2023-04-16 04:55:58 +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" >
2023-04-16 04:55:58 +08:00
< meta name = "author" content = "Krahets" >
< link rel = "canonical" href = "https://www.hello-algo.com/chapter_backtracking/backtracking_algorithm/" >
2023-06-02 01:35:09 +08:00
< link rel = "prev" href = "../" >
2023-04-16 04:55:58 +08:00
2023-04-24 03:30:35 +08:00
< link rel = "next" href = "../permutations_problem/" >
2023-04-16 04:55:58 +08:00
< link rel = "icon" href = "../../assets/images/favicon.png" >
2023-05-31 01:03:26 +08:00
< meta name = "generator" content = "mkdocs-1.4.2, mkdocs-material-9.1.11" >
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< title > 12.1. < / title >
2023-04-16 04:55:58 +08:00
2023-05-31 01:03:26 +08:00
< link rel = "stylesheet" href = "../../assets/stylesheets/main.85bb2934.min.css" >
2023-04-16 04:55:58 +08:00
2023-05-31 01:03:26 +08:00
< link rel = "stylesheet" href = "../../assets/stylesheets/palette.a6bdf11c.min.css" >
2023-04-16 04:55:58 +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" >
2023-04-16 04:55:58 +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 = "#121" class = "md-skip" >
2023-04-16 04:55:58 +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" >
< 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" >
2023-06-02 01:35:09 +08:00
12.1. 回溯算法
2023-04-16 04:55:58 +08:00
< / span >
< / div >
< / div >
< / div >
2023-05-31 01:03:26 +08:00
< form class = "md-header__option" data-md-component = "palette" >
2023-04-16 04:55:58 +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 >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 7a5 5 0 0 1 5 5 5 5 0 0 1-5 5 5 5 0 0 1-5-5 5 5 0 0 1 5-5m0 2a3 3 0 0 0-3 3 3 3 0 0 0 3 3 3 3 0 0 0 3-3 3 3 0 0 0-3-3m0-7 2.39 3.42C13.65 5.15 12.84 5 12 5c-.84 0-1.65.15-2.39.42L12 2M3.34 7l4.16-.35A7.2 7.2 0 0 0 5.94 8.5c-.44.74-.69 1.5-.83 2.29L3.34 7m.02 10 1.76-3.77a7.131 7.131 0 0 0 2.38 4.14L3.36 17M20.65 7l-1.77 3.79a7.023 7.023 0 0 0-2.38-4.15l4.15.36m-.01 10-4.14.36c.59-.51 1.12-1.14 1.54-1.86.42-.73.69-1.5.83-2.29L20.64 17M12 22l-2.41-3.44c.74.27 1.55.44 2.41.44.82 0 1.63-.17 2.37-.44L12 22Z" / > < / svg >
< / label >
2023-04-16 04:55:58 +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 >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m17.75 4.09-2.53 1.94.91 3.06-2.63-1.81-2.63 1.81.91-3.06-2.53-1.94L12.44 4l1.06-3 1.06 3 3.19.09m3.5 6.91-1.64 1.25.59 1.98-1.7-1.17-1.7 1.17.59-1.98L15.75 11l2.06-.05L18.5 9l.69 1.95 2.06.05m-2.28 4.95c.83-.08 1.72 1.1 1.19 1.85-.32.45-.66.87-1.08 1.27C15.17 23 8.84 23 4.94 19.07c-3.91-3.9-3.91-10.24 0-14.14.4-.4.82-.76 1.27-1.08.75-.53 1.93.36 1.85 1.19-.27 2.86.69 5.83 2.89 8.02a9.96 9.96 0 0 0 8.02 2.89m-1.64 2.02a12.08 12.08 0 0 1-7.8-3.47c-2.17-2.19-3.33-5-3.49-7.82-2.81 3.14-2.7 7.96.31 10.98 3.02 3.01 7.84 3.12 10.98.31Z" / > < / svg >
< / label >
2023-04-16 04:55:58 +08:00
2023-05-31 01:03:26 +08:00
< / form >
2023-04-16 04:55:58 +08:00
< label class = "md-header__button md-icon" for = "__search" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z" / > < / svg >
< / label >
< div class = "md-search" data-md-component = "search" role = "dialog" >
< label class = "md-search__overlay" for = "__search" > < / label >
< div class = "md-search__inner" role = "search" >
< form class = "md-search__form" name = "search" >
< input type = "text" class = "md-search__input" name = "query" aria-label = "搜索" placeholder = "搜索" autocapitalize = "off" autocorrect = "off" autocomplete = "off" spellcheck = "false" data-md-component = "search-query" required >
< label class = "md-search__icon md-icon" for = "__search" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z" / > < / svg >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / label >
< nav class = "md-search__options" aria-label = "查找" >
< a href = "javascript:void(0)" class = "md-search__icon md-icon" title = "分享" aria-label = "分享" data-clipboard data-clipboard-text = "" data-md-component = "search-share" tabindex = "-1" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z" / > < / svg >
< / a >
< button type = "reset" class = "md-search__icon md-icon" title = "清空当前内容" aria-label = "清空当前内容" tabindex = "-1" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41Z" / > < / svg >
< / button >
< / nav >
< div class = "md-search__suggest" data-md-component = "search-suggest" > < / div >
< / form >
< div class = "md-search__output" >
< div class = "md-search__scrollwrap" data-md-scrollfix >
< div class = "md-search-result" data-md-component = "search-result" >
< div class = "md-search-result__meta" >
正在初始化搜索引擎
< / div >
< ol class = "md-search-result__list" role = "presentation" > < / ol >
< / div >
< / div >
< / div >
< / div >
< / div >
< div class = "md-header__source" >
< a href = "https://github.com/krahets/hello-algo" title = "前往仓库" class = "md-source" data-md-component = "source" >
< div class = "md-source__icon md-icon" >
2023-04-16 16:40:06 +08:00
< 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 >
2023-04-16 04:55:58 +08:00
< / div >
< div class = "md-source__repository" >
krahets/hello-algo
< / div >
< / a >
< / div >
< / nav >
< / header >
< div class = "md-container" data-md-component = "container" >
< main class = "md-main" data-md-component = "main" >
< div class = "md-main__inner md-grid" >
< div class = "md-sidebar md-sidebar--primary" data-md-component = "sidebar" data-md-type = "navigation" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--primary" aria-label = "导航栏" data-md-level = "0" >
< label class = "md-nav__title" for = "__drawer" >
< a href = "../.." title = "Hello 算法" class = "md-nav__button md-logo" aria-label = "Hello 算法" data-md-component = "logo" >
< 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" >
2023-04-16 16:40:06 +08:00
< 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 >
2023-04-16 04:55:58 +08:00
< / div >
< div class = "md-source__repository" >
krahets/hello-algo
< / div >
< / a >
< / div >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_1" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
2023-07-01 03:04:10 +08:00
< a href = "../../chapter_preface/" > 0. 前言< / a >
2023-06-02 01:35:09 +08:00
< label for = "__nav_1" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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 >
2023-07-01 03:04:10 +08:00
0. 前言
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_preface/about_the_book/" class = "md-nav__link" >
0.1. 关于本书
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_preface/suggestions/" class = "md-nav__link" >
0.2. 如何使用本书
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_preface/summary/" class = "md-nav__link" >
0.3. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_2" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
2023-07-01 03:04:10 +08:00
< a href = "../../chapter_introduction/" > 1. 初识算法< / a >
2023-06-02 01:35:09 +08:00
< label for = "__nav_2" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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 >
2023-07-01 03:04:10 +08:00
1. 初识算法
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/algorithms_are_everywhere/" class = "md-nav__link" >
1.1. 算法无处不在
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/what_is_dsa/" class = "md-nav__link" >
