通常使用固定大小的内存空间< / td >
< td > 累积函数调用可能使用大量的栈帧空间< / td >
< / tr >
< tr >
< td > 适用问题< / td >
< td > 适用于简单循环任务，代码直观、可读性好< / td >
< td > 适用于子问题分解，如树、图、分治、回溯等，代码结构简洁、清晰< / td >
< / tr >
< / tbody >
< / table >
< / div >
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > 如果感觉以下内容理解困难，可以在读完“栈”章节后再来复习。< / p >
< / div >
2023-12-14 02:53:40 +08:00
< p > 那么，迭代和递归具有什么内在联系呢？以上述递归函数为例，求和操作在递归的“归”阶段进行。这意味着最初被调用的函数实际上是最后完成其求和操作的，< strong > 这种工作机制与栈的“先入后出”原则异曲同工< / strong > 。< / p >
2023-09-12 00:56:10 +08:00
< p > 事实上，“调用栈”和“栈帧空间”这类递归术语已经暗示了递归与栈之间的密切关系。< / p >
< ol >
< li > < strong > 递< / strong > ：当函数被调用时，系统会在“调用栈”上为该函数分配新的栈帧，用于存储函数的局部变量、参数、返回地址等数据。< / li >
2023-12-14 02:53:40 +08:00
< li > < strong > 归< / strong > ：当函数完成执行并返回时，对应的栈帧会被从“调用栈”上移除，恢复之前函数的执行环境。< / li >
2023-09-12 00:56:10 +08:00
< / ol >
< p > 因此，< strong > 我们可以使用一个显式的栈来模拟调用栈的行为< / strong > ，从而将递归转化为迭代形式：< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "8:12" > < input checked = "checked" id = "__tabbed_8_1" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_2" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_3" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_4" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_5" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_6" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_7" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_8" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_9" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_10" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_11" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_12" name = "__tabbed_8" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_8_1" > Python< / label > < label for = "__tabbed_8_2" > C++< / label > < label for = "__tabbed_8_3" > Java< / label > < label for = "__tabbed_8_4" > C#< / label > < label for = "__tabbed_8_5" > Go< / label > < label for = "__tabbed_8_6" > Swift< / label > < label for = "__tabbed_8_7" > JS< / label > < label for = "__tabbed_8_8" > TS< / label > < label for = "__tabbed_8_9" > Dart< / label > < label for = "__tabbed_8_10" > Rust< / label > < label for = "__tabbed_8_11" > C< / label > < label for = "__tabbed_8_12" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-84-1" name = "__codelineno-84-1" href = "#__codelineno-84-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > for_loop_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< a id = "__codelineno-84-2" name = "__codelineno-84-2" href = "#__codelineno-84-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 使用迭代模拟递归" " " < / span >
< a id = "__codelineno-84-3" name = "__codelineno-84-3" href = "#__codelineno-84-3" > < / a > < span class = "c1" > # 使用一个显式的栈来模拟系统调用栈< / span >
< a id = "__codelineno-84-4" name = "__codelineno-84-4" href = "#__codelineno-84-4" > < / a > < span class = "n" > stack< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-84-5" name = "__codelineno-84-5" href = "#__codelineno-84-5" > < / a > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-84-6" name = "__codelineno-84-6" href = "#__codelineno-84-6" > < / a > < span class = "c1" > # 递：递归调用< / span >
< a id = "__codelineno-84-7" name = "__codelineno-84-7" href = "#__codelineno-84-7" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-84-8" name = "__codelineno-84-8" href = "#__codelineno-84-8" > < / a > < span class = "c1" > # 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-84-9" name = "__codelineno-84-9" href = "#__codelineno-84-9" > < / a > < span class = "n" > stack< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-84-10" name = "__codelineno-84-10" href = "#__codelineno-84-10" > < / a > < span class = "c1" > # 归：返回结果< / span >
< a id = "__codelineno-84-11" name = "__codelineno-84-11" href = "#__codelineno-84-11" > < / a > < span class = "k" > while< / span > < span class = "n" > stack< / span > < span class = "p" > :< / span >
< a id = "__codelineno-84-12" name = "__codelineno-84-12" href = "#__codelineno-84-12" > < / a > < span class = "c1" > # 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-84-13" name = "__codelineno-84-13" href = "#__codelineno-84-13" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > stack< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-84-14" name = "__codelineno-84-14" href = "#__codelineno-84-14" > < / a > < span class = "c1" > # res = 1+2+3+...+n< / span >
< a id = "__codelineno-84-15" name = "__codelineno-84-15" href = "#__codelineno-84-15" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-85-1" name = "__codelineno-85-1" href = "#__codelineno-85-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
< a id = "__codelineno-85-2" name = "__codelineno-85-2" href = "#__codelineno-85-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > forLoopRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-85-3" name = "__codelineno-85-3" href = "#__codelineno-85-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈< / span >
< a id = "__codelineno-85-4" name = "__codelineno-85-4" href = "#__codelineno-85-4" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-85-5" name = "__codelineno-85-5" href = "#__codelineno-85-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-85-6" name = "__codelineno-85-6" href = "#__codelineno-85-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-85-7" name = "__codelineno-85-7" href = "#__codelineno-85-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-85-8" name = "__codelineno-85-8" href = "#__codelineno-85-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-85-9" name = "__codelineno-85-9" href = "#__codelineno-85-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-85-10" name = "__codelineno-85-10" href = "#__codelineno-85-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-85-11" name = "__codelineno-85-11" href = "#__codelineno-85-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-85-12" name = "__codelineno-85-12" href = "#__codelineno-85-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > empty< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-85-13" name = "__codelineno-85-13" href = "#__codelineno-85-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-85-14" name = "__codelineno-85-14" href = "#__codelineno-85-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > top< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-85-15" name = "__codelineno-85-15" href = "#__codelineno-85-15" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-85-16" name = "__codelineno-85-16" href = "#__codelineno-85-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-85-17" name = "__codelineno-85-17" href = "#__codelineno-85-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-85-18" name = "__codelineno-85-18" href = "#__codelineno-85-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-85-19" name = "__codelineno-85-19" href = "#__codelineno-85-19" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-86-1" name = "__codelineno-86-1" href = "#__codelineno-86-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
< a id = "__codelineno-86-2" name = "__codelineno-86-2" href = "#__codelineno-86-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > forLoopRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-86-3" name = "__codelineno-86-3" href = "#__codelineno-86-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈< / span >
< a id = "__codelineno-86-4" name = "__codelineno-86-4" href = "#__codelineno-86-4" > < / a > < span class = "w" > < / span > < span class = "n" > Stack< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > Stack< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-86-5" name = "__codelineno-86-5" href = "#__codelineno-86-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-86-6" name = "__codelineno-86-6" href = "#__codelineno-86-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-86-7" name = "__codelineno-86-7" href = "#__codelineno-86-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-86-8" name = "__codelineno-86-8" href = "#__codelineno-86-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-86-9" name = "__codelineno-86-9" href = "#__codelineno-86-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "na" > push< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-86-10" name = "__codelineno-86-10" href = "#__codelineno-86-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-86-11" name = "__codelineno-86-11" href = "#__codelineno-86-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-86-12" name = "__codelineno-86-12" href = "#__codelineno-86-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "na" > isEmpty< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-86-13" name = "__codelineno-86-13" href = "#__codelineno-86-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-86-14" name = "__codelineno-86-14" href = "#__codelineno-86-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "na" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-86-15" name = "__codelineno-86-15" href = "#__codelineno-86-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-86-16" name = "__codelineno-86-16" href = "#__codelineno-86-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-86-17" name = "__codelineno-86-17" href = "#__codelineno-86-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-86-18" name = "__codelineno-86-18" href = "#__codelineno-86-18" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-87-1" name = "__codelineno-87-1" href = "#__codelineno-87-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-87-2" name = "__codelineno-87-2" href = "#__codelineno-87-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > ForLoopRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-87-3" name = "__codelineno-87-3" href = "#__codelineno-87-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈< / span >
2023-10-08 01:43:42 +08:00
< a id = "__codelineno-87-4" name = "__codelineno-87-4" href = "#__codelineno-87-4" > < / a > < span class = "w" > < / span > < span class = "n" > Stack< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > ();< / span >
2023-10-06 14:10:31 +08:00
