2023-04-17 21:00:28 +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" >
2023-06-22 00:23:01 +08:00
< meta name = "description" content = "动画图解、一键运行的数据结构与算法教程" >
2023-04-17 21:00:28 +08:00
< meta name = "author" content = "Krahets" >
< link rel = "canonical" href = "https://www.hello-algo.com/chapter_tree/array_representation_of_tree/" >
< link rel = "prev" href = "../binary_tree_traversal/" >
< link rel = "next" href = "../binary_search_tree/" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< link rel = "icon" href = "../../assets/images/favicon.png" >
2023-07-17 17:51:12 +08:00
< meta name = "generator" content = "mkdocs-1.4.2, mkdocs-material-9.2.0-b0" >
2023-04-17 21:00:28 +08:00
2023-05-21 19:29:51 +08:00
< title > 7.3. < / title >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< link rel = "stylesheet" href = "../../assets/stylesheets/main.0c456da8.min.css" >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< link rel = "stylesheet" href = "../../assets/stylesheets/palette.ecc896b0.min.css" >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +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 >
< / head >
2023-05-31 01:03:26 +08:00
< body dir = "ltr" data-md-color-scheme = "default" data-md-color-primary = "white" data-md-color-accent = "indigo" >
2023-04-17 21:00:28 +08:00
< script > var palette = _ _md _get ( "__palette" ) ; if ( palette && "object" == typeof palette . color ) for ( var key of Object . keys ( palette . color ) ) document . body . setAttribute ( "data-md-color-" + key , palette . color [ key ] ) < / script >
< 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" >
2023-05-21 19:29:51 +08:00
< a href = "#73" class = "md-skip" >
2023-04-17 21:00:28 +08:00
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" >
< img src = "../../assets/images/logo.png" alt = "logo" >
< / a >
< label class = "md-header__button md-icon" for = "__drawer" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< 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" >
2023-05-21 19:29:51 +08:00
7.3. 二叉树数组表示
2023-04-17 21:00:28 +08:00
< / span >
< / div >
< / div >
< / div >
2023-05-31 01:03:26 +08:00
< form class = "md-header__option" data-md-component = "palette" >
2023-04-17 21:00:28 +08:00
2023-05-31 01:03:26 +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_1" >
< label class = "md-header__button md-icon" title = "Switch to dark mode" for = "__palette_2" hidden >
2023-07-19 01:44:47 +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 >
2023-05-31 01:03:26 +08:00
< / label >
2023-04-17 21:00:28 +08:00
2023-05-31 01:03:26 +08:00
2023-06-18 03:47:44 +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_2" >
2023-05-31 01:03:26 +08:00
< label class = "md-header__button md-icon" title = "Switch to light mode" for = "__palette_1" hidden >
2023-07-19 01:44:47 +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 >
2023-05-31 01:03:26 +08:00
< / label >
2023-04-17 21:00:28 +08:00
2023-05-31 01:03:26 +08:00
< / form >
2023-04-17 21:00:28 +08:00
< label class = "md-header__button md-icon" for = "__search" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< 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" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< 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 >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< 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" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< 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" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< 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" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.4.0 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 >
< / 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" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< 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" >
< img src = "../../assets/images/logo.png" alt = "logo" >
< / 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" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.4.0 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 >
< / div >
< div class = "md-source__repository" >
krahets/hello-algo
< / div >
< / a >
< / div >
< ul class = "md-nav__list" data-md-scrollfix >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_1" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< 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" >
0. 前言
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_1" >
< 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 >
0. 前言
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/about_the_book/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
0.1. 关于本书
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/suggestions/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
0.2. 如何使用本书
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
0.3. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_2" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_introduction/" class = "md-nav__link " >
2023-07-19 16:10:17 +08:00
< 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 >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
1. 初识算法
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_2" >
< 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 >
1. 初识算法
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/algorithms_are_everywhere/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
1.1. 算法无处不在
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/what_is_dsa/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
1.2. 算法是什么
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
1.3. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_3" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_computational_complexity/" 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" >
2. 复杂度
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_3" >
< 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 = "false" >
< label class = "md-nav__title" for = "__nav_3" >
< span class = "md-nav__icon md-icon" > < / span >
2. 复杂度
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/performance_evaluation/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2.1. 算法效率评估
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/time_complexity/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2.2. 时间复杂度
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/space_complexity/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2.3. 空间复杂度
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2.4. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-05-17 04:37:57 +08:00
2023-07-17 17:51:12 +08:00
2023-05-17 04:37:57 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_4" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_data_structure/" class = "md-nav__link " >
2023-04-17 21:00:28 +08:00
2023-07-19 16:10:17 +08:00
< 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 >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
3. 数据结构
< / span >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_4" >
< 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 >
3. 数据结构
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-07-17 17:51:12 +08:00
< 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 >
2023-05-17 04:37:57 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-05-17 04:37:57 +08:00
2023-07-17 17:51:12 +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 >
2023-05-17 04:37:57 +08:00
2023-07-17 17:51:12 +08:00
2023-05-17 04:37:57 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/number_encoding/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
3.3. 数字编码 *
< / span >
2023-05-17 04:37:57 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-05-17 04:37:57 +08:00
2023-07-17 17:51:12 +08:00
2023-05-17 04:37:57 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/character_encoding/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
3.4. 字符编码 *
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
3.5. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_array_and_linkedlist/" class = "md-nav__link " >
2023-07-19 16:10:17 +08:00
< 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 >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
4. 数组与链表
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_5" >
< 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 >
4. 数组与链表
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
4.1. 数组
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
4.2. 链表
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
4.3. 列表
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
4.4. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< 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" >
5. 栈与队列
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_6" >
< 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 >
5. 栈与队列
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
5.1. 栈
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
5.2. 队列
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
5.3. 双向队列
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
5.4. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:07:42 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< 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" >
6. 散列表
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_7" >
< 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 >
6. 散列表
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
6.1. 哈希表
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
6.2. 哈希冲突
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-16 21:22:53 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_algorithm/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
6.3. 哈希算法
< / span >
2023-06-16 21:22:53 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-07-17 17:51:12 +08:00
2023-06-16 21:22:53 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
6.4. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--active md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" checked >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< 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 = "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" >
7. 树
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_8" >
< 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 = "true" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
7. 树
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../binary_tree/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
7.1. 二叉树
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../binary_tree_traversal/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
7.2. 二叉树遍历
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +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" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
7.3. 二叉树数组表示
< / span >
2023-04-17 21:00:28 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
7.3. 二叉树数组表示
< / span >
2023-04-17 21:00:28 +08:00
< / 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" >
2023-05-21 19:29:51 +08:00
< a href = "#731" class = "md-nav__link" >
7.3.1. 表示完美二叉树
2023-04-17 21:00:28 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#732" class = "md-nav__link" >
7.3.2. 表示任意二叉树
2023-04-17 21:00:28 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#733" class = "md-nav__link" >
7.3.3. 优势与局限性
2023-04-17 21:00:28 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../binary_search_tree/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
7.4. 二叉搜索树
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../avl_tree/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
7.5. AVL 树 *
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
7.6. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-06-12 23:05:10 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< 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" >
8. 堆
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_9" >
< 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 >
8. 堆
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
8.1. 堆
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
8.2. 建堆操作
< / span >
2023-06-12 23:05:10 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-12 23:05:10 +08:00
2023-07-17 17:51:12 +08:00
2023-06-12 23:05:10 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/top_k/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
8.3. Top-K 问题
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
8.4. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< 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" >
9. 图
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_10" >
< 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 >
9. 图
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
9.1. 图
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
9.2. 图基础操作
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
9.3. 图的遍历
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
9.4. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< 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" >
10. 搜索
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_11" >
< 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 >
10. 搜索
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
10.1. 二分查找
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
10.2. 二分查找边界
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_searching/replace_linear_by_hashing/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
10.3. 哈希优化策略
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
10.4. 重识搜索算法
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
10.5. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-05-21 19:29:51 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-05-24 00:32:47 +08:00