1.2. 算法是什么
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_introduction/summary/" class = "md-nav__link" >
1.3. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_3" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
2023-06-30 05:09:58 +08:00
< a href = "../../chapter_computational_complexity/" > 2. 复杂度< / a >
2023-06-02 01:35:09 +08:00
< label for = "__nav_3" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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 >
2023-06-30 05:09:58 +08:00
2. 复杂度
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/performance_evaluation/" class = "md-nav__link" >
2.1. 算法效率评估
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/time_complexity/" class = "md-nav__link" >
2.2. 时间复杂度
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/space_complexity/" class = "md-nav__link" >
2.3. 空间复杂度
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_computational_complexity/summary/" class = "md-nav__link" >
2023-04-17 18:24:27 +08:00
2.4. 小结
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_4" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-05-17 04:37:57 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
2023-06-30 05:09:58 +08:00
< a href = "../../chapter_data_structure/" > 3. 数据结构< / a >
2023-06-02 01:35:09 +08:00
< label for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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 >
2023-06-30 05:09:58 +08:00
3. 数据结构
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
2023-05-17 04:37:57 +08:00
< a href = "../../chapter_data_structure/classification_of_data_structure/" class = "md-nav__link" >
3.1. 数据结构分类
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-17 04:37:57 +08:00
< a href = "../../chapter_data_structure/basic_data_types/" class = "md-nav__link" >
3.2. 基本数据类型
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/number_encoding/" class = "md-nav__link" >
3.3. 数字编码 *
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/character_encoding/" class = "md-nav__link" >
3.4. 字符编码 *
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
2023-05-17 04:37:57 +08:00
3.5. 小结
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_array_and_linkedlist/" > 4. 数组与链表< / a >
< label for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
4.1. 数组
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
4.2. 链表
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
4.3. 列表
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
4.4. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_stack_and_queue/" > 5. 栈与队列< / a >
< label for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
5.1. 栈
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
5.2. 队列
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
5.3. 双向队列
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
5.4. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-05-21 19:07:42 +08:00
2023-05-21 19:29:51 +08:00
2023-06-16 21:22:53 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_hashing/" > 6. 散列表< / a >
< label for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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 >
2023-05-21 19:29:51 +08:00
6. 散列表
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
2023-06-16 21:22:53 +08:00
6.1. 哈希表（ ）
2023-05-21 19:29:51 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
2023-06-14 03:58:26 +08:00
6.2. 哈希冲突（ ）
2023-04-16 04:55:58 +08:00
< / a >
< / li >
2023-05-21 19:07:42 +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" >
6.3. 哈希算法（ ）
< / a >
< / li >
2023-05-21 19:07:42 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
2023-06-16 21:22:53 +08:00
6.4. 小结
2023-05-21 19:07:42 +08:00
< / a >
< / li >
2023-04-16 04:55:58 +08:00
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-05-21 19:29:51 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_tree/" > 7. 树< / a >
< label for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
2023-05-21 19:29:51 +08:00
7. 树
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
7.1. 二叉树
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
7.2. 二叉树遍历
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
7.3. 二叉树数组表示
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
7.4. 二叉搜索树
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
7.5. AVL 树 *
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
7.6. 小结
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-06-12 23:05:10 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_heap/" > 8. 堆< / a >
< label for = "__nav_9" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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 >
2023-05-21 19:29:51 +08:00
8. 堆
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
8.1. 堆
2023-04-17 18:24:27 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
2023-06-12 23:05:10 +08:00
8.2. 建堆操作
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/top_k/" class = "md-nav__link" >
2023-06-12 23:14:10 +08:00
8.3. Top-K 问题（ ）
2023-04-17 18:24:27 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
2023-06-12 23:05:10 +08:00
8.4. 小结
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-05-21 19:29:51 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_graph/" > 9. 图< / a >
< label for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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 >
2023-05-21 19:29:51 +08:00
9. 图
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
9.1. 图
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
9.2. 图基础操作
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
9.3. 图的遍历
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
9.4. 小结
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-05-21 19:29:51 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_searching/" > 10. 搜索< / a >
< label for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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 >
2023-06-02 01:35:09 +08:00
10. 搜索
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +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" >
2023-06-21 02:55:52 +08:00
10.1. 二分查找
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
2023-06-21 02:55:52 +08:00
10.2. 二分查找边界
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< 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" >
10.3. 哈希优化策略
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
10.4. 重识搜索算法
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
10.5. 小结
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-05-24 00:32:47 +08:00
2023-05-26 04:48:01 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_sorting/" > 11. 排序< / a >
< label for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
< 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 >
2023-06-02 01:35:09 +08:00
11. 排序
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/sorting_algorithm/" class = "md-nav__link" >
11.1. 排序算法
< / a >
< / li >
2023-05-24 00:32:47 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/selection_sort/" class = "md-nav__link" >
2023-06-21 02:55:52 +08:00
11.2. 选择排序
2023-05-24 00:32:47 +08:00
< / a >
< / li >
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
2023-05-24 00:32:47 +08:00
11.3. 冒泡排序
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
2023-05-24 00:32:47 +08:00
11.4. 插入排序