< a id = "__codelineno-87-5" name = "__codelineno-87-5" href = "#__codelineno-87-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-87-6" name = "__codelineno-87-6" href = "#__codelineno-87-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-87-7" name = "__codelineno-87-7" href = "#__codelineno-87-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-87-8" name = "__codelineno-87-8" href = "#__codelineno-87-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-87-9" name = "__codelineno-87-9" href = "#__codelineno-87-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > Push< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-87-10" name = "__codelineno-87-10" href = "#__codelineno-87-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-87-11" name = "__codelineno-87-11" href = "#__codelineno-87-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-87-12" name = "__codelineno-87-12" href = "#__codelineno-87-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-87-13" name = "__codelineno-87-13" href = "#__codelineno-87-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-87-14" name = "__codelineno-87-14" href = "#__codelineno-87-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > Pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-87-15" name = "__codelineno-87-15" href = "#__codelineno-87-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-87-16" name = "__codelineno-87-16" href = "#__codelineno-87-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-87-17" name = "__codelineno-87-17" href = "#__codelineno-87-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-87-18" name = "__codelineno-87-18" href = "#__codelineno-87-18" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-08 01:43:42 +08:00
< div class = "highlight" > < span class = "filename" > recursion.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-88-1" name = "__codelineno-88-1" href = "#__codelineno-88-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
< a id = "__codelineno-88-2" name = "__codelineno-88-2" href = "#__codelineno-88-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > forLoopRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-88-3" name = "__codelineno-88-3" href = "#__codelineno-88-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈< / span >
< a id = "__codelineno-88-4" name = "__codelineno-88-4" href = "#__codelineno-88-4" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > list< / span > < span class = "p" > .< / span > < span class = "nx" > New< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-88-5" name = "__codelineno-88-5" href = "#__codelineno-88-5" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-88-6" name = "__codelineno-88-6" href = "#__codelineno-88-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-88-7" name = "__codelineno-88-7" href = "#__codelineno-88-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > --< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-88-8" name = "__codelineno-88-8" href = "#__codelineno-88-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-88-9" name = "__codelineno-88-9" href = "#__codelineno-88-9" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > PushBack< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-88-10" name = "__codelineno-88-10" href = "#__codelineno-88-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-88-11" name = "__codelineno-88-11" href = "#__codelineno-88-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-88-12" name = "__codelineno-88-12" href = "#__codelineno-88-12" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > Len< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-88-13" name = "__codelineno-88-13" href = "#__codelineno-88-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-88-14" name = "__codelineno-88-14" href = "#__codelineno-88-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > Back< / span > < span class = "p" > ().< / span > < span class = "nx" > Value< / span > < span class = "p" > .(< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span >
< a id = "__codelineno-88-15" name = "__codelineno-88-15" href = "#__codelineno-88-15" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > Remove< / span > < span class = "p" > (< / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > Back< / span > < span class = "p" > ())< / span >
< a id = "__codelineno-88-16" name = "__codelineno-88-16" href = "#__codelineno-88-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-88-17" name = "__codelineno-88-17" href = "#__codelineno-88-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-88-18" name = "__codelineno-88-18" href = "#__codelineno-88-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span >
< a id = "__codelineno-88-19" name = "__codelineno-88-19" href = "#__codelineno-88-19" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-89-1" name = "__codelineno-89-1" href = "#__codelineno-89-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
< a id = "__codelineno-89-2" name = "__codelineno-89-2" href = "#__codelineno-89-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > forLoopRecur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-89-3" name = "__codelineno-89-3" href = "#__codelineno-89-3" > < / a > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈< / span >
< a id = "__codelineno-89-4" name = "__codelineno-89-4" href = "#__codelineno-89-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > stack< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-89-5" name = "__codelineno-89-5" href = "#__codelineno-89-5" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-89-6" name = "__codelineno-89-6" href = "#__codelineno-89-6" > < / a > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-89-7" name = "__codelineno-89-7" href = "#__codelineno-89-7" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "n" > n< / span > < span class = "p" > ,< / span > < span class = "n" > to< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-89-8" name = "__codelineno-89-8" href = "#__codelineno-89-8" > < / a > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-89-9" name = "__codelineno-89-9" href = "#__codelineno-89-9" > < / a > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-89-10" name = "__codelineno-89-10" href = "#__codelineno-89-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-89-11" name = "__codelineno-89-11" href = "#__codelineno-89-11" > < / a > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-89-12" name = "__codelineno-89-12" href = "#__codelineno-89-12" > < / a > < span class = "k" > while< / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "bp" > isEmpty< / span > < span class = "p" > {< / span >
< a id = "__codelineno-89-13" name = "__codelineno-89-13" href = "#__codelineno-89-13" > < / a > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-89-14" name = "__codelineno-89-14" href = "#__codelineno-89-14" > < / a > < span class = "n" > res< / span > < span class = "o" > +=< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-89-15" name = "__codelineno-89-15" href = "#__codelineno-89-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-89-16" name = "__codelineno-89-16" href = "#__codelineno-89-16" > < / a > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-89-17" name = "__codelineno-89-17" href = "#__codelineno-89-17" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-89-18" name = "__codelineno-89-18" href = "#__codelineno-89-18" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-90-1" name = "__codelineno-90-1" href = "#__codelineno-90-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
< a id = "__codelineno-90-2" name = "__codelineno-90-2" href = "#__codelineno-90-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > forLoopRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-90-3" name = "__codelineno-90-3" href = "#__codelineno-90-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈< / span >
< a id = "__codelineno-90-4" name = "__codelineno-90-4" href = "#__codelineno-90-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-90-5" name = "__codelineno-90-5" href = "#__codelineno-90-5" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-90-6" name = "__codelineno-90-6" href = "#__codelineno-90-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-90-7" name = "__codelineno-90-7" href = "#__codelineno-90-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-90-8" name = "__codelineno-90-8" href = "#__codelineno-90-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-90-9" name = "__codelineno-90-9" href = "#__codelineno-90-9" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-90-10" name = "__codelineno-90-10" href = "#__codelineno-90-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-90-11" name = "__codelineno-90-11" href = "#__codelineno-90-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-90-12" name = "__codelineno-90-12" href = "#__codelineno-90-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span >
< a id = "__codelineno-90-13" name = "__codelineno-90-13" href = "#__codelineno-90-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-90-14" name = "__codelineno-90-14" href = "#__codelineno-90-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-90-15" name = "__codelineno-90-15" href = "#__codelineno-90-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-90-16" name = "__codelineno-90-16" href = "#__codelineno-90-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-90-17" name = "__codelineno-90-17" href = "#__codelineno-90-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-90-18" name = "__codelineno-90-18" href = "#__codelineno-90-18" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-91-1" name = "__codelineno-91-1" href = "#__codelineno-91-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
< a id = "__codelineno-91-2" name = "__codelineno-91-2" href = "#__codelineno-91-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > forLoopRecur< / span > < span class = "p" > (< / span > < span class = "nx" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-91-3" name = "__codelineno-91-3" href = "#__codelineno-91-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈 < / span >
< a id = "__codelineno-91-4" name = "__codelineno-91-4" href = "#__codelineno-91-4" > < / a > < span class = "w" > < / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-91-5" name = "__codelineno-91-5" href = "#__codelineno-91-5" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-91-6" name = "__codelineno-91-6" href = "#__codelineno-91-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-91-7" name = "__codelineno-91-7" href = "#__codelineno-91-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-91-8" name = "__codelineno-91-8" href = "#__codelineno-91-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-91-9" name = "__codelineno-91-9" href = "#__codelineno-91-9" > < / a > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-91-10" name = "__codelineno-91-10" href = "#__codelineno-91-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-91-11" name = "__codelineno-91-11" href = "#__codelineno-91-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-91-12" name = "__codelineno-91-12" href = "#__codelineno-91-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span >