2023-07-17 17:51:12 +08:00
2023-05-26 04:48:01 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-05-21 19:29:51 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
2023-06-02 01:35:09 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
< 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" >
11. 排序
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_12" >
< 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 >
11. 排序
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_sorting/sorting_algorithm/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.1. 排序算法
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-05-24 00:32:47 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.2. 选择排序
< / span >
2023-05-24 00:32:47 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-05-24 00:32:47 +08:00
2023-07-17 17:51:12 +08:00
2023-05-24 00:32:47 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.3. 冒泡排序
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.4. 插入排序
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.5. 快速排序
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.6. 归并排序
< / span >
2023-05-21 19:29:51 +08:00
< / a >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-05-21 19:29:51 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-05-26 04:48:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.7. 堆排序
< / span >
2023-05-26 04:48:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-05-26 04:48:01 +08:00
2023-07-17 17:51:12 +08:00
2023-05-26 04:48:01 +08:00
2023-05-21 19:29:51 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.8. 桶排序
< / span >
2023-05-21 19:29:51 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.9. 计数排序
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.10. 基数排序
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
11.11. 小结
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-24 03:30:35 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
2023-07-17 20:19:46 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 04:21:02 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
2023-07-19 16:10:17 +08:00
< 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 >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
12. 分治
< / span >
2023-07-17 18:38:57 +08:00
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-17 17:51:12 +08:00
< / a >
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_13" >
< 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 >
12. 分治
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/divide_and_conquer/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
12.1. 分治算法
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-16 04:19:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 04:21:02 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/binary_search_recur/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
12.2. 分治搜索策略
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-17 04:21:02 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-17 04:21:02 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 04:21:02 +08:00
2023-07-16 04:19:01 +08:00
< li class = "md-nav__item" >
2023-07-17 02:17:51 +08:00
< a href = "../../chapter_divide_and_conquer/build_binary_tree_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
12.3. 构建树问题
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-16 04:19:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_divide_and_conquer/hanota_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
12.4. 汉诺塔问题
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-17 02:17:51 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-17 02:17:51 +08:00
2023-07-17 20:19:46 +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 >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-07-16 04:19:01 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-07-16 04:19:01 +08:00
2023-07-17 17:51:12 +08:00
2023-05-04 05:22:36 +08:00
2023-07-17 17:51:12 +08:00
2023-06-21 02:55:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-02 01:35:09 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_14" >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< 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" >
13. 回溯
< / span >
< / a >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_14" >
< 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 >
13. 回溯
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/backtracking_algorithm/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
13.1. 回溯算法
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-24 03:30:35 +08:00
2023-07-17 17:51:12 +08:00
2023-04-24 03:30:35 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/permutations_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
13.2. 全排列问题
< / span >
2023-04-24 03:30:35 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-05-04 05:22:36 +08:00
2023-07-17 17:51:12 +08:00
2023-05-04 05:22:36 +08:00
2023-06-21 02:55:52 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/subset_sum_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
13.3. 子集和问题
< / span >
2023-06-21 02:55:52 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-21 02:55:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-21 02:55:52 +08:00
2023-05-04 05:22:36 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/n_queens_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
13.4. N 皇后问题
< / span >
2023-05-04 05:22:36 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_backtracking/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
13.5. 小结
< / span >
2023-06-22 00:23:01 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-06-22 00:23:01 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-07-01 22:39:28 +08:00
2023-07-17 17:51:12 +08:00
2023-07-06 00:08:29 +08:00
2023-07-17 17:51:12 +08:00
2023-07-07 21:39:04 +08:00
2023-07-17 17:51:12 +08:00
2023-07-11 19:21:38 +08:00
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
2023-07-17 17:51:12 +08:00
2023-07-13 05:26:03 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_15" >
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
< 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" >
14. 动态规划
< / span >
2023-07-17 18:38:57 +08:00
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-17 17:51:12 +08:00
< / a >
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
< label class = "md-nav__link " for = "__nav_15" >
< 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 >
14. 动态规划
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/intro_to_dynamic_programming/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
14.1. 初探动态规划
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-01 22:39:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-01 22:39:28 +08:00
2023-07-17 17:51:12 +08:00
2023-07-01 22:39:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/dp_problem_features/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
14.2. DP 问题特性
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-06-30 04:33:52 +08:00
< / a >
2023-07-06 00:08:29 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-07-06 00:08:29 +08:00
2023-07-17 17:51:12 +08:00
2023-07-06 00:08:29 +08:00
2023-07-07 21:39:04 +08:00
< li class = "md-nav__item" >
2023-07-09 03:02:15 +08:00
< a href = "../../chapter_dynamic_programming/dp_solution_pipeline/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
14.3. DP 解题思路
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-07 21:39:04 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-07-07 21:39:04 +08:00
2023-07-17 17:51:12 +08:00
2023-07-07 21:39:04 +08:00
2023-07-06 00:08:29 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/knapsack_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
14.4. 0-1 背包问题
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-06 00:08:29 +08:00
< / a >
2023-07-11 19:21:38 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-07-11 19:21:38 +08:00
2023-07-17 17:51:12 +08:00
2023-07-11 19:21:38 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/unbounded_knapsack_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
14.5. 完全背包问题
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-11 19:21:38 +08:00
< / a >
2023-07-13 05:26:03 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-07-13 05:26:03 +08:00
2023-07-17 17:51:12 +08:00
2023-07-13 05:26:03 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/edit_distance_problem/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
14.6. 编辑距离问题
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-13 05:26:03 +08:00
< / a >
2023-07-14 02:56:32 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
2023-07-17 17:51:12 +08:00
2023-07-14 02:56:32 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/summary/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
14.7. 小结
< / span >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-14 02:56:32 +08:00
< / a >
2023-06-30 04:33:52 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-06-30 04:33:52 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
2023-07-21 21:53:15 +08:00
2023-07-21 22:50:40 +08:00
2023-07-21 15:14:51 +08:00
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-30 04:33:52 +08:00
2023-07-17 17:51:12 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_16" >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< div class = "md-nav__link md-nav__container" >
2023-07-20 18:24:35 +08:00
< a href = "../../chapter_greedy/" class = "md-nav__link " >
2023-07-17 17:51:12 +08:00
2023-07-20 18:24:35 +08:00
< 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 >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-07-20 18:24:35 +08:00
15. 贪心
2023-07-17 17:51:12 +08:00
< / span >
2023-07-20 18:24:35 +08:00
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
2023-07-17 17:51:12 +08:00
< / a >
< label class = "md-nav__link " for = "__nav_16" >
< 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 >
2023-07-20 18:24:35 +08:00
15. 贪心
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< 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 >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
< 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 >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
2023-07-21 15:14:51 +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 >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
2023-07-21 21:53:15 +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 >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
2023-07-21 22:50:40 +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 >
< span class = "md-status md-status--new" title = "最近添加" >
< / span >
< / a >
< / li >
2023-07-20 18:24:35 +08:00
< / ul >
< / nav >
< / li >
< 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" >
16. 附录
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_17" >
< 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 >
16. 附录
2023-07-17 17:51:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/installation/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-07-20 18:24:35 +08:00
16.1. 编程环境安装
2023-07-17 17:51:12 +08:00
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/contribution/" class = "md-nav__link" >
2023-07-17 17:51:12 +08:00
< span class = "md-ellipsis" >
2023-07-20 18:24:35 +08:00
16.2. 一起参与创作
2023-07-17 17:51:12 +08:00
< / span >
2023-04-17 21:00:28 +08:00
< / a >
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / li >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
2023-07-20 18:24:35 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_18" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< 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 >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< / div >
2023-07-20 18:24:35 +08:00
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_18_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_18" >
2023-07-17 17:51:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
参考文献
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< / ul >
< / nav >
2023-04-17 21:00:28 +08:00
< / 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" >
2023-05-21 19:29:51 +08:00
< a href = "#731" class = "md-nav__link" >
7.3.1. 表示完美二叉树
2023-04-17 21:00:28 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#732" class = "md-nav__link" >
7.3.2. 表示任意二叉树
2023-04-17 21:00:28 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#733" class = "md-nav__link" >
7.3.3. 优势与局限性
2023-04-17 21:00:28 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-content" data-md-component = "content" >
< article class = "md-content__inner md-typeset" >
< a href = "https://github.com/krahets/hello-algo/tree/main/docs/chapter_tree/array_representation_of_tree.md" title = "编辑此页" class = "md-content__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z" / > < / svg >
< / a >
2023-05-21 19:29:51 +08:00
< h1 id = "73" > 7.3. 二叉树数组表示< a class = "headerlink" href = "#73" title = "Permanent link" > ¶ < / a > < / h1 >
2023-04-17 21:00:28 +08:00
< p > 在链表表示下，二叉树的存储单元为节点 < code > TreeNode< / code > ，节点之间通过指针相连接。在上节中，我们学习了在链表表示下的二叉树的各项基本操作。< / p >
< p > 那么，能否用「数组」来表示二叉树呢？答案是肯定的。< / p >
2023-05-21 19:29:51 +08:00
< h2 id = "731" > 7.3.1. 表示完美二叉树< a class = "headerlink" href = "#731" title = "Permanent link" > ¶ < / a > < / h2 >
2023-07-24 03:03:58 +08:00
< p > 先分析一个简单案例。给定一个完美二叉树，我们将所有节点按照层序遍历的顺序存储在一个数组中，则每个节点都对应唯一的数组索引。< / p >
2023-04-17 21:00:28 +08:00
< p > 根据层序遍历的特性，我们可以推导出父节点索引与子节点索引之间的“映射公式”：< strong > 若节点的索引为 < span class = "arithmatex" > \(i\)< / span > ，则该节点的左子节点索引为 < span class = "arithmatex" > \(2i + 1\)< / span > ，右子节点索引为 < span class = "arithmatex" > \(2i + 2\)< / span > < / strong > 。< / p >
2023-06-17 00:46:16 +08:00
< p > < img alt = "完美二叉树的数组表示" src = "../array_representation_of_tree.assets/array_representation_binary_tree.png" / > < / p >