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
2023-05-24 00:32:47 +08:00
11.5. 快速排序
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
2023-05-24 00:32:47 +08:00
11.6. 归并排序
2023-04-16 04:55:58 +08:00
< / a >
< / li >
2023-05-26 04:48:01 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/heap_sort/" class = "md-nav__link" >
2023-06-21 02:55:52 +08:00
11.7. 堆排序
2023-05-26 04:48:01 +08:00
< / a >
< / li >
2023-04-16 04:55:58 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bucket_sort/" class = "md-nav__link" >
2023-05-26 04:48:01 +08:00
11.8. 桶排序
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/counting_sort/" class = "md-nav__link" >
2023-05-26 04:48:01 +08:00
11.9. 计数排序
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/radix_sort/" class = "md-nav__link" >
2023-05-26 04:48:01 +08:00
11.10. 基数排序
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
2023-05-26 04:48:01 +08:00
11.11. 小结
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--active md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
2023-05-21 19:29:51 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" checked >
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +08:00
2023-04-24 03:30:35 +08:00
2023-05-04 05:22:36 +08:00
2023-06-21 02:55:52 +08:00
2023-06-22 00:23:01 +08:00
2023-04-16 04:55:58 +08:00
2023-06-02 01:35:09 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../" > 12. 回溯< / a >
< label for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
2023-05-21 19:29:51 +08:00
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_13" >
2023-04-16 04:55:58 +08:00
< span class = "md-nav__icon md-icon" > < / span >
2023-06-02 01:35:09 +08:00
12. 回溯
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
2023-06-02 01:35:09 +08:00
2023-04-16 04:55:58 +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" >
2023-06-02 01:35:09 +08:00
12.1. 回溯算法
2023-04-16 04:55:58 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
2023-06-02 01:35:09 +08:00
12.1. 回溯算法
2023-04-16 04:55:58 +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 = "#1211" class = "md-nav__link" >
12.1.1. 尝试与回退
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#1212" class = "md-nav__link" >
12.1.2. 剪枝
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#1213" class = "md-nav__link" >
12.1.3. 常用术语
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#1214" class = "md-nav__link" >
12.1.4. 框架代码
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#1215" class = "md-nav__link" >
2023-07-11 19:21:38 +08:00
12.1.5. 优势与局限性
2023-04-16 04:55:58 +08:00
< / a >
2023-06-22 00:23:01 +08:00
< / li >
< li class = "md-nav__item" >
< a href = "#1216" class = "md-nav__link" >
2023-07-11 19:21:38 +08:00
12.1.6. 典型例题
2023-06-22 00:23:01 +08:00
< / a >
2023-04-16 04:55:58 +08:00
< / li >
< / ul >
< / nav >
< / li >
2023-04-24 03:30:35 +08:00
< li class = "md-nav__item" >
< a href = "../permutations_problem/" class = "md-nav__link" >
2023-06-02 01:35:09 +08:00
12.2. 全排列问题
2023-04-24 03:30:35 +08:00
< / a >
< / li >
2023-05-04 05:22:36 +08:00
2023-06-21 02:55:52 +08:00
< li class = "md-nav__item" >
< a href = "../subset_sum_problem/" class = "md-nav__link" >
2023-07-14 02:56:32 +08:00
12.3. 子集和问题
2023-06-21 02:55:52 +08:00
< / a >
< / li >
2023-05-04 05:22:36 +08:00
< li class = "md-nav__item" >
< a href = "../n_queens_problem/" class = "md-nav__link" >
2023-06-21 02:55:52 +08:00
12.4. N 皇后问题
2023-05-04 05:22:36 +08:00
< / a >
< / li >
2023-06-22 00:23:01 +08:00
< li class = "md-nav__item" >
< a href = "../summary/" class = "md-nav__link" >
12.5. 小结
< / a >
< / li >
2023-04-16 04:55:58 +08:00
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
2023-05-21 19:29:51 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_14" >
2023-04-16 04:55:58 +08:00
2023-06-30 04:33:52 +08:00
2023-04-16 04:55:58 +08:00
2023-07-01 22:39:28 +08:00
2023-07-06 00:08:29 +08:00
2023-07-07 21:39:04 +08:00
2023-07-11 19:21:38 +08:00
2023-07-13 05:26:03 +08:00
2023-07-14 02:56:32 +08:00
2023-07-13 05:26:03 +08:00
2023-04-16 04:55:58 +08:00
2023-06-30 04:33:52 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_dynamic_programming/" > 13. 动态规划< / a >
< label for = "__nav_14" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2023-04-16 04:55:58 +08:00
2023-05-21 19:29:51 +08:00
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_14_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_14" >
2023-04-16 04:55:58 +08:00
< span class = "md-nav__icon md-icon" > < / span >
2023-06-30 04:33:52 +08:00
13. 动态规划
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/intro_to_dynamic_programming/" class = "md-nav__link" >
2023-07-01 22:39:28 +08:00
13.1. 初探动态规划（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/dp_problem_features/" class = "md-nav__link" >
13.2. DP 问题特性（ ）
2023-06-30 04:33:52 +08:00
< / a >
< / li >
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" >
13.3. DP 解题思路（ ）
2023-07-07 21:39:04 +08:00
< / a >
< / li >
2023-07-06 00:08:29 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/knapsack_problem/" class = "md-nav__link" >
2023-07-07 21:39:04 +08:00
13.4. 0-1 背包问题（ ）
2023-07-06 00:08:29 +08:00
< / a >
< / li >
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" >
13.5. 完全背包问题（ ）
< / a >
< / li >
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" >
13.6. 编辑距离问题（ ）
< / a >
< / li >
2023-07-14 02:56:32 +08:00
< li class = "md-nav__item" >
< a href = "../../chapter_dynamic_programming/summary/" class = "md-nav__link" >
13.7. 小结（ ）
< / a >
< / li >
2023-06-30 04:33:52 +08:00
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-06-30 04:33:52 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_15" >
< label class = "md-nav__link" for = "__nav_15" id = "__nav_15_label" tabindex = "0" >
14. 附录
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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. 附录
2023-04-16 04:55:58 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/installation/" class = "md-nav__link" >
2023-06-30 04:33:52 +08:00
14.1. 编程环境安装
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/contribution/" class = "md-nav__link" >
2023-06-30 04:33:52 +08:00
14.2. 一起参与创作
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-06-30 04:49:34 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2023-04-16 04:55:58 +08:00
2023-06-30 04:33:52 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_16" >
2023-04-16 04:55:58 +08:00
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_reference/" > 参考文献< / a >
< / div >
2023-06-30 04:33:52 +08:00
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_16_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_16" >
2023-04-16 04:55:58 +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 >
< / 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 = "#1211" class = "md-nav__link" >
12.1.1. 尝试与回退
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#1212" class = "md-nav__link" >
12.1.2. 剪枝
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#1213" class = "md-nav__link" >
12.1.3. 常用术语
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#1214" class = "md-nav__link" >
12.1.4. 框架代码
2023-04-16 04:55:58 +08:00
< / a >
< / li >
< li class = "md-nav__item" >
2023-05-21 19:29:51 +08:00
< a href = "#1215" class = "md-nav__link" >
2023-07-11 19:21:38 +08:00