< a id = "__codelineno-91-13" name = "__codelineno-91-13" href = "#__codelineno-91-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-91-14" name = "__codelineno-91-14" href = "#__codelineno-91-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "nx" > stack< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-91-15" name = "__codelineno-91-15" href = "#__codelineno-91-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-91-16" name = "__codelineno-91-16" href = "#__codelineno-91-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-91-17" name = "__codelineno-91-17" href = "#__codelineno-91-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-91-18" name = "__codelineno-91-18" href = "#__codelineno-91-18" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-92-1" name = "__codelineno-92-1" href = "#__codelineno-92-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
< a id = "__codelineno-92-2" name = "__codelineno-92-2" href = "#__codelineno-92-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > forLoopRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-92-3" name = "__codelineno-92-3" href = "#__codelineno-92-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈< / span >
< a id = "__codelineno-92-4" name = "__codelineno-92-4" href = "#__codelineno-92-4" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [];< / span >
< a id = "__codelineno-92-5" name = "__codelineno-92-5" href = "#__codelineno-92-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-92-6" name = "__codelineno-92-6" href = "#__codelineno-92-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-92-7" name = "__codelineno-92-7" href = "#__codelineno-92-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-92-8" name = "__codelineno-92-8" href = "#__codelineno-92-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-92-9" name = "__codelineno-92-9" href = "#__codelineno-92-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > add< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-92-10" name = "__codelineno-92-10" href = "#__codelineno-92-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-92-11" name = "__codelineno-92-11" href = "#__codelineno-92-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-92-12" name = "__codelineno-92-12" href = "#__codelineno-92-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > isEmpty< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-92-13" name = "__codelineno-92-13" href = "#__codelineno-92-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-92-14" name = "__codelineno-92-14" href = "#__codelineno-92-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > removeLast< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-92-15" name = "__codelineno-92-15" href = "#__codelineno-92-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-92-16" name = "__codelineno-92-16" href = "#__codelineno-92-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-92-17" name = "__codelineno-92-17" href = "#__codelineno-92-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-92-18" name = "__codelineno-92-18" href = "#__codelineno-92-18" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-06 14:10:31 +08:00
< div class = "highlight" > < span class = "filename" > recursion.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-93-1" name = "__codelineno-93-1" href = "#__codelineno-93-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
< a id = "__codelineno-93-2" name = "__codelineno-93-2" href = "#__codelineno-93-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > for_loop_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > : < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "kt" > i32< / span > < span class = "p" > {< / span >
< a id = "__codelineno-93-3" name = "__codelineno-93-3" href = "#__codelineno-93-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈< / span >
< a id = "__codelineno-93-4" name = "__codelineno-93-4" href = "#__codelineno-93-4" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Vec< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-93-5" name = "__codelineno-93-5" href = "#__codelineno-93-5" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-93-6" name = "__codelineno-93-6" href = "#__codelineno-93-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-93-7" name = "__codelineno-93-7" href = "#__codelineno-93-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 1< / span > < span class = "o" > ..=< / span > < span class = "n" > n< / span > < span class = "p" > ).< / span > < span class = "n" > rev< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-93-8" name = "__codelineno-93-8" href = "#__codelineno-93-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