2023-04-17 21:00:28 +08:00
< p align = "center" > Fig. 完美二叉树的数组表示 < / p >
2023-07-24 03:03:58 +08:00
< p > < strong > 映射公式的角色相当于链表中的指针< / strong > 。给定数组中的任意一个节点，我们都可以通过映射公式来访问它的左（右）子节点。< / p >
2023-05-21 19:29:51 +08:00
< h2 id = "732" > 7.3.2. 表示任意二叉树< a class = "headerlink" href = "#732" title = "Permanent link" > ¶ < / a > < / h2 >
2023-07-24 03:03:58 +08:00
< p > 然而完美二叉树是一个特例，在二叉树的中间层，通常存在许多 < span class = "arithmatex" > \(\text{None}\)< / span > 。由于层序遍历序列并不包含这些 < span class = "arithmatex" > \(\text{None}\)< / span > ，因此我们无法仅凭该序列来推测 < span class = "arithmatex" > \(\text{None}\)< / span > 的数量和分布位置。< strong > 这意味着存在多种二叉树结构都符合该层序遍历序列< / strong > 。显然在这种情况下，上述的数组表示方法已经失效。< / p >
2023-06-17 00:46:16 +08:00
< p > < img alt = "层序遍历序列对应多种二叉树可能性" src = "../array_representation_of_tree.assets/array_representation_without_empty.png" / > < / p >
2023-04-17 21:00:28 +08:00
< p align = "center" > Fig. 层序遍历序列对应多种二叉树可能性 < / p >
2023-07-24 03:03:58 +08:00
< p > 为了解决此问题，< strong > 我们可以考虑在层序遍历序列中显式地写出所有 < span class = "arithmatex" > \(\text{None}\)< / span > < / strong > 。如下图所示，这样处理后，层序遍历序列就可以唯一表示二叉树了。< / p >
2023-06-02 02:38:32 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:11" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Java< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Python< / label > < label for = "__tabbed_1_4" > Go< / label > < label for = "__tabbed_1_5" > JavaScript< / label > < label for = "__tabbed_1_6" > TypeScript< / label > < label for = "__tabbed_1_7" > C< / label > < label for = "__tabbed_1_8" > C#< / label > < label for = "__tabbed_1_9" > Swift< / label > < label for = "__tabbed_1_10" > Zig< / label > < label for = "__tabbed_1_11" > Dart< / label > < / div >
2023-04-17 21:00:28 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 二叉树的数组表示 */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "c1" > // 使用 int 的包装类 Integer ，就可以使用 null 来标记空位< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > Integer< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 4< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 6< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 9< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 12< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 15< / span > < span class = "w" > < / span > < span class = "p" > };< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 二叉树的数组表示 */< / span >
2023-07-19 16:10:17 +08:00
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "c1" > // 使用 int 最大值 INT_MAX 标记空位< / span >
2023-04-18 20:19:15 +08:00
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 4< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 6< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 9< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 12< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 15< / span > < span class = "p" > };< / span >
2023-04-17 21:00:28 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "c1" > # 二叉树的数组表示< / span >
2023-07-24 03:03:58 +08:00
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "c1" > # 使用 None 来表示空位< / span >
2023-04-17 21:00:28 +08:00
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "n" > tree< / span > < span class = "o" > =< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 3< / span > < span class = "p" > ,< / span > < span class = "mi" > 4< / span > < span class = "p" > ,< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span > < span class = "mi" > 6< / span > < span class = "p" > ,< / span > < span class = "mi" > 7< / span > < span class = "p" > ,< / span > < span class = "mi" > 8< / span > < span class = "p" > ,< / span > < span class = "mi" > 9< / span > < span class = "p" > ,< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span > < span class = "mi" > 12< / span > < span class = "p" > ,< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span > < span class = "mi" > 15< / span > < span class = "p" > ]< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 二叉树的数组表示 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "c1" > // 使用 any 类型的切片, 就可以使用 nil 来标记空位< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "nx" > tree< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > any< / span > < span class = "p" > {< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 4< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 6< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 9< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 12< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 15< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 二叉树的数组表示 */< / span >
2023-07-24 03:03:58 +08:00
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "c1" > // 使用 null 来表示空位< / span >
2023-04-17 21:00:28 +08:00
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > tree< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 3< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 4< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 6< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 9< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 12< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 15< / span > < span class = "p" > ];< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 二叉树的数组表示 */< / span >
2023-07-24 03:03:58 +08:00
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "c1" > // 使用 null 来表示空位< / span >
2023-04-17 21:00:28 +08:00
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > tree< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > number< / span > < span class = "w" > < / span > < span class = "o" > |< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )[]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 3< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 4< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 6< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 9< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 12< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mf" > 15< / span > < span class = "p" > ];< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-18 20:19:15 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* 二叉树的数组表示 */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a > < span class = "c1" > // 使用 int 最大值标记空位，因此要求节点值不能为 INT_MAX< / span >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 4< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 6< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 9< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 12< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 15< / span > < span class = "p" > };< / span >
2023-04-17 21:00:28 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 二叉树的数组表示 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "c1" > // 使用 int? 可空类型 ，就可以使用 null 来标记空位< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "kt" > int?< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 3< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 4< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 6< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 7< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 9< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 12< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 15< / span > < span class = "w" > < / span > < span class = "p" > };< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 二叉树的数组表示 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "c1" > // 使用 Int? 可空类型 ，就可以使用 nil 来标记空位< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "kd" > let< / span > < span class = "nv" > tree< / 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 > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 3< / span > < span class = "p" > ,< / span > < span class = "mi" > 4< / span > < span class = "p" > ,< / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "mi" > 6< / span > < span class = "p" > ,< / span > < span class = "mi" > 7< / span > < span class = "p" > ,< / span > < span class = "mi" > 8< / span > < span class = "p" > ,< / span > < span class = "mi" > 9< / span > < span class = "p" > ,< / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "mi" > 12< / span > < span class = "p" > ,< / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "kc" > nil< / span > < span class = "p" > ,< / span > < span class = "mi" > 15< / span > < span class = "p" > ]< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a >
< / code > < / pre > < / div >
< / div >
2023-06-02 02:38:32 +08:00
< div class = "tabbed-block" >
2023-06-02 15:07:41 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 二叉树的数组表示 */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a > < span class = "c1" > // 使用 int? 可空类型 ，就可以使用 null 来标记空位< / span >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < 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" > tree< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 3< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 4< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 6< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 7< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 8< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 9< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 12< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "m" > 15< / span > < span class = "p" > ];< / span >
2023-06-02 02:38:32 +08:00
< / code > < / pre > < / div >
< / div >
2023-04-17 21:00:28 +08:00
< / div >
< / div >
2023-06-17 00:46:16 +08:00
< p > < img alt = "任意类型二叉树的数组表示" src = "../array_representation_of_tree.assets/array_representation_with_empty.png" / > < / p >
2023-04-17 21:00:28 +08:00
< p align = "center" > Fig. 任意类型二叉树的数组表示 < / p >
2023-07-24 03:03:58 +08:00
< p > 值得说明的是，< strong > 完全二叉树非常适合使用数组来表示< / strong > 。回顾完全二叉树的定义，< span class = "arithmatex" > \(\text{None}\)< / span > 只出现在最底层且靠右的位置，< strong > 因此所有 < span class = "arithmatex" > \(\text{None}\)< / span > 一定出现在层序遍历序列的末尾< / strong > 。这意味着使用数组表示完全二叉树时，可以省略存储所有 < span class = "arithmatex" > \(\text{None}\)< / span > ，非常方便。< / p >
< p > < img alt = "完全二叉树的数组表示" src = "../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" / > < / p >
< p align = "center" > Fig. 完全二叉树的数组表示 < / p >
< p > 如下代码给出了数组表示下的二叉树的简单实现，包括以下操作：< / p >
2023-07-19 16:10:17 +08:00
< ul >
2023-07-24 03:03:58 +08:00
< li > 给定某节点，获取它的值、左（右）子节点、父节点；< / li >
< li > 获取前序遍历、中序遍历、后序遍历、层序遍历序列；< / li >
2023-07-19 16:10:17 +08:00
< / ul >
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:11" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Java< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Python< / label > < label for = "__tabbed_2_4" > Go< / label > < label for = "__tabbed_2_5" > JavaScript< / label > < label for = "__tabbed_2_6" > TypeScript< / label > < label for = "__tabbed_2_7" > C< / label > < label for = "__tabbed_2_8" > C#< / label > < label for = "__tabbed_2_9" > Swift< / label > < label for = "__tabbed_2_10" > Zig< / label > < label for = "__tabbed_2_11" > Dart< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > array_binary_tree.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 数组表示下的二叉树类 */< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "kd" > class< / span > < span class = "nc" > ArrayBinaryTree< / 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 = "kd" > private< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 构造方法 */< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "nf" > ArrayBinaryTree< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > arr< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "n" > tree< / 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" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > (< / span > < span class = "n" > arr< / 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 = "p" > }< / span >
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 节点数量 */< / span >
< a id = "__codelineno-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-11-13" name = "__codelineno-11-13" href = "#__codelineno-11-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / a >
< a id = "__codelineno-11-15" name = "__codelineno-11-15" href = "#__codelineno-11-15" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的值 */< / span >
< a id = "__codelineno-11-16" name = "__codelineno-11-16" href = "#__codelineno-11-16" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > Integer< / span > < span class = "w" > < / span > < span class = "nf" > val< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-17" name = "__codelineno-11-17" href = "#__codelineno-11-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若索引越界，则返回 null ，代表空位< / span >
< a id = "__codelineno-11-18" name = "__codelineno-11-18" href = "#__codelineno-11-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "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 = "n" > size< / span > < span class = "p" > ())< / span >
< a id = "__codelineno-11-19" name = "__codelineno-11-19" href = "#__codelineno-11-19" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-20" name = "__codelineno-11-20" href = "#__codelineno-11-20" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "p" > .< / span > < span class = "na" > get< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-11-21" name = "__codelineno-11-21" href = "#__codelineno-11-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-22" name = "__codelineno-11-22" href = "#__codelineno-11-22" > < / a >
< a id = "__codelineno-11-23" name = "__codelineno-11-23" href = "#__codelineno-11-23" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的左子节点的索引 */< / span >