12.1.5. 优势与局限性
2023-04-16 04:55:58 +08:00
< / a >
2023-06-22 00:23:01 +08:00
< / li >
< li class = "md-nav__item" >
< a href = "#1216" class = "md-nav__link" >
2023-07-11 19:21:38 +08:00
12.1.6. 典型例题
2023-06-22 00:23:01 +08:00
< / a >
2023-04-16 04:55:58 +08:00
< / 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_backtracking/backtracking_algorithm.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 = "121" > 12.1. 回溯算法< a class = "headerlink" href = "#121" title = "Permanent link" > ¶ < / a > < / h1 >
2023-04-16 04:55:58 +08:00
< p > 「回溯算法 Backtracking Algorithm」是一种通过穷举来解决问题的方法， ， ， ， < / p >
2023-07-11 19:21:38 +08:00
< p > 回溯算法通常采用「深度优先搜索」来遍历解空间。在二叉树章节中，我们提到前序、中序和后序遍历都属于深度优先搜索。接下来我们先用前序遍历构造一个回溯问题，逐步了解回溯算法的工作原理。< / p >
2023-04-16 04:55:58 +08:00
< div class = "admonition question" >
2023-05-21 19:58:42 +08:00
< p class = "admonition-title" > 例题一< / p >
< p > 给定一个二叉树，搜索并记录所有值为 < span class = "arithmatex" > \(7\)< / span > 的节点，返回节点列表。< / p >
2023-04-16 04:55:58 +08:00
< / div >
< p > < strong > 解题思路< / strong > ：前序遍历这颗树，并判断当前节点的值是否为 < span class = "arithmatex" > \(7\)< / span > ，若是则将该节点的值加入到结果列表 < code > res< / code > 之中。< / 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 >
2023-04-16 04:55:58 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-04-22 01:35:59 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 前序遍历：例题一 */< / span >
2023-04-16 04:55:58 +08:00
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / 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 = "p" > {< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
2023-04-16 05:14:41 +08:00
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / 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" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-22 01:35:59 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 前序遍历：例题一 */< / span >
2023-04-16 16:35:31 +08:00
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > root< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / 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" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-22 01:35:59 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > pre_order< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 前序遍历：例题一" " " < / span >
2023-04-16 04:55:58 +08:00
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "k" > if< / span > < span class = "n" > root< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "k" > if< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "o" > ==< / span > < span class = "mi" > 7< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "c1" > # 记录解< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "n" > pre_order< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "n" > pre_order< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > )< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-16 14:51:45 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 前序遍历：例题一 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > preOrderI< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nb" > int< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrderI< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrderI< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-16 14:51:45 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 前序遍历：例题一 */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / 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 = "p" > {< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-16 14:51:45 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 前序遍历：例题一 */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / 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 = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / 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 = "p" > {< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-22 01:35:59 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > preOrder< / span > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-22 01:35:59 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 前序遍历：例题一 */< / span >
2023-04-23 14:58:11 +08:00
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / 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" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-04 05:22:36 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 前序遍历：例题一 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?)< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "k" > guard< / span > < span class = "kd" > let< / span > < span class = "nv" > root< / span > < span class = "p" > =< / span > < span class = "n" > root< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "k" > if< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > ==< / span > < span class = "mi" > 7< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "kr" > left< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-04-22 01:35:59 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > preOrder< / span > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
2023-06-02 02:38:32 +08:00
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_i_compact.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > preOrder< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
2023-04-16 04:55:58 +08:00
< / div >
< / div >
< p > < img alt = "在前序遍历中搜索节点" src = "../backtracking_algorithm.assets/preorder_find_nodes.png" / > < / p >
< p align = "center" > Fig. 在前序遍历中搜索节点 < / p >
2023-05-21 19:29:51 +08:00
< h2 id = "1211" > 12.1.1. 尝试与回退< a class = "headerlink" href = "#1211" title = "Permanent link" > ¶ < / a > < / h2 >
2023-04-16 04:55:58 +08:00
< p > < strong > 之所以称之为回溯算法，是因为该算法在搜索解空间时会采用“尝试”与“回退”的策略< / strong > 。当算法在搜索过程中遇到某个状态无法继续前进或无法得到满足条件的解时，它会撤销上一步的选择，退回到之前的状态，并尝试其他可能的选择。< / p >
< p > 对于例题一，访问每个节点都代表一次“尝试”，而越过叶结点或返回父节点的 < code > return< / code > 则表示“回退”。< / p >
< p > 值得说明的是，< strong > 回退并不等价于函数返回< / strong > 。为解释这一点，我们对例题一稍作拓展。< / p >
< div class = "admonition question" >
2023-05-21 19:58:42 +08:00
< p class = "admonition-title" > 例题二< / p >
< p > 在二叉树中搜索所有值为 < span class = "arithmatex" > \(7\)< / span > 的节点，< strong > 返回根节点到这些节点的路径< / strong > 。< / p >
2023-04-16 04:55:58 +08:00
< / div >
< p > < strong > 解题思路< / strong > ：在例题一代码的基础上，我们需要借助一个列表 < code > path< / code > 记录访问过的节点路径。当访问到值为 < span class = "arithmatex" > \(7\)< / span > 的节点时，则复制 < code > path< / code > 并添加进结果列表 < code > res< / code > 。遍历完成后，< code > res< / code > 中保存的就是所有的解。< / p >
2023-06-02 02:38:32 +08:00
< 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 >
2023-04-16 04:55:58 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 前序遍历：例题二 */< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > )< / 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 = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / 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 = "p" > {< / span >
2023-04-16 16:35:31 +08:00
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-04-16 16:35:31 +08:00
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > ));< / span >
2023-04-16 16:35:31 +08:00
< a id = "__codelineno-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > left< / 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 = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > );< / span >
2023-04-16 16:35:31 +08:00