< a id = "__codelineno-93-9" name = "__codelineno-93-9" href = "#__codelineno-93-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-93-10" name = "__codelineno-93-10" href = "#__codelineno-93-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-93-11" name = "__codelineno-93-11" href = "#__codelineno-93-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-93-12" name = "__codelineno-93-12" href = "#__codelineno-93-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > is_empty< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-93-13" name = "__codelineno-93-13" href = "#__codelineno-93-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-93-14" name = "__codelineno-93-14" href = "#__codelineno-93-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ().< / span > < span class = "n" > unwrap< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-93-15" name = "__codelineno-93-15" href = "#__codelineno-93-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-93-16" name = "__codelineno-93-16" href = "#__codelineno-93-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-93-17" name = "__codelineno-93-17" href = "#__codelineno-93-17" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span >
< a id = "__codelineno-93-18" name = "__codelineno-93-18" href = "#__codelineno-93-18" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-17 20:29:42 +08:00
< div class = "highlight" > < span class = "filename" > recursion.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-94-1" name = "__codelineno-94-1" href = "#__codelineno-94-1" > < / a > < span class = "cm" > /* 使用迭代模拟递归 */< / span >
< a id = "__codelineno-94-2" name = "__codelineno-94-2" href = "#__codelineno-94-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > forLoopRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-94-3" name = "__codelineno-94-3" href = "#__codelineno-94-3" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > [< / span > < span class = "mi" > 1000< / span > < span class = "p" > ];< / span > < span class = "w" > < / span > < span class = "c1" > // 借助一个大数组来模拟栈< / span >
2023-10-26 03:00:40 +08:00
< a id = "__codelineno-94-4" name = "__codelineno-94-4" href = "#__codelineno-94-4" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > top< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > -1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 栈顶索引< / span >
2023-10-17 20:29:42 +08:00
< a id = "__codelineno-94-5" name = "__codelineno-94-5" href = "#__codelineno-94-5" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-94-6" name = "__codelineno-94-6" href = "#__codelineno-94-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-94-7" name = "__codelineno-94-7" href = "#__codelineno-94-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-94-8" name = "__codelineno-94-8" href = "#__codelineno-94-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“入栈操作”模拟“递”< / span >
2023-10-26 03:00:40 +08:00
< a id = "__codelineno-94-9" name = "__codelineno-94-9" href = "#__codelineno-94-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > top< / span > < span class = "o" > ++< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ;< / span >
2023-10-17 20:29:42 +08:00
< a id = "__codelineno-94-10" name = "__codelineno-94-10" href = "#__codelineno-94-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-94-11" name = "__codelineno-94-11" href = "#__codelineno-94-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-94-12" name = "__codelineno-94-12" href = "#__codelineno-94-12" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > top< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-94-13" name = "__codelineno-94-13" href = "#__codelineno-94-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过“出栈操作”模拟“归”< / span >
< a id = "__codelineno-94-14" name = "__codelineno-94-14" href = "#__codelineno-94-14" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > [< / span > < span class = "n" > top< / span > < span class = "o" > --< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-94-15" name = "__codelineno-94-15" href = "#__codelineno-94-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-94-16" name = "__codelineno-94-16" href = "#__codelineno-94-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-94-17" name = "__codelineno-94-17" href = "#__codelineno-94-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-94-18" name = "__codelineno-94-18" href = "#__codelineno-94-18" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-10-25 00:05:17 +08:00
< div class = "highlight" > < span class = "filename" > recursion.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-95-1" name = "__codelineno-95-1" href = "#__codelineno-95-1" > < / a > < span class = "c1" > // 使用迭代模拟递归< / span >
< a id = "__codelineno-95-2" name = "__codelineno-95-2" href = "#__codelineno-95-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > forLoopRecur< / span > < span class = "p" > (< / span > < span class = "kr" > comptime< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-95-3" name = "__codelineno-95-3" href = "#__codelineno-95-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用一个显式的栈来模拟系统调用栈< / span >
< a id = "__codelineno-95-4" name = "__codelineno-95-4" href = "#__codelineno-95-4" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "n" > n< / span > < span class = "p" > ]< / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-95-5" name = "__codelineno-95-5" href = "#__codelineno-95-5" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > i32< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-95-6" name = "__codelineno-95-6" href = "#__codelineno-95-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 递：递归调用< / span >