< a id = "__codelineno-11-24" name = "__codelineno-11-24" href = "#__codelineno-11-24" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > Integer< / span > < span class = "w" > < / span > < span class = "nf" > left< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-25" name = "__codelineno-11-25" href = "#__codelineno-11-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 2< / 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 = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-26" name = "__codelineno-11-26" href = "#__codelineno-11-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-27" name = "__codelineno-11-27" href = "#__codelineno-11-27" > < / a >
< a id = "__codelineno-11-28" name = "__codelineno-11-28" href = "#__codelineno-11-28" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的右子节点的索引 */< / span >
< a id = "__codelineno-11-29" name = "__codelineno-11-29" href = "#__codelineno-11-29" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > Integer< / span > < span class = "w" > < / span > < span class = "nf" > right< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-30" name = "__codelineno-11-30" href = "#__codelineno-11-30" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 2< / 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 = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-31" name = "__codelineno-11-31" href = "#__codelineno-11-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-32" name = "__codelineno-11-32" href = "#__codelineno-11-32" > < / a >
< a id = "__codelineno-11-33" name = "__codelineno-11-33" href = "#__codelineno-11-33" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的父节点的索引 */< / span >
< a id = "__codelineno-11-34" name = "__codelineno-11-34" href = "#__codelineno-11-34" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > Integer< / span > < span class = "w" > < / span > < span class = "nf" > parent< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-35" name = "__codelineno-11-35" href = "#__codelineno-11-35" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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" > 1< / span > < span class = "p" > )< / 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-11-36" name = "__codelineno-11-36" href = "#__codelineno-11-36" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-37" name = "__codelineno-11-37" href = "#__codelineno-11-37" > < / a >
< a id = "__codelineno-11-38" name = "__codelineno-11-38" href = "#__codelineno-11-38" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 层序遍历 */< / span >
< a id = "__codelineno-11-39" name = "__codelineno-11-39" href = "#__codelineno-11-39" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nf" > levelOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-40" name = "__codelineno-11-40" href = "#__codelineno-11-40" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-11-41" name = "__codelineno-11-41" href = "#__codelineno-11-41" > < / a > < span class = "w" > < / span > < span class = "c1" > // 直接遍历数组< / span >
< a id = "__codelineno-11-42" name = "__codelineno-11-42" href = "#__codelineno-11-42" > < / 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" > 0< / 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" > size< / 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-11-43" name = "__codelineno-11-43" href = "#__codelineno-11-43" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-44" name = "__codelineno-11-44" href = "#__codelineno-11-44" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-11-45" name = "__codelineno-11-45" href = "#__codelineno-11-45" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-46" name = "__codelineno-11-46" href = "#__codelineno-11-46" > < / 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-11-47" name = "__codelineno-11-47" href = "#__codelineno-11-47" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-48" name = "__codelineno-11-48" href = "#__codelineno-11-48" > < / a >
< a id = "__codelineno-11-49" name = "__codelineno-11-49" href = "#__codelineno-11-49" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 深度优先遍历 */< / span >
< a id = "__codelineno-11-50" name = "__codelineno-11-50" href = "#__codelineno-11-50" > < / a > < span class = "w" > < / span > < span class = "kd" > private< / span > < span class = "w" > < / span > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > Integer< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / 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-11-51" name = "__codelineno-11-51" href = "#__codelineno-11-51" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若为空位，则返回< / span >
< a id = "__codelineno-11-52" name = "__codelineno-11-52" href = "#__codelineno-11-52" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-53" name = "__codelineno-11-53" href = "#__codelineno-11-53" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-54" name = "__codelineno-11-54" href = "#__codelineno-11-54" > < / a > < span class = "w" > < / span > < span class = "c1" > // 前序遍历< / span >
< a id = "__codelineno-11-55" name = "__codelineno-11-55" href = "#__codelineno-11-55" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > order< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "s" > " pre" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-56" name = "__codelineno-11-56" href = "#__codelineno-11-56" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-11-57" name = "__codelineno-11-57" href = "#__codelineno-11-57" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-11-58" name = "__codelineno-11-58" href = "#__codelineno-11-58" > < / a > < span class = "w" > < / span > < span class = "c1" > // 中序遍历< / span >
< a id = "__codelineno-11-59" name = "__codelineno-11-59" href = "#__codelineno-11-59" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > order< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "s" > " in" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-60" name = "__codelineno-11-60" href = "#__codelineno-11-60" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-11-61" name = "__codelineno-11-61" href = "#__codelineno-11-61" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > right< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-11-62" name = "__codelineno-11-62" href = "#__codelineno-11-62" > < / a > < span class = "w" > < / span > < span class = "c1" > // 后序遍历< / span >
< a id = "__codelineno-11-63" name = "__codelineno-11-63" href = "#__codelineno-11-63" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > order< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "s" > " post" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-64" name = "__codelineno-11-64" href = "#__codelineno-11-64" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-11-65" name = "__codelineno-11-65" href = "#__codelineno-11-65" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-66" name = "__codelineno-11-66" href = "#__codelineno-11-66" > < / a >
< a id = "__codelineno-11-67" name = "__codelineno-11-67" href = "#__codelineno-11-67" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 前序遍历 */< / span >
< a id = "__codelineno-11-68" name = "__codelineno-11-68" href = "#__codelineno-11-68" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-69" name = "__codelineno-11-69" href = "#__codelineno-11-69" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-11-70" name = "__codelineno-11-70" href = "#__codelineno-11-70" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " pre" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-11-71" name = "__codelineno-11-71" href = "#__codelineno-11-71" > < / 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-11-72" name = "__codelineno-11-72" href = "#__codelineno-11-72" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-73" name = "__codelineno-11-73" href = "#__codelineno-11-73" > < / a >
< a id = "__codelineno-11-74" name = "__codelineno-11-74" href = "#__codelineno-11-74" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 中序遍历 */< / span >
< a id = "__codelineno-11-75" name = "__codelineno-11-75" href = "#__codelineno-11-75" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nf" > inOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-76" name = "__codelineno-11-76" href = "#__codelineno-11-76" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-11-77" name = "__codelineno-11-77" href = "#__codelineno-11-77" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " in" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-11-78" name = "__codelineno-11-78" href = "#__codelineno-11-78" > < / 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-11-79" name = "__codelineno-11-79" href = "#__codelineno-11-79" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-80" name = "__codelineno-11-80" href = "#__codelineno-11-80" > < / a >
< a id = "__codelineno-11-81" name = "__codelineno-11-81" href = "#__codelineno-11-81" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 后序遍历 */< / span >
< a id = "__codelineno-11-82" name = "__codelineno-11-82" href = "#__codelineno-11-82" > < / a > < span class = "w" > < / span > < span class = "kd" > public< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nf" > postOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-83" name = "__codelineno-11-83" href = "#__codelineno-11-83" > < / a > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-11-84" name = "__codelineno-11-84" href = "#__codelineno-11-84" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " post" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-11-85" name = "__codelineno-11-85" href = "#__codelineno-11-85" > < / 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-11-86" name = "__codelineno-11-86" href = "#__codelineno-11-86" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-87" name = "__codelineno-11-87" href = "#__codelineno-11-87" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > array_binary_tree.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "cm" > /* 数组表示下的二叉树类 */< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "k" > class< / span > < span class = "w" > < / span > < span class = "nc" > ArrayBinaryTree< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-3" name = "__codelineno-12-3" href = "#__codelineno-12-3" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "o" > :< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 构造方法 */< / span >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < span class = "w" > < / span > < span class = "n" > ArrayBinaryTree< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > arr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-6" name = "__codelineno-12-6" href = "#__codelineno-12-6" > < / a > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > arr< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / a >
< a id = "__codelineno-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 节点数量 */< / span >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-11" name = "__codelineno-12-11" href = "#__codelineno-12-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-12-12" name = "__codelineno-12-12" href = "#__codelineno-12-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-13" name = "__codelineno-12-13" href = "#__codelineno-12-13" > < / a >
< a id = "__codelineno-12-14" name = "__codelineno-12-14" href = "#__codelineno-12-14" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的值 */< / span >
< a id = "__codelineno-12-15" name = "__codelineno-12-15" href = "#__codelineno-12-15" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-16" name = "__codelineno-12-16" href = "#__codelineno-12-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若索引越界，则返回 INT_MAX ，代表空位< / span >
< a id = "__codelineno-12-17" name = "__codelineno-12-17" href = "#__codelineno-12-17" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "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 = "n" > size< / span > < span class = "p" > ())< / span >
< a id = "__codelineno-12-18" name = "__codelineno-12-18" href = "#__codelineno-12-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-19" name = "__codelineno-12-19" href = "#__codelineno-12-19" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-12-20" name = "__codelineno-12-20" href = "#__codelineno-12-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-21" name = "__codelineno-12-21" href = "#__codelineno-12-21" > < / a >
< a id = "__codelineno-12-22" name = "__codelineno-12-22" href = "#__codelineno-12-22" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的左子节点的索引 */< / span >
< a id = "__codelineno-12-23" name = "__codelineno-12-23" href = "#__codelineno-12-23" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-24" name = "__codelineno-12-24" href = "#__codelineno-12-24" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 2< / 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 = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-25" name = "__codelineno-12-25" href = "#__codelineno-12-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-26" name = "__codelineno-12-26" href = "#__codelineno-12-26" > < / a >
< a id = "__codelineno-12-27" name = "__codelineno-12-27" href = "#__codelineno-12-27" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的右子节点的索引 */< / span >
< a id = "__codelineno-12-28" name = "__codelineno-12-28" href = "#__codelineno-12-28" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-29" name = "__codelineno-12-29" href = "#__codelineno-12-29" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 2< / 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 = "mi" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-30" name = "__codelineno-12-30" href = "#__codelineno-12-30" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-31" name = "__codelineno-12-31" href = "#__codelineno-12-31" > < / a >
< a id = "__codelineno-12-32" name = "__codelineno-12-32" href = "#__codelineno-12-32" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的父节点的索引 */< / span >