< a id = "__codelineno-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-11-15" name = "__codelineno-11-15" href = "#__codelineno-11-15" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "na" > remove< / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
2023-04-16 16:35:31 +08:00
< a id = "__codelineno-11-16" name = "__codelineno-11-16" href = "#__codelineno-11-16" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "cm" > /* 前序遍历：例题二 */< / span >
< a id = "__codelineno-12-2" name = "__codelineno-12-2" href = "#__codelineno-12-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > root< / span > < span class = "p" > )< / 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" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-4" name = "__codelineno-12-4" href = "#__codelineno-12-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-12-5" name = "__codelineno-12-5" href = "#__codelineno-12-5" > < / a > < 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 = "c1" > // 尝试< / span >
< a id = "__codelineno-12-7" name = "__codelineno-12-7" href = "#__codelineno-12-7" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-8" name = "__codelineno-12-8" href = "#__codelineno-12-8" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-12-9" name = "__codelineno-12-9" href = "#__codelineno-12-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-12-10" name = "__codelineno-12-10" href = "#__codelineno-12-10" > < / 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" > path< / 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 = "p" > }< / span >
< a id = "__codelineno-12-12" name = "__codelineno-12-12" href = "#__codelineno-12-12" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-13" name = "__codelineno-12-13" href = "#__codelineno-12-13" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-12-14" name = "__codelineno-12-14" href = "#__codelineno-12-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-12-15" name = "__codelineno-12-15" href = "#__codelineno-12-15" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > pop_back< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-12-16" name = "__codelineno-12-16" href = "#__codelineno-12-16" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > pre_order< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "kc" > None< / 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" > " " " 前序遍历：例题二" " " < / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "k" > if< / span > < span class = "n" > root< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "c1" > # 尝试< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "n" > path< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "k" > if< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "o" > ==< / span > < span class = "mi" > 7< / span > < span class = "p" > :< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "c1" > # 记录解< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "nb" > list< / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a > < span class = "n" > pre_order< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "n" > pre_order< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / a > < span class = "c1" > # 回退< / span >
< a id = "__codelineno-13-13" name = "__codelineno-13-13" href = "#__codelineno-13-13" > < / a > < span class = "n" > path< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-14-1" name = "__codelineno-14-1" href = "#__codelineno-14-1" > < / a > < span class = "cm" > /* 前序遍历：例题二 */< / span >
< a id = "__codelineno-14-2" name = "__codelineno-14-2" href = "#__codelineno-14-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > preOrderII< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-14-4" name = "__codelineno-14-4" href = "#__codelineno-14-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-14-5" name = "__codelineno-14-5" href = "#__codelineno-14-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-14-6" name = "__codelineno-14-6" href = "#__codelineno-14-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-14-7" name = "__codelineno-14-7" href = "#__codelineno-14-7" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-8" name = "__codelineno-14-8" href = "#__codelineno-14-8" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nb" > int< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-14-9" name = "__codelineno-14-9" href = "#__codelineno-14-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-14-10" name = "__codelineno-14-10" href = "#__codelineno-14-10" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "p" > )< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-14-11" name = "__codelineno-14-11" href = "#__codelineno-14-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-14-12" name = "__codelineno-14-12" href = "#__codelineno-14-12" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrderII< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > )< / span >
< a id = "__codelineno-14-13" name = "__codelineno-14-13" href = "#__codelineno-14-13" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrderII< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > )< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-14-14" name = "__codelineno-14-14" href = "#__codelineno-14-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-14-15" name = "__codelineno-14-15" href = "#__codelineno-14-15" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "p" > )[:< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "p" > )< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-14-16" name = "__codelineno-14-16" href = "#__codelineno-14-16" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "cm" > /* 前序遍历：例题二 */< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / 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 = "p" > {< / span >
< a id = "__codelineno-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-8" name = "__codelineno-15-8" href = "#__codelineno-15-8" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-15-9" name = "__codelineno-15-9" href = "#__codelineno-15-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-15-10" name = "__codelineno-15-10" href = "#__codelineno-15-10" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > ([...< / span > < span class = "nx" > path< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-15-12" name = "__codelineno-15-12" href = "#__codelineno-15-12" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-13" name = "__codelineno-15-13" href = "#__codelineno-15-13" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-15-14" name = "__codelineno-15-14" href = "#__codelineno-15-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-15-15" name = "__codelineno-15-15" href = "#__codelineno-15-15" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-15-16" name = "__codelineno-15-16" href = "#__codelineno-15-16" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "cm" > /* 前序遍历：例题二 */< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span >
< a id = "__codelineno-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / 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-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [][]< / span >