< a id = "__codelineno-95-7" name = "__codelineno-95-7" href = "#__codelineno-95-7" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > usize< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-95-8" name = "__codelineno-95-8" href = "#__codelineno-95-8" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-95-9" name = "__codelineno-95-9" href = "#__codelineno-95-9" > < / a > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > @intCast< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-95-10" name = "__codelineno-95-10" href = "#__codelineno-95-10" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-95-11" name = "__codelineno-95-11" href = "#__codelineno-95-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-95-12" name = "__codelineno-95-12" href = "#__codelineno-95-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 归：返回结果< / span >
< a id = "__codelineno-95-13" name = "__codelineno-95-13" href = "#__codelineno-95-13" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > index< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > usize< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-95-14" name = "__codelineno-95-14" href = "#__codelineno-95-14" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > index< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-95-15" name = "__codelineno-95-15" href = "#__codelineno-95-15" > < / a > < span class = "w" > < / span > < span class = "n" > index< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-95-16" name = "__codelineno-95-16" href = "#__codelineno-95-16" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "w" > < / span > < span class = "o" > +=< / span > < span class = "w" > < / span > < span class = "n" > stack< / span > < span class = "p" > [< / span > < span class = "n" > index< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-95-17" name = "__codelineno-95-17" href = "#__codelineno-95-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-95-18" name = "__codelineno-95-18" href = "#__codelineno-95-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // res = 1+2+3+...+n< / span >
< a id = "__codelineno-95-19" name = "__codelineno-95-19" href = "#__codelineno-95-19" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-95-20" name = "__codelineno-95-20" href = "#__codelineno-95-20" > < / a > < span class = "p" > }< / span >
2023-09-12 00:56:10 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-12-14 02:53:40 +08:00
< p > 观察以上代码，当递归转化为迭代后，代码变得更加复杂了。尽管迭代和递归在很多情况下可以互相转化，但不一定值得这样做，有以下两点原因。< / p >
2023-09-12 00:56:10 +08:00
< ul >
< li > 转化后的代码可能更加难以理解，可读性更差。< / li >
< li > 对于某些复杂问题，模拟系统调用栈的行为可能非常困难。< / li >
< / ul >
2023-12-14 02:53:40 +08:00
< p > 总之，< strong > 选择迭代还是递归取决于特定问题的性质< / strong > 。在编程实践中，权衡两者的优劣并根据情境选择合适的方法至关重要。< / p >
2023-08-24 17:47:31 +08:00
2023-09-21 20:44:52 +08:00
<!-- Source file information -->
2023-08-24 17:47:31 +08:00
2023-09-21 20:44:52 +08:00
<!-- Was this page helpful? -->
2023-08-24 17:47:31 +08:00
2023-09-21 20:44:52 +08:00
<!-- Previous and next pages link -->
< nav
class="md-footer__inner md-grid"
aria-label="页脚"
>
<!-- Link to previous page -->
< a
href="../performance_evaluation/"
class="md-footer__link md-footer__link--prev"
aria-label="上一页: 2.1 & nbsp; 算法效率评估"
rel="prev"
>
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / div >
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
上一页
< / span >
< div class = "md-ellipsis" >
2.1 算法效率评估
< / div >
< / div >
< / a >
<!-- Link to next page -->
< a
href="../time_complexity/"
class="md-footer__link md-footer__link--next"
aria-label="下一页: 2.3 & nbsp; 时间复杂度"
rel="next"
>
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
下一页
< / span >
< div class = "md-ellipsis" >
2.3 时间复杂度
< / div >
< / div >
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z" / > < / svg >
< / div >
< / a >
< / nav >
<!-- Comment system -->
2023-10-06 13:31:31 +08:00
2023-10-09 18:19:36 +08:00
2023-09-22 13:41:28 +08:00
< h5 align = "center" id = "__comments" > 欢迎在评论区留下你的见解、疑惑或建议< / h5 >
2023-10-06 13:31:31 +08:00
2023-08-24 17:47:31 +08:00
<!-- Insert generated snippet here -->
< script
src="https://giscus.app/client.js"
data-repo="krahets/hello-algo"
data-repo-id="R_kgDOIXtSqw"
data-category="Announcements"
data-category-id="DIC_kwDOIXtSq84CSZk_"
data-mapping="pathname"
data-strict="1"
data-reactions-enabled="1"
data-emit-metadata="0"
data-input-position="top"
data-theme="preferred_color_scheme"
data-lang="zh-CN"
crossorigin="anonymous"
async
>
< / script >
<!-- Synchronize Giscus theme with palette -->
< script >
var giscus = document.querySelector("script[src*=giscus]")
/* Set palette on initial load */
var palette = __md_get("__palette")
if (palette & & typeof palette.color === "object") {
2023-09-12 03:15:25 +08:00
var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
2023-08-24 17:47:31 +08:00
giscus.setAttribute("data-theme", theme)
}
/* Register event handlers after documented loaded */
document.addEventListener("DOMContentLoaded", function() {
var ref = document.querySelector("[data-md-component=palette]")
ref.addEventListener("change", function() {
var palette = __md_get("__palette")
if (palette & & typeof palette.color === "object") {
2023-09-12 03:15:25 +08:00
var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
2023-08-24 17:47:31 +08:00
/* Instruct Giscus to change theme */
var frame = document.querySelector(".giscus-frame")
frame.contentWindow.postMessage(
{ giscus: { setConfig: { theme } } },
"https://giscus.app"
)
}
})
})
< / script >
< / article >
< / div >