< a id = "__codelineno-12-33" name = "__codelineno-12-33" href = "#__codelineno-12-33" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-34" name = "__codelineno-12-34" href = "#__codelineno-12-34" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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" > 1< / span > < span class = "p" > )< / 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-12-35" name = "__codelineno-12-35" href = "#__codelineno-12-35" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-36" name = "__codelineno-12-36" href = "#__codelineno-12-36" > < / a >
< a id = "__codelineno-12-37" name = "__codelineno-12-37" href = "#__codelineno-12-37" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 层序遍历 */< / span >
< a id = "__codelineno-12-38" name = "__codelineno-12-38" href = "#__codelineno-12-38" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > levelOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-39" name = "__codelineno-12-39" href = "#__codelineno-12-39" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-40" name = "__codelineno-12-40" href = "#__codelineno-12-40" > < / a > < span class = "w" > < / span > < span class = "c1" > // 直接遍历数组< / span >
< a id = "__codelineno-12-41" name = "__codelineno-12-41" href = "#__codelineno-12-41" > < / 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" > 0< / 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" > size< / 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-12-42" name = "__codelineno-12-42" href = "#__codelineno-12-42" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > )< / span >
< a id = "__codelineno-12-43" name = "__codelineno-12-43" href = "#__codelineno-12-43" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-12-44" name = "__codelineno-12-44" href = "#__codelineno-12-44" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-45" name = "__codelineno-12-45" href = "#__codelineno-12-45" > < / 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-12-46" name = "__codelineno-12-46" href = "#__codelineno-12-46" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-47" name = "__codelineno-12-47" href = "#__codelineno-12-47" > < / a >
< a id = "__codelineno-12-48" name = "__codelineno-12-48" href = "#__codelineno-12-48" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 前序遍历 */< / span >
< a id = "__codelineno-12-49" name = "__codelineno-12-49" href = "#__codelineno-12-49" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-50" name = "__codelineno-12-50" href = "#__codelineno-12-50" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-51" name = "__codelineno-12-51" href = "#__codelineno-12-51" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " pre" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-52" name = "__codelineno-12-52" href = "#__codelineno-12-52" > < / 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-12-53" name = "__codelineno-12-53" href = "#__codelineno-12-53" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-54" name = "__codelineno-12-54" href = "#__codelineno-12-54" > < / a >
< a id = "__codelineno-12-55" name = "__codelineno-12-55" href = "#__codelineno-12-55" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 中序遍历 */< / span >
< a id = "__codelineno-12-56" name = "__codelineno-12-56" href = "#__codelineno-12-56" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > inOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-57" name = "__codelineno-12-57" href = "#__codelineno-12-57" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-58" name = "__codelineno-12-58" href = "#__codelineno-12-58" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " in" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-59" name = "__codelineno-12-59" href = "#__codelineno-12-59" > < / 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-12-60" name = "__codelineno-12-60" href = "#__codelineno-12-60" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-61" name = "__codelineno-12-61" href = "#__codelineno-12-61" > < / a >
< a id = "__codelineno-12-62" name = "__codelineno-12-62" href = "#__codelineno-12-62" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 后序遍历 */< / span >
< a id = "__codelineno-12-63" name = "__codelineno-12-63" href = "#__codelineno-12-63" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > postOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-64" name = "__codelineno-12-64" href = "#__codelineno-12-64" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-65" name = "__codelineno-12-65" href = "#__codelineno-12-65" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " post" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-66" name = "__codelineno-12-66" href = "#__codelineno-12-66" > < / 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-12-67" name = "__codelineno-12-67" href = "#__codelineno-12-67" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-68" name = "__codelineno-12-68" href = "#__codelineno-12-68" > < / a >
< a id = "__codelineno-12-69" name = "__codelineno-12-69" href = "#__codelineno-12-69" > < / a > < span class = "w" > < / span > < span class = "k" > private< / span > < span class = "o" > :< / span >
< a id = "__codelineno-12-70" name = "__codelineno-12-70" href = "#__codelineno-12-70" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-71" name = "__codelineno-12-71" href = "#__codelineno-12-71" > < / a >
< a id = "__codelineno-12-72" name = "__codelineno-12-72" href = "#__codelineno-12-72" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 深度优先遍历 */< / span >
< a id = "__codelineno-12-73" name = "__codelineno-12-73" href = "#__codelineno-12-73" > < / a > < span class = "w" > < / span > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-74" name = "__codelineno-12-74" href = "#__codelineno-12-74" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若为空位，则返回< / span >
< a id = "__codelineno-12-75" name = "__codelineno-12-75" href = "#__codelineno-12-75" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > INT_MAX< / span > < span class = "p" > )< / span >
< a id = "__codelineno-12-76" name = "__codelineno-12-76" href = "#__codelineno-12-76" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-77" name = "__codelineno-12-77" href = "#__codelineno-12-77" > < / a > < span class = "w" > < / span > < span class = "c1" > // 前序遍历< / span >
< a id = "__codelineno-12-78" name = "__codelineno-12-78" href = "#__codelineno-12-78" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > order< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "s" > " pre" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-12-79" name = "__codelineno-12-79" href = "#__codelineno-12-79" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-12-80" name = "__codelineno-12-80" href = "#__codelineno-12-80" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-81" name = "__codelineno-12-81" href = "#__codelineno-12-81" > < / a > < span class = "w" > < / span > < span class = "c1" > // 中序遍历< / span >
< a id = "__codelineno-12-82" name = "__codelineno-12-82" href = "#__codelineno-12-82" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > order< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "s" > " in" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-12-83" name = "__codelineno-12-83" href = "#__codelineno-12-83" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-12-84" name = "__codelineno-12-84" href = "#__codelineno-12-84" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > right< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-85" name = "__codelineno-12-85" href = "#__codelineno-12-85" > < / a > < span class = "w" > < / span > < span class = "c1" > // 后序遍历< / span >
< a id = "__codelineno-12-86" name = "__codelineno-12-86" href = "#__codelineno-12-86" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > order< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "s" > " post" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-12-87" name = "__codelineno-12-87" href = "#__codelineno-12-87" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-12-88" name = "__codelineno-12-88" href = "#__codelineno-12-88" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-12-89" name = "__codelineno-12-89" href = "#__codelineno-12-89" > < / a > < span class = "p" > };< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > array_binary_tree.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "k" > class< / span > < span class = "nc" > ArrayBinaryTree< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 数组表示下的二叉树类" " " < / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "k" > def< / span > < span class = "fm" > __init__< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > arr< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "o" > |< / span > < span class = "kc" > None< / span > < span class = "p" > ]):< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 构造方法" " " < / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __tree< / span > < span class = "o" > =< / span > < span class = "nb" > list< / span > < span class = "p" > (< / span > < span class = "n" > arr< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "k" > def< / span > < span class = "nf" > size< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 节点数量" " " < / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a > < span class = "k" > return< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __tree< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / a > < span class = "k" > def< / span > < span class = "nf" > val< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > i< / 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-13-13" name = "__codelineno-13-13" href = "#__codelineno-13-13" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取索引为 i 节点的值" " " < / span >
< a id = "__codelineno-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / a > < span class = "c1" > # 若索引越界，则返回 None ，代表空位< / span >
< a id = "__codelineno-13-15" name = "__codelineno-13-15" href = "#__codelineno-13-15" > < / a > < span class = "k" > if< / span > < span class = "n" > i< / span > < span class = "o" > < < / span > < span class = "mi" > 0< / span > < span class = "ow" > or< / span > < span class = "n" > i< / span > < span class = "o" > > =< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > size< / span > < span class = "p" > ():< / span >
< a id = "__codelineno-13-16" name = "__codelineno-13-16" href = "#__codelineno-13-16" > < / a > < span class = "k" > return< / span > < span class = "kc" > None< / span >
< a id = "__codelineno-13-17" name = "__codelineno-13-17" href = "#__codelineno-13-17" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __tree< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-13-18" name = "__codelineno-13-18" href = "#__codelineno-13-18" > < / a >
< a id = "__codelineno-13-19" name = "__codelineno-13-19" href = "#__codelineno-13-19" > < / a > < span class = "k" > def< / span > < span class = "nf" > left< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > i< / 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 = "o" > |< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-20" name = "__codelineno-13-20" href = "#__codelineno-13-20" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取索引为 i 节点的左子节点的索引" " " < / span >
< a id = "__codelineno-13-21" name = "__codelineno-13-21" href = "#__codelineno-13-21" > < / a > < span class = "k" > return< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-13-22" name = "__codelineno-13-22" href = "#__codelineno-13-22" > < / a >
< a id = "__codelineno-13-23" name = "__codelineno-13-23" href = "#__codelineno-13-23" > < / a > < span class = "k" > def< / span > < span class = "nf" > right< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > i< / 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 = "o" > |< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-24" name = "__codelineno-13-24" href = "#__codelineno-13-24" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取索引为 i 节点的右子节点的索引" " " < / span >
< a id = "__codelineno-13-25" name = "__codelineno-13-25" href = "#__codelineno-13-25" > < / a > < span class = "k" > return< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-13-26" name = "__codelineno-13-26" href = "#__codelineno-13-26" > < / a >
< a id = "__codelineno-13-27" name = "__codelineno-13-27" href = "#__codelineno-13-27" > < / a > < span class = "k" > def< / span > < span class = "nf" > parent< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > i< / 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 = "o" > |< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-28" name = "__codelineno-13-28" href = "#__codelineno-13-28" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 获取索引为 i 节点的父节点的索引" " " < / span >
< a id = "__codelineno-13-29" name = "__codelineno-13-29" href = "#__codelineno-13-29" > < / a > < span class = "k" > return< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "o" > //< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-13-30" name = "__codelineno-13-30" href = "#__codelineno-13-30" > < / a >
< a id = "__codelineno-13-31" name = "__codelineno-13-31" href = "#__codelineno-13-31" > < / a > < span class = "k" > def< / span > < span class = "nf" > level_order< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-13-32" name = "__codelineno-13-32" href = "#__codelineno-13-32" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 层序遍历" " " < / span >
< a id = "__codelineno-13-33" name = "__codelineno-13-33" href = "#__codelineno-13-33" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-13-34" name = "__codelineno-13-34" href = "#__codelineno-13-34" > < / a > < span class = "c1" > # 直接遍历数组< / span >