< a id = "__codelineno-16-6" name = "__codelineno-16-6" href = "#__codelineno-16-6" > < / a > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-7" name = "__codelineno-16-7" href = "#__codelineno-16-7" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / 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 = "p" > {< / span >
< a id = "__codelineno-16-8" name = "__codelineno-16-8" href = "#__codelineno-16-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-16-9" name = "__codelineno-16-9" href = "#__codelineno-16-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-10" name = "__codelineno-16-10" href = "#__codelineno-16-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-16-11" name = "__codelineno-16-11" href = "#__codelineno-16-11" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-16-12" name = "__codelineno-16-12" href = "#__codelineno-16-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-16-13" name = "__codelineno-16-13" href = "#__codelineno-16-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-16-14" name = "__codelineno-16-14" href = "#__codelineno-16-14" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > ([...< / span > < span class = "nx" > path< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-16-15" name = "__codelineno-16-15" href = "#__codelineno-16-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-16-16" name = "__codelineno-16-16" href = "#__codelineno-16-16" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-16-17" name = "__codelineno-16-17" href = "#__codelineno-16-17" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-16-18" name = "__codelineno-16-18" href = "#__codelineno-16-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-16-19" name = "__codelineno-16-19" href = "#__codelineno-16-19" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-16-20" name = "__codelineno-16-20" href = "#__codelineno-16-20" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.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 = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > preOrder< / span > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "cm" > /* 前序遍历：例题二 */< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > root< / 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 = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < 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 = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > left< / 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 = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > RemoveAt< / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
2023-05-04 05:22:36 +08:00
< a id = "__codelineno-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "cm" > /* 前序遍历：例题二 */< / span >
< a id = "__codelineno-19-2" name = "__codelineno-19-2" href = "#__codelineno-19-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?)< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-3" name = "__codelineno-19-3" href = "#__codelineno-19-3" > < / a > < span class = "k" > guard< / span > < span class = "kd" > let< / span > < span class = "nv" > root< / span > < span class = "p" > =< / span > < span class = "n" > root< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-4" name = "__codelineno-19-4" href = "#__codelineno-19-4" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-19-5" name = "__codelineno-19-5" href = "#__codelineno-19-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-6" name = "__codelineno-19-6" href = "#__codelineno-19-6" > < / a > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-19-7" name = "__codelineno-19-7" href = "#__codelineno-19-7" > < / a > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-8" name = "__codelineno-19-8" href = "#__codelineno-19-8" > < / a > < span class = "k" > if< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > ==< / span > < span class = "mi" > 7< / span > < span class = "p" > {< / span >
< a id = "__codelineno-19-9" name = "__codelineno-19-9" href = "#__codelineno-19-9" > < / a > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-19-10" name = "__codelineno-19-10" href = "#__codelineno-19-10" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-11" name = "__codelineno-19-11" href = "#__codelineno-19-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-19-12" name = "__codelineno-19-12" href = "#__codelineno-19-12" > < / a > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "kr" > left< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-13" name = "__codelineno-19-13" href = "#__codelineno-19-13" > < / a > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-19-14" name = "__codelineno-19-14" href = "#__codelineno-19-14" > < / a > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-19-15" name = "__codelineno-19-15" href = "#__codelineno-19-15" > < / a > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-19-16" name = "__codelineno-19-16" href = "#__codelineno-19-16" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.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 = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > preOrder< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_ii_compact.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 = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > preOrder< / span > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 在每次“尝试”中，我们通过将当前节点添加进 < code > path< / code > 来记录路径；而在“回退”前，我们需要将该节点从 < code > path< / code > 中弹出，< strong > 以恢复本次尝试之前的状态< / strong > 。换句话说，< strong > 我们可以将尝试和回退理解为“前进”与“撤销”< / strong > ，两个操作是互为相反的。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:11" > < input checked = "checked" id = "__tabbed_3_1" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_2" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_3" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_4" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_5" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_6" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_7" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_8" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_9" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_10" name = "__tabbed_3" type = "radio" / > < input id = "__tabbed_3_11" name = "__tabbed_3" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > < 1> < / label > < label for = "__tabbed_3_2" > < 2> < / label > < label for = "__tabbed_3_3" > < 3> < / label > < label for = "__tabbed_3_4" > < 4> < / label > < label for = "__tabbed_3_5" > < 5> < / label > < label for = "__tabbed_3_6" > < 6> < / label > < label for = "__tabbed_3_7" > < 7> < / label > < label for = "__tabbed_3_8" > < 8> < / label > < label for = "__tabbed_3_9" > < 9> < / label > < label for = "__tabbed_3_10" > < 10> < / label > < label for = "__tabbed_3_11" > < 11> < / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-05-10 20:59:40 +08:00
< p > < img alt = "尝试与回退" src = "../backtracking_algorithm.assets/preorder_find_paths_step1.png" / > < / p >
2023-04-16 04:55:58 +08:00