< script > var tabs = _ _md _get ( "__tabs" ) ; if ( Array . isArray ( tabs ) ) e : for ( var set of document . querySelectorAll ( ".tabbed-set" ) ) { var tab , labels = set . querySelector ( ".tabbed-labels" ) ; for ( tab of tabs ) for ( var label of labels . getElementsByTagName ( "label" ) ) if ( label . innerText . trim ( ) === tab ) { var input = document . getElementById ( label . htmlFor ) ; input . checked = ! 0 ; continue e } } < / script >
2023-12-07 20:12:31 +08:00
< script > var target = document . getElementById ( location . hash . slice ( 1 ) ) ; target && target . name && ( target . checked = target . name . startsWith ( "__tabbed_" ) ) < / script >
2023-08-24 17:47:31 +08:00
< / div >
< button type = "button" class = "md-top md-icon" data-md-component = "top" hidden >
2023-12-07 20:12:31 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8v12Z" / > < / svg >
回到页面顶部
< / button >
2023-08-24 17:47:31 +08:00
< / main >
2023-10-06 13:31:31 +08:00
< footer class = "md-footer" >
< nav class = "md-footer__inner md-grid" aria-label = "页脚" >
2023-12-07 20:12:31 +08:00
< a href = "../performance_evaluation/" class = "md-footer__link md-footer__link--prev" aria-label = "上一页: 2.1 &nbsp; 算法效率评估" >
2023-10-06 13:31:31 +08:00
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / div >
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
上一页
< / span >
< div class = "md-ellipsis" >
2.1 算法效率评估
< / div >
< / div >
< / a >
2023-12-07 20:12:31 +08:00
< a href = "../time_complexity/" class = "md-footer__link md-footer__link--next" aria-label = "下一页: 2.3 &nbsp; 时间复杂度" >
2023-10-06 13:31:31 +08:00
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
下一页
< / span >
< div class = "md-ellipsis" >
2.3 时间复杂度
< / div >
< / div >
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z" / > < / svg >
< / div >
< / a >
< / nav >
2023-08-24 17:47:31 +08:00
< div class = "md-footer-meta md-typeset" >
< div class = "md-footer-meta__inner md-grid" >
< div class = "md-copyright" >
< div class = "md-copyright__highlight" >
2023-09-22 13:08:10 +08:00
Copyright © 2022 - 2023 Krahets
2023-08-24 17:47:31 +08:00
< / div >
< / div >
< div class = "md-social" >
< a href = "https://github.com/krahets" target = "_blank" rel = "noopener" title = "github.com" class = "md-social__link" >
2023-12-07 20:12:31 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg >
2023-08-24 17:47:31 +08:00
< / a >
< a href = "https://twitter.com/krahets" target = "_blank" rel = "noopener" title = "twitter.com" class = "md-social__link" >
2023-12-07 20:12:31 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 512 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z" / > < / svg >
2023-08-24 17:47:31 +08:00
< / a >
< a href = "https://leetcode.cn/u/jyd/" target = "_blank" rel = "noopener" title = "leetcode.cn" class = "md-social__link" >
2023-12-07 20:12:31 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 640 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3l89.3 89.4-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z" / > < / svg >
2023-08-24 17:47:31 +08:00
< / a >
< / div >
< / div >
< / div >
< / footer >
< / div >
< div class = "md-dialog" data-md-component = "dialog" >
< div class = "md-dialog__inner md-typeset" > < / div >
< / div >
2023-12-07 20:12:31 +08:00
2023-12-07 23:44:02 +08:00
< script id = "__config" type = "application/json" > { "base" : "../.." , "features" : [ "content.action.edit" , "content.code.annotate" , "content.code.copy" , "content.tabs.link" , "content.tooltips" , "navigation.indexes" , "navigation.top" , "navigation.footer" , "navigation.tracking" , "search.highlight" , "search.share" , "search.suggest" , "toc.follow" ] , "search" : "../../assets/javascripts/workers/search.f886a092.min.js" , "translations" : { "clipboard.copied" : "\u5df2\u590d\u5236" , "clipboard.copy" : "\u590d\u5236" , "search.result.more.one" : "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.more.other" : "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 # \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.none" : "\u6ca1\u6709\u627e\u5230\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.one" : "\u627e\u5230 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.other" : "# \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c" , "search.result.placeholder" : "\u952e\u5165\u4ee5\u5f00\u59cb\u641c\u7d22" , "search.result.term.missing" : "\u7f3a\u5c11" , "select.version" : "\u9009\u62e9\u5f53\u524d\u7248\u672c" } } < / script >
2023-08-24 17:47:31 +08:00
2023-12-07 20:12:31 +08:00
< script src = "../../assets/javascripts/bundle.d7c377c4.min.js" > < / script >
2023-08-24 17:47:31 +08:00
2023-09-24 17:12:06 +08:00
< script src = "../../javascripts/mathjax.js" > < / script >
2023-08-24 17:47:31 +08:00
2023-09-24 17:12:06 +08:00
< script src = "https://polyfill.io/v3/polyfill.min.js?features=es6" > < / script >
2023-08-24 17:47:31 +08:00
2023-09-24 17:12:06 +08:00
< script src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" > < / script >
2023-08-24 17:47:31 +08:00
2023-09-22 13:08:10 +08:00
< script > document $ . subscribe ( ( ) => { const lightbox = GLightbox ( { "touchNavigation" : true , "loop" : false , "zoomable" : true , "draggable" : false , "openEffect" : "zoom" , "closeEffect" : "zoom" , "slideEffect" : "none" } ) ; } ) < / script > < / body >
2023-08-24 17:47:31 +08:00
< / html >