< a id = "__codelineno-13-35" name = "__codelineno-13-35" href = "#__codelineno-13-35" > < / 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 = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > size< / span > < span class = "p" > ()):< / span >
< a id = "__codelineno-13-36" name = "__codelineno-13-36" href = "#__codelineno-13-36" > < / a > < span class = "k" > if< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "ow" > is< / span > < span class = "ow" > not< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-37" name = "__codelineno-13-37" href = "#__codelineno-13-37" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-13-38" name = "__codelineno-13-38" href = "#__codelineno-13-38" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span >
< a id = "__codelineno-13-39" name = "__codelineno-13-39" href = "#__codelineno-13-39" > < / a >
< a id = "__codelineno-13-40" name = "__codelineno-13-40" href = "#__codelineno-13-40" > < / a > < span class = "k" > def< / span > < span class = "nf" > __dfs< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span > < span class = "n" > order< / span > < span class = "p" > :< / span > < span class = "nb" > str< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-13-41" name = "__codelineno-13-41" href = "#__codelineno-13-41" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 深度优先遍历" " " < / span >
< a id = "__codelineno-13-42" name = "__codelineno-13-42" href = "#__codelineno-13-42" > < / a > < span class = "k" > if< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-43" name = "__codelineno-13-43" href = "#__codelineno-13-43" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-13-44" name = "__codelineno-13-44" href = "#__codelineno-13-44" > < / a > < span class = "c1" > # 前序遍历< / span >
< a id = "__codelineno-13-45" name = "__codelineno-13-45" href = "#__codelineno-13-45" > < / a > < span class = "k" > if< / span > < span class = "n" > order< / span > < span class = "o" > ==< / span > < span class = "s2" > " pre" < / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-46" name = "__codelineno-13-46" href = "#__codelineno-13-46" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-13-47" name = "__codelineno-13-47" href = "#__codelineno-13-47" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __dfs< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "n" > order< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-48" name = "__codelineno-13-48" href = "#__codelineno-13-48" > < / a > < span class = "c1" > # 中序遍历< / span >
< a id = "__codelineno-13-49" name = "__codelineno-13-49" href = "#__codelineno-13-49" > < / a > < span class = "k" > if< / span > < span class = "n" > order< / span > < span class = "o" > ==< / span > < span class = "s2" > " in" < / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-50" name = "__codelineno-13-50" href = "#__codelineno-13-50" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-13-51" name = "__codelineno-13-51" href = "#__codelineno-13-51" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __dfs< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "n" > order< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-52" name = "__codelineno-13-52" href = "#__codelineno-13-52" > < / a > < span class = "c1" > # 后序遍历< / span >
< a id = "__codelineno-13-53" name = "__codelineno-13-53" href = "#__codelineno-13-53" > < / a > < span class = "k" > if< / span > < span class = "n" > order< / span > < span class = "o" > ==< / span > < span class = "s2" > " post" < / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-54" name = "__codelineno-13-54" href = "#__codelineno-13-54" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-13-55" name = "__codelineno-13-55" href = "#__codelineno-13-55" > < / a >
< a id = "__codelineno-13-56" name = "__codelineno-13-56" href = "#__codelineno-13-56" > < / a > < span class = "k" > def< / span > < span class = "nf" > pre_order< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-13-57" name = "__codelineno-13-57" href = "#__codelineno-13-57" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 前序遍历" " " < / span >
< a id = "__codelineno-13-58" name = "__codelineno-13-58" href = "#__codelineno-13-58" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-13-59" name = "__codelineno-13-59" href = "#__codelineno-13-59" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __dfs< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > order< / span > < span class = "o" > =< / span > < span class = "s2" > " pre" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-60" name = "__codelineno-13-60" href = "#__codelineno-13-60" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span >
< a id = "__codelineno-13-61" name = "__codelineno-13-61" href = "#__codelineno-13-61" > < / a >
< a id = "__codelineno-13-62" name = "__codelineno-13-62" href = "#__codelineno-13-62" > < / a > < span class = "k" > def< / span > < span class = "nf" > in_order< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-13-63" name = "__codelineno-13-63" href = "#__codelineno-13-63" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 中序遍历" " " < / span >
< a id = "__codelineno-13-64" name = "__codelineno-13-64" href = "#__codelineno-13-64" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-13-65" name = "__codelineno-13-65" href = "#__codelineno-13-65" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __dfs< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > order< / span > < span class = "o" > =< / span > < span class = "s2" > " in" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-66" name = "__codelineno-13-66" href = "#__codelineno-13-66" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span >
< a id = "__codelineno-13-67" name = "__codelineno-13-67" href = "#__codelineno-13-67" > < / a >
< a id = "__codelineno-13-68" name = "__codelineno-13-68" href = "#__codelineno-13-68" > < / a > < span class = "k" > def< / span > < span class = "nf" > post_order< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-13-69" name = "__codelineno-13-69" href = "#__codelineno-13-69" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 后序遍历" " " < / span >
< a id = "__codelineno-13-70" name = "__codelineno-13-70" href = "#__codelineno-13-70" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-13-71" name = "__codelineno-13-71" href = "#__codelineno-13-71" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > __dfs< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > order< / span > < span class = "o" > =< / span > < span class = "s2" > " post" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-72" name = "__codelineno-13-72" href = "#__codelineno-13-72" > < / a > < span class = "k" > return< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > res< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > array_binary_tree.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "p" > [< / span > < span class = "nx" > class< / span > < span class = "p" > ]{< / span > < span class = "nx" > arrayBinaryTree< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{}< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > array_binary_tree.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{< / span > < span class = "nx" > ArrayBinaryTree< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{}< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > array_binary_tree.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{< / span > < span class = "nx" > ArrayBinaryTree< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{}< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > array_binary_tree.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > arrayBinaryTree< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{}< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-21 15:14:51 +08:00
< div class = "highlight" > < span class = "filename" > array_binary_tree.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* 数组表示下的二叉树类 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "k" > class< / span > < span class = "w" > < / span > < span class = "nc" > ArrayBinaryTree< / 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 = "k" > private< / span > < 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" > tree< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 构造方法 */< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "nf" > ArrayBinaryTree< / span > < span class = "p" > (< / 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" > arr< / 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 = "n" > tree< / 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" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int?< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > arr< / 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 = "p" > }< / span >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 节点数量 */< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a >
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的值 */< / span >
< a id = "__codelineno-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int?< / span > < span class = "w" > < / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-17" name = "__codelineno-18-17" href = "#__codelineno-18-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若索引越界，则返回 null ，代表空位< / span >
< a id = "__codelineno-18-18" name = "__codelineno-18-18" href = "#__codelineno-18-18" > < / a > < span class = "w" > < / span > < span class = "k" > if< / 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 = "m" > 0< / 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 = "n" > size< / span > < span class = "p" > ())< / span >
< a id = "__codelineno-18-19" name = "__codelineno-18-19" href = "#__codelineno-18-19" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-20" name = "__codelineno-18-20" href = "#__codelineno-18-20" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > tree< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-18-21" name = "__codelineno-18-21" href = "#__codelineno-18-21" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-22" name = "__codelineno-18-22" href = "#__codelineno-18-22" > < / a >
< a id = "__codelineno-18-23" name = "__codelineno-18-23" href = "#__codelineno-18-23" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的左子节点的索引 */< / span >
< a id = "__codelineno-18-24" name = "__codelineno-18-24" href = "#__codelineno-18-24" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > left< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-25" name = "__codelineno-18-25" href = "#__codelineno-18-25" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 2< / 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 = "m" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-26" name = "__codelineno-18-26" href = "#__codelineno-18-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-27" name = "__codelineno-18-27" href = "#__codelineno-18-27" > < / a >
< a id = "__codelineno-18-28" name = "__codelineno-18-28" href = "#__codelineno-18-28" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的右子节点的索引 */< / span >
< a id = "__codelineno-18-29" name = "__codelineno-18-29" href = "#__codelineno-18-29" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > right< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-30" name = "__codelineno-18-30" href = "#__codelineno-18-30" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 2< / 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 = "m" > 2< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-31" name = "__codelineno-18-31" href = "#__codelineno-18-31" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-32" name = "__codelineno-18-32" href = "#__codelineno-18-32" > < / a >
< a id = "__codelineno-18-33" name = "__codelineno-18-33" href = "#__codelineno-18-33" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 获取索引为 i 节点的父节点的索引 */< / span >
< a id = "__codelineno-18-34" name = "__codelineno-18-34" href = "#__codelineno-18-34" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > parent< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-35" name = "__codelineno-18-35" href = "#__codelineno-18-35" > < / a > < span class = "w" > < / span > < span class = "k" > return< / 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 = "m" > 1< / span > < span class = "p" > )< / 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-18-36" name = "__codelineno-18-36" href = "#__codelineno-18-36" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-37" name = "__codelineno-18-37" href = "#__codelineno-18-37" > < / a >
< a id = "__codelineno-18-38" name = "__codelineno-18-38" href = "#__codelineno-18-38" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 层序遍历 */< / span >
< a id = "__codelineno-18-39" name = "__codelineno-18-39" href = "#__codelineno-18-39" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < 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" > levelOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-40" name = "__codelineno-18-40" href = "#__codelineno-18-40" > < / 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" > 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" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-41" name = "__codelineno-18-41" href = "#__codelineno-18-41" > < / a > < span class = "w" > < / span > < span class = "c1" > // 直接遍历数组< / span >
< a id = "__codelineno-18-42" name = "__codelineno-18-42" href = "#__codelineno-18-42" > < / 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" > 0< / 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" > size< / 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-18-43" name = "__codelineno-18-43" href = "#__codelineno-18-43" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ).< / span > < span class = "n" > HasValue< / span > < span class = "p" > )< / span >