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step2" src = "../backtracking_algorithm.assets/preorder_find_paths_step2.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step3" src = "../backtracking_algorithm.assets/preorder_find_paths_step3.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step4" src = "../backtracking_algorithm.assets/preorder_find_paths_step4.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step5" src = "../backtracking_algorithm.assets/preorder_find_paths_step5.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step6" src = "../backtracking_algorithm.assets/preorder_find_paths_step6.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step7" src = "../backtracking_algorithm.assets/preorder_find_paths_step7.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step8" src = "../backtracking_algorithm.assets/preorder_find_paths_step8.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step9" src = "../backtracking_algorithm.assets/preorder_find_paths_step9.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step10" src = "../backtracking_algorithm.assets/preorder_find_paths_step10.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "preorder_find_paths_step11" src = "../backtracking_algorithm.assets/preorder_find_paths_step11.png" / > < / p >
< / div >
< / div >
< / div >
2023-05-21 19:29:51 +08:00
< h2 id = "1212" > 12.1.2. 剪枝< a class = "headerlink" href = "#1212" title = "Permanent link" > ¶ < / a > < / h2 >
2023-04-16 04:55:58 +08:00
< p > 复杂的回溯问题通常包含一个或多个约束条件，< strong > 约束条件通常可用于“剪枝”< / strong > 。< / p >
< div class = "admonition question" >
2023-05-21 19:58:42 +08:00
< p class = "admonition-title" > 例题三< / p >
< p > 在二叉树中搜索所有值为 < span class = "arithmatex" > \(7\)< / span > 的节点，返回根节点到这些节点的路径，< strong > 路径中不能包含值为 < span class = "arithmatex" > \(3\)< / span > 的节点< / strong > 。< / p >
2023-06-01 18:47:10 +08:00
< / div >
2023-04-16 04:55:58 +08:00
< p > < strong > 解题思路< / strong > ：在例题二的基础上添加剪枝操作，当遇到值为 < span class = "arithmatex" > \(3\)< / span > 的节点时，则终止继续搜索。< / p >
2023-06-02 02:38:32 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "4:11" > < input checked = "checked" id = "__tabbed_4_1" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_2" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_3" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_4" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_5" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_6" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_7" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_8" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_9" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_10" name = "__tabbed_4" type = "radio" / > < input id = "__tabbed_4_11" name = "__tabbed_4" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_4_1" > Java< / label > < label for = "__tabbed_4_2" > C++< / label > < label for = "__tabbed_4_3" > Python< / label > < label for = "__tabbed_4_4" > Go< / label > < label for = "__tabbed_4_5" > JavaScript< / label > < label for = "__tabbed_4_6" > TypeScript< / label > < label for = "__tabbed_4_7" > C< / label > < label for = "__tabbed_4_8" > C#< / label > < label for = "__tabbed_4_9" > Swift< / label > < label for = "__tabbed_4_10" > Zig< / label > < label for = "__tabbed_4_11" > Dart< / label > < / div >
2023-04-16 04:55:58 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "cm" > /* 前序遍历：例题三 */< / span >
< a id = "__codelineno-22-2" name = "__codelineno-22-2" href = "#__codelineno-22-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-3" name = "__codelineno-22-3" href = "#__codelineno-22-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝< / span >
< a id = "__codelineno-22-4" name = "__codelineno-22-4" href = "#__codelineno-22-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-5" name = "__codelineno-22-5" href = "#__codelineno-22-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-22-6" name = "__codelineno-22-6" href = "#__codelineno-22-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-7" name = "__codelineno-22-7" href = "#__codelineno-22-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-22-8" name = "__codelineno-22-8" href = "#__codelineno-22-8" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-9" name = "__codelineno-22-9" href = "#__codelineno-22-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-22-10" name = "__codelineno-22-10" href = "#__codelineno-22-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-22-11" name = "__codelineno-22-11" href = "#__codelineno-22-11" > < / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-22-12" name = "__codelineno-22-12" href = "#__codelineno-22-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-22-13" name = "__codelineno-22-13" href = "#__codelineno-22-13" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-14" name = "__codelineno-22-14" href = "#__codelineno-22-14" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-15" name = "__codelineno-22-15" href = "#__codelineno-22-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-22-16" name = "__codelineno-22-16" href = "#__codelineno-22-16" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "na" > remove< / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-22-17" name = "__codelineno-22-17" href = "#__codelineno-22-17" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / a > < span class = "cm" > /* 前序遍历：例题三 */< / span >
< a id = "__codelineno-23-2" name = "__codelineno-23-2" href = "#__codelineno-23-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > root< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-23-3" name = "__codelineno-23-3" href = "#__codelineno-23-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-23-4" name = "__codelineno-23-4" href = "#__codelineno-23-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-23-5" name = "__codelineno-23-5" href = "#__codelineno-23-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-23-6" name = "__codelineno-23-6" href = "#__codelineno-23-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-23-7" name = "__codelineno-23-7" href = "#__codelineno-23-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-23-8" name = "__codelineno-23-8" href = "#__codelineno-23-8" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-23-9" name = "__codelineno-23-9" href = "#__codelineno-23-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-23-10" name = "__codelineno-23-10" href = "#__codelineno-23-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-23-11" name = "__codelineno-23-11" href = "#__codelineno-23-11" > < / 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" > path< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-23-12" name = "__codelineno-23-12" href = "#__codelineno-23-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-23-13" name = "__codelineno-23-13" href = "#__codelineno-23-13" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-23-14" name = "__codelineno-23-14" href = "#__codelineno-23-14" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-23-15" name = "__codelineno-23-15" href = "#__codelineno-23-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-23-16" name = "__codelineno-23-16" href = "#__codelineno-23-16" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > pop_back< / span > < span class = "p" > ();< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-23-17" name = "__codelineno-23-17" href = "#__codelineno-23-17" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-24-1" name = "__codelineno-24-1" href = "#__codelineno-24-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > pre_order< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-24-2" name = "__codelineno-24-2" href = "#__codelineno-24-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 前序遍历：例题三" " " < / span >