< a id = "__codelineno-18-44" name = "__codelineno-18-44" href = "#__codelineno-18-44" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ).< / span > < span class = "n" > Value< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-45" name = "__codelineno-18-45" href = "#__codelineno-18-45" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-46" name = "__codelineno-18-46" href = "#__codelineno-18-46" > < / 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-18-47" name = "__codelineno-18-47" href = "#__codelineno-18-47" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-48" name = "__codelineno-18-48" href = "#__codelineno-18-48" > < / a >
< a id = "__codelineno-18-49" name = "__codelineno-18-49" href = "#__codelineno-18-49" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 深度优先遍历 */< / span >
< a id = "__codelineno-18-50" name = "__codelineno-18-50" href = "#__codelineno-18-50" > < / a > < span class = "w" > < / span > < span class = "k" > private< / span > < span class = "w" > < / span > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < 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" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-51" name = "__codelineno-18-51" href = "#__codelineno-18-51" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若为空位，则返回< / span >
< a id = "__codelineno-18-52" name = "__codelineno-18-52" href = "#__codelineno-18-52" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > !< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ).< / span > < span class = "n" > HasValue< / span > < span class = "p" > )< / span >
< a id = "__codelineno-18-53" name = "__codelineno-18-53" href = "#__codelineno-18-53" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-54" name = "__codelineno-18-54" href = "#__codelineno-18-54" > < / a > < span class = "w" > < / span > < span class = "c1" > // 前序遍历< / span >
< a id = "__codelineno-18-55" name = "__codelineno-18-55" href = "#__codelineno-18-55" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > order< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "s" > " pre" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-18-56" name = "__codelineno-18-56" href = "#__codelineno-18-56" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ).< / span > < span class = "n" > Value< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-57" name = "__codelineno-18-57" href = "#__codelineno-18-57" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-58" name = "__codelineno-18-58" href = "#__codelineno-18-58" > < / a > < span class = "w" > < / span > < span class = "c1" > // 中序遍历< / span >
< a id = "__codelineno-18-59" name = "__codelineno-18-59" href = "#__codelineno-18-59" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > order< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "s" > " in" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-18-60" name = "__codelineno-18-60" href = "#__codelineno-18-60" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ).< / span > < span class = "n" > Value< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-61" name = "__codelineno-18-61" href = "#__codelineno-18-61" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > right< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-62" name = "__codelineno-18-62" href = "#__codelineno-18-62" > < / a > < span class = "w" > < / span > < span class = "c1" > // 后序遍历< / span >
< a id = "__codelineno-18-63" name = "__codelineno-18-63" href = "#__codelineno-18-63" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > order< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "s" > " post" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-18-64" name = "__codelineno-18-64" href = "#__codelineno-18-64" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ).< / span > < span class = "n" > Value< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-65" name = "__codelineno-18-65" href = "#__codelineno-18-65" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-66" name = "__codelineno-18-66" href = "#__codelineno-18-66" > < / a >
< a id = "__codelineno-18-67" name = "__codelineno-18-67" href = "#__codelineno-18-67" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 前序遍历 */< / span >
< a id = "__codelineno-18-68" name = "__codelineno-18-68" href = "#__codelineno-18-68" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < 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" > preOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-69" name = "__codelineno-18-69" href = "#__codelineno-18-69" > < / 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" > 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" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-70" name = "__codelineno-18-70" href = "#__codelineno-18-70" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " pre" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-71" name = "__codelineno-18-71" href = "#__codelineno-18-71" > < / 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-18-72" name = "__codelineno-18-72" href = "#__codelineno-18-72" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-73" name = "__codelineno-18-73" href = "#__codelineno-18-73" > < / a >
< a id = "__codelineno-18-74" name = "__codelineno-18-74" href = "#__codelineno-18-74" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 中序遍历 */< / span >
< a id = "__codelineno-18-75" name = "__codelineno-18-75" href = "#__codelineno-18-75" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < 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" > inOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-76" name = "__codelineno-18-76" href = "#__codelineno-18-76" > < / 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" > 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" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-77" name = "__codelineno-18-77" href = "#__codelineno-18-77" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " in" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-78" name = "__codelineno-18-78" href = "#__codelineno-18-78" > < / 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-18-79" name = "__codelineno-18-79" href = "#__codelineno-18-79" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-80" name = "__codelineno-18-80" href = "#__codelineno-18-80" > < / a >
< a id = "__codelineno-18-81" name = "__codelineno-18-81" href = "#__codelineno-18-81" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 后序遍历 */< / span >
< a id = "__codelineno-18-82" name = "__codelineno-18-82" href = "#__codelineno-18-82" > < / a > < span class = "w" > < / span > < span class = "k" > public< / span > < 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" > postOrder< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-83" name = "__codelineno-18-83" href = "#__codelineno-18-83" > < / 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" > 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" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-84" name = "__codelineno-18-84" href = "#__codelineno-18-84" > < / a > < span class = "w" > < / span > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " post" < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-85" name = "__codelineno-18-85" href = "#__codelineno-18-85" > < / 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-18-86" name = "__codelineno-18-86" href = "#__codelineno-18-86" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-87" name = "__codelineno-18-87" href = "#__codelineno-18-87" > < / a > < span class = "p" > }< / span >
2023-07-19 16:10:17 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-07-24 13:09:54 +08:00
< div class = "highlight" > < span class = "filename" > array_binary_tree.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "cm" > /* 数组表示下的二叉树类 */< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / a > < span class = "kd" > class< / span > < span class = "nc" > ArrayBinaryTree< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "kd" > private< / span > < span class = "kd" > var< / span > < span class = "nv" > tree< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ?]< / span >
< a id = "__codelineno-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / a > < span class = "cm" > /* 构造方法 */< / span >
< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "kd" > init< / span > < span class = "p" > (< / span > < span class = "n" > arr< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ?])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / a > < span class = "n" > tree< / span > < span class = "p" > =< / span > < span class = "n" > arr< / span >
< a id = "__codelineno-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "cm" > /* 节点数量 */< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / a > < span class = "kd" > func< / span > < span class = "nf" > size< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "nb" > Int< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / a > < span class = "n" > tree< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-19-13" name = "__codelineno-19-13" href = "#__codelineno-19-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-14" name = "__codelineno-19-14" href = "#__codelineno-19-14" > < / a >
< a id = "__codelineno-19-15" name = "__codelineno-19-15" href = "#__codelineno-19-15" > < / a > < span class = "cm" > /* 获取索引为 i 节点的值 */< / span >
< a id = "__codelineno-19-16" name = "__codelineno-19-16" href = "#__codelineno-19-16" > < / a > < span class = "kd" > func< / span > < span class = "nf" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / 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 > < span class = "p" > {< / span >
< a id = "__codelineno-19-17" name = "__codelineno-19-17" href = "#__codelineno-19-17" > < / a > < span class = "c1" > // 若索引越界，则返回 null ，代表空位< / span >
< a id = "__codelineno-19-18" name = "__codelineno-19-18" href = "#__codelineno-19-18" > < / a > < span class = "k" > if< / span > < span class = "n" > i< / span > < span class = "o" > < < / span > < span class = "mi" > 0< / span > < span class = "o" > ||< / span > < span class = "n" > i< / span > < span class = "o" > > =< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-19" name = "__codelineno-19-19" href = "#__codelineno-19-19" > < / a > < span class = "k" > return< / span > < span class = "kc" > nil< / span >
< a id = "__codelineno-19-20" name = "__codelineno-19-20" href = "#__codelineno-19-20" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-21" name = "__codelineno-19-21" href = "#__codelineno-19-21" > < / a > < span class = "k" > return< / span > < span class = "n" > tree< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-19-22" name = "__codelineno-19-22" href = "#__codelineno-19-22" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-23" name = "__codelineno-19-23" href = "#__codelineno-19-23" > < / a >
< a id = "__codelineno-19-24" name = "__codelineno-19-24" href = "#__codelineno-19-24" > < / a > < span class = "cm" > /* 获取索引为 i 节点的左子节点的索引 */< / span >
< a id = "__codelineno-19-25" name = "__codelineno-19-25" href = "#__codelineno-19-25" > < / a > < span class = "kd" > func< / span > < span class = "nf" > left< / span > < span class = "p" > (< / span > < span class = "n" > i< / 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-19-26" name = "__codelineno-19-26" href = "#__codelineno-19-26" > < / a > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-19-27" name = "__codelineno-19-27" href = "#__codelineno-19-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-28" name = "__codelineno-19-28" href = "#__codelineno-19-28" > < / a >
< a id = "__codelineno-19-29" name = "__codelineno-19-29" href = "#__codelineno-19-29" > < / a > < span class = "cm" > /* 获取索引为 i 节点的右子节点的索引 */< / span >
< a id = "__codelineno-19-30" name = "__codelineno-19-30" href = "#__codelineno-19-30" > < / a > < span class = "kd" > func< / span > < span class = "nf" > right< / span > < span class = "p" > (< / span > < span class = "n" > i< / 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-19-31" name = "__codelineno-19-31" href = "#__codelineno-19-31" > < / a > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > i< / span > < span class = "o" > +< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-19-32" name = "__codelineno-19-32" href = "#__codelineno-19-32" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-33" name = "__codelineno-19-33" href = "#__codelineno-19-33" > < / a >
< a id = "__codelineno-19-34" name = "__codelineno-19-34" href = "#__codelineno-19-34" > < / a > < span class = "cm" > /* 获取索引为 i 节点的父节点的索引 */< / span >
< a id = "__codelineno-19-35" name = "__codelineno-19-35" href = "#__codelineno-19-35" > < / a > < span class = "kd" > func< / span > < span class = "nf" > parent< / span > < span class = "p" > (< / span > < span class = "n" > i< / 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-19-36" name = "__codelineno-19-36" href = "#__codelineno-19-36" > < / a > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-19-37" name = "__codelineno-19-37" href = "#__codelineno-19-37" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-38" name = "__codelineno-19-38" href = "#__codelineno-19-38" > < / a >
< a id = "__codelineno-19-39" name = "__codelineno-19-39" href = "#__codelineno-19-39" > < / a > < span class = "cm" > /* 层序遍历 */< / span >
< a id = "__codelineno-19-40" name = "__codelineno-19-40" href = "#__codelineno-19-40" > < / a > < span class = "kd" > func< / span > < span class = "nf" > levelOrder< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-41" name = "__codelineno-19-41" href = "#__codelineno-19-41" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / 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-19-42" name = "__codelineno-19-42" href = "#__codelineno-19-42" > < / a > < span class = "c1" > // 直接遍历数组< / span >
< a id = "__codelineno-19-43" name = "__codelineno-19-43" href = "#__codelineno-19-43" > < / 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 = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > to< / span > < span class = "p" > :< / span > < span class = "n" > size< / span > < span class = "p" > (),< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-44" name = "__codelineno-19-44" href = "#__codelineno-19-44" > < / a > < span class = "k" > if< / span > < span class = "kd" > let< / span > < span class = "nv" > val< / span > < span class = "p" > =< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-45" name = "__codelineno-19-45" href = "#__codelineno-19-45" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-46" name = "__codelineno-19-46" href = "#__codelineno-19-46" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-47" name = "__codelineno-19-47" href = "#__codelineno-19-47" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-48" name = "__codelineno-19-48" href = "#__codelineno-19-48" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-19-49" name = "__codelineno-19-49" href = "#__codelineno-19-49" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-50" name = "__codelineno-19-50" href = "#__codelineno-19-50" > < / a >
< a id = "__codelineno-19-51" name = "__codelineno-19-51" href = "#__codelineno-19-51" > < / a > < span class = "cm" > /* 深度优先遍历 */< / span >
< a id = "__codelineno-19-52" name = "__codelineno-19-52" href = "#__codelineno-19-52" > < / a > < span class = "kd" > private< / span > < span class = "kd" > func< / span > < span class = "nf" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "n" > order< / span > < span class = "p" > :< / span > < span class = "nb" > String< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-53" name = "__codelineno-19-53" href = "#__codelineno-19-53" > < / a > < span class = "c1" > // 若为空位，则返回< / span >
< a id = "__codelineno-19-54" name = "__codelineno-19-54" href = "#__codelineno-19-54" > < / a > < span class = "k" > guard< / span > < span class = "kd" > let< / span > < span class = "nv" > val< / span > < span class = "p" > =< / span > < span class = "n" > val< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-55" name = "__codelineno-19-55" href = "#__codelineno-19-55" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-19-56" name = "__codelineno-19-56" href = "#__codelineno-19-56" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-57" name = "__codelineno-19-57" href = "#__codelineno-19-57" > < / a > < span class = "c1" > // 前序遍历< / span >
< a id = "__codelineno-19-58" name = "__codelineno-19-58" href = "#__codelineno-19-58" > < / a > < span class = "k" > if< / span > < span class = "n" > order< / span > < span class = "p" > ==< / span > < span class = "s" > " pre" < / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-59" name = "__codelineno-19-59" href = "#__codelineno-19-59" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-60" name = "__codelineno-19-60" href = "#__codelineno-19-60" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-61" name = "__codelineno-19-61" href = "#__codelineno-19-61" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "kr" > left< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "n" > order< / span > < span class = "p" > :< / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-62" name = "__codelineno-19-62" href = "#__codelineno-19-62" > < / a > < span class = "c1" > // 中序遍历< / span >
< a id = "__codelineno-19-63" name = "__codelineno-19-63" href = "#__codelineno-19-63" > < / a > < span class = "k" > if< / span > < span class = "n" > order< / span > < span class = "p" > ==< / span > < span class = "s" > " in" < / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-64" name = "__codelineno-19-64" href = "#__codelineno-19-64" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-65" name = "__codelineno-19-65" href = "#__codelineno-19-65" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-66" name = "__codelineno-19-66" href = "#__codelineno-19-66" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "kr" > right< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "n" > i< / span > < span class = "p" > ),< / span > < span class = "n" > order< / span > < span class = "p" > :< / span > < span class = "n" > order< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-67" name = "__codelineno-19-67" href = "#__codelineno-19-67" > < / a > < span class = "c1" > // 后序遍历< / span >
< a id = "__codelineno-19-68" name = "__codelineno-19-68" href = "#__codelineno-19-68" > < / a > < span class = "k" > if< / span > < span class = "n" > order< / span > < span class = "p" > ==< / span > < span class = "s" > " post" < / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-69" name = "__codelineno-19-69" href = "#__codelineno-19-69" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-70" name = "__codelineno-19-70" href = "#__codelineno-19-70" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-71" name = "__codelineno-19-71" href = "#__codelineno-19-71" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-72" name = "__codelineno-19-72" href = "#__codelineno-19-72" > < / a >
< a id = "__codelineno-19-73" name = "__codelineno-19-73" href = "#__codelineno-19-73" > < / a > < span class = "cm" > /* 前序遍历 */< / span >
< a id = "__codelineno-19-74" name = "__codelineno-19-74" href = "#__codelineno-19-74" > < / a > < span class = "kd" > func< / span > < span class = "nf" > preOrder< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-75" name = "__codelineno-19-75" href = "#__codelineno-19-75" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / 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-19-76" name = "__codelineno-19-76" href = "#__codelineno-19-76" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > order< / span > < span class = "p" > :< / span > < span class = "s" > " pre" < / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-77" name = "__codelineno-19-77" href = "#__codelineno-19-77" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-19-78" name = "__codelineno-19-78" href = "#__codelineno-19-78" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-79" name = "__codelineno-19-79" href = "#__codelineno-19-79" > < / a >
< a id = "__codelineno-19-80" name = "__codelineno-19-80" href = "#__codelineno-19-80" > < / a > < span class = "cm" > /* 中序遍历 */< / span >
< a id = "__codelineno-19-81" name = "__codelineno-19-81" href = "#__codelineno-19-81" > < / a > < span class = "kd" > func< / span > < span class = "nf" > inOrder< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-82" name = "__codelineno-19-82" href = "#__codelineno-19-82" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / 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-19-83" name = "__codelineno-19-83" href = "#__codelineno-19-83" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > order< / span > < span class = "p" > :< / span > < span class = "s" > " in" < / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-84" name = "__codelineno-19-84" href = "#__codelineno-19-84" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-19-85" name = "__codelineno-19-85" href = "#__codelineno-19-85" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-86" name = "__codelineno-19-86" href = "#__codelineno-19-86" > < / a >
< a id = "__codelineno-19-87" name = "__codelineno-19-87" href = "#__codelineno-19-87" > < / a > < span class = "cm" > /* 后序遍历 */< / span >
< a id = "__codelineno-19-88" name = "__codelineno-19-88" href = "#__codelineno-19-88" > < / a > < span class = "kd" > func< / span > < span class = "nf" > postOrder< / span > < span class = "p" > ()< / span > < span class = "p" > -> < / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-89" name = "__codelineno-19-89" href = "#__codelineno-19-89" > < / a > < span class = "kd" > var< / span > < span class = "nv" > res< / 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-19-90" name = "__codelineno-19-90" href = "#__codelineno-19-90" > < / a > < span class = "n" > dfs< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > order< / span > < span class = "p" > :< / span > < span class = "s" > " post" < / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-91" name = "__codelineno-19-91" href = "#__codelineno-19-91" > < / a > < span class = "k" > return< / span > < span class = "n" > res< / span >
< a id = "__codelineno-19-92" name = "__codelineno-19-92" href = "#__codelineno-19-92" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-93" name = "__codelineno-19-93" href = "#__codelineno-19-93" > < / a > < span class = "p" > }< / span >
2023-07-19 16:10:17 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > array_binary_tree.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > ArrayBinaryTree< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{}< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > array_binary_tree.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > ArrayBinaryTree< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{}< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-05-21 19:29:51 +08:00
< h2 id = "733" > 7.3.3. 优势与局限性< a class = "headerlink" href = "#733" title = "Permanent link" > ¶ < / a > < / h2 >
2023-07-24 03:03:58 +08:00
< p > 二叉树的数组表示的优点包括：< / p >
2023-04-17 21:00:28 +08:00
< ul >
2023-07-24 03:03:58 +08:00
< li > 数组存储在连续的内存空间中，对缓存友好，访问与遍历速度较快；< / li >
2023-04-17 21:00:28 +08:00
< li > 不需要存储指针，比较节省空间；< / li >
< li > 允许随机访问节点；< / li >
< / ul >
< p > 然而，数组表示也具有一些局限性：< / p >
< ul >
2023-07-24 03:03:58 +08:00
< li > 数组存储需要连续内存空间，因此不适合存储数据量过大的树；< / li >
2023-04-17 21:00:28 +08:00
< li > 增删节点需要通过数组插入与删除操作实现，效率较低；< / li >
2023-07-24 03:03:58 +08:00
< li > 当二叉树中存在大量 < span class = "arithmatex" > \(\text{None}\)< / span > 时，数组中包含的节点数据比重较低，空间利用率较低；< / li >
2023-04-17 21:00:28 +08:00
< / ul >
< h2 id = "__comments" > 评论< / h2 >
<!-- 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"
2023-06-01 18:47:10 +08:00
data-input-position="top"
2023-04-17 21:00:28 +08:00
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") {
var theme = palette.color.scheme === "slate" ? "dark" : "light"
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") {
var theme = palette.color.scheme === "slate" ? "dark" : "light"
/* 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 >
< / div >
< button type = "button" class = "md-top md-icon" data-md-component = "top" hidden >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +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 >
< / main >
< footer class = "md-footer" >
< nav class = "md-footer__inner md-grid" aria-label = "页脚" >
2023-05-21 19:29:51 +08:00
< a href = "../binary_tree_traversal/" class = "md-footer__link md-footer__link--prev" aria-label = "上一页: 7.2. &nbsp; 二叉树遍历" rel = "prev" >
2023-04-17 21:00:28 +08:00
< div class = "md-footer__button md-icon" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< 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" >
2023-05-21 19:29:51 +08:00
7.2. 二叉树遍历
2023-04-17 21:00:28 +08:00
< / div >
< / div >
< / a >
2023-05-21 19:29:51 +08:00
< a href = "../binary_search_tree/" class = "md-footer__link md-footer__link--next" aria-label = "下一页: 7.4. &nbsp; 二叉搜索树" rel = "next" >
2023-04-17 21:00:28 +08:00
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
下一页
< / span >
< div class = "md-ellipsis" >
2023-05-21 19:29:51 +08:00
7.4. 二叉搜索树
2023-04-17 21:00:28 +08:00
< / div >
< / div >
< div class = "md-footer__button md-icon" >
2023-07-17 17:51:12 +08:00
2023-04-17 21:00:28 +08:00
< 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 >
< div class = "md-footer-meta md-typeset" >
< div class = "md-footer-meta__inner md-grid" >
< div class = "md-copyright" >
< div class = "md-copyright__highlight" >
Copyright © 2023 Krahets
< / div >
< / div >
< div class = "md-social" >
< a href = "https://github.com/krahets" target = "_blank" rel = "noopener" title = "github.com" class = "md-social__link" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.4.0 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 >
< / a >
< a href = "https://twitter.com/krahets" target = "_blank" rel = "noopener" title = "twitter.com" class = "md-social__link" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 512 512" > <!-- ! Font Awesome Free 6.4.0 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 >
< / a >
< a href = "https://leetcode.cn/u/jyd/" target = "_blank" rel = "noopener" title = "leetcode.cn" class = "md-social__link" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 640 512" > <!-- ! Font Awesome Free 6.4.0 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 >
< / a >
< / div >
< / div >
< / div >
< / footer >
< / div >
< div class = "md-dialog" data-md-component = "dialog" >
< div class = "md-dialog__inner md-typeset" > < / div >
< / div >
2023-07-17 18:38:57 +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.instant" , "navigation.top" , "navigation.footer" , "navigation.tracking" , "search.highlight" , "search.share" , "search.suggest" , "toc.follow" ] , "search" : "../../assets/javascripts/workers/search.780af0f4.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 >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< script src = "../../assets/javascripts/bundle.f11ae8b1.min.js" > < / script >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< script src = "../../javascripts/mathjax.js" > < / script >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< script src = "https://polyfill.io/v3/polyfill.min.js?features=es6" > < / script >
2023-04-17 21:00:28 +08:00
2023-07-17 17:51:12 +08:00
< script src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" > < / script >
2023-04-17 21:00:28 +08:00
< / body >
< / html >