< a id = "__codelineno-24-3" name = "__codelineno-24-3" href = "#__codelineno-24-3" > < / a > < span class = "c1" > # 剪枝< / span >
< a id = "__codelineno-24-4" name = "__codelineno-24-4" href = "#__codelineno-24-4" > < / a > < span class = "k" > if< / span > < span class = "n" > root< / span > < span class = "ow" > is< / span > < span class = "kc" > None< / span > < span class = "ow" > or< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "o" > ==< / span > < span class = "mi" > 3< / span > < span class = "p" > :< / span >
< a id = "__codelineno-24-5" name = "__codelineno-24-5" href = "#__codelineno-24-5" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-24-6" name = "__codelineno-24-6" href = "#__codelineno-24-6" > < / a > < span class = "c1" > # 尝试< / span >
< a id = "__codelineno-24-7" name = "__codelineno-24-7" href = "#__codelineno-24-7" > < / a > < span class = "n" > path< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > )< / span >
< a id = "__codelineno-24-8" name = "__codelineno-24-8" href = "#__codelineno-24-8" > < / a > < span class = "k" > if< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "o" > ==< / span > < span class = "mi" > 7< / span > < span class = "p" > :< / span >
< a id = "__codelineno-24-9" name = "__codelineno-24-9" href = "#__codelineno-24-9" > < / a > < span class = "c1" > # 记录解< / span >
< a id = "__codelineno-24-10" name = "__codelineno-24-10" href = "#__codelineno-24-10" > < / a > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "nb" > list< / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-24-11" name = "__codelineno-24-11" href = "#__codelineno-24-11" > < / a > < span class = "n" > pre_order< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > )< / span >
< a id = "__codelineno-24-12" name = "__codelineno-24-12" href = "#__codelineno-24-12" > < / a > < span class = "n" > pre_order< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-24-13" name = "__codelineno-24-13" href = "#__codelineno-24-13" > < / a > < span class = "c1" > # 回退< / span >
< a id = "__codelineno-24-14" name = "__codelineno-24-14" href = "#__codelineno-24-14" > < / a > < span class = "n" > path< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-25-1" name = "__codelineno-25-1" href = "#__codelineno-25-1" > < / a > < span class = "cm" > /* 前序遍历：例题三 */< / span >
< a id = "__codelineno-25-2" name = "__codelineno-25-2" href = "#__codelineno-25-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > preOrderIII< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-25-3" name = "__codelineno-25-3" href = "#__codelineno-25-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝< / span >
< a id = "__codelineno-25-4" name = "__codelineno-25-4" href = "#__codelineno-25-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-25-5" name = "__codelineno-25-5" href = "#__codelineno-25-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
< a id = "__codelineno-25-6" name = "__codelineno-25-6" href = "#__codelineno-25-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-25-7" name = "__codelineno-25-7" href = "#__codelineno-25-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-25-8" name = "__codelineno-25-8" href = "#__codelineno-25-8" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > )< / span >
< a id = "__codelineno-25-9" name = "__codelineno-25-9" href = "#__codelineno-25-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nb" > int< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-25-10" name = "__codelineno-25-10" href = "#__codelineno-25-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-25-11" name = "__codelineno-25-11" href = "#__codelineno-25-11" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "p" > )< / span >
< a id = "__codelineno-25-12" name = "__codelineno-25-12" href = "#__codelineno-25-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-25-13" name = "__codelineno-25-13" href = "#__codelineno-25-13" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrderIII< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > )< / span >
< a id = "__codelineno-25-14" name = "__codelineno-25-14" href = "#__codelineno-25-14" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrderIII< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > )< / span >
< a id = "__codelineno-25-15" name = "__codelineno-25-15" href = "#__codelineno-25-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-25-16" name = "__codelineno-25-16" href = "#__codelineno-25-16" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "p" > )[:< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > path< / span > < span class = "p" > )< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-25-17" name = "__codelineno-25-17" href = "#__codelineno-25-17" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-26-1" name = "__codelineno-26-1" href = "#__codelineno-26-1" > < / a > < span class = "cm" > /* 前序遍历：例题三 */< / span >
< a id = "__codelineno-26-2" name = "__codelineno-26-2" href = "#__codelineno-26-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-3" name = "__codelineno-26-3" href = "#__codelineno-26-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝< / span >
< a id = "__codelineno-26-4" name = "__codelineno-26-4" href = "#__codelineno-26-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 3< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-5" name = "__codelineno-26-5" href = "#__codelineno-26-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-26-6" name = "__codelineno-26-6" href = "#__codelineno-26-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-26-7" name = "__codelineno-26-7" href = "#__codelineno-26-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-26-8" name = "__codelineno-26-8" href = "#__codelineno-26-8" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-26-9" name = "__codelineno-26-9" href = "#__codelineno-26-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-26-10" name = "__codelineno-26-10" href = "#__codelineno-26-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-26-11" name = "__codelineno-26-11" href = "#__codelineno-26-11" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > ([...< / span > < span class = "nx" > path< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-26-12" name = "__codelineno-26-12" href = "#__codelineno-26-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-26-13" name = "__codelineno-26-13" href = "#__codelineno-26-13" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-26-14" name = "__codelineno-26-14" href = "#__codelineno-26-14" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-26-15" name = "__codelineno-26-15" href = "#__codelineno-26-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-26-16" name = "__codelineno-26-16" href = "#__codelineno-26-16" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-26-17" name = "__codelineno-26-17" href = "#__codelineno-26-17" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-27-1" name = "__codelineno-27-1" href = "#__codelineno-27-1" > < / a > < span class = "cm" > /* 前序遍历：例题三 */< / span >
< a id = "__codelineno-27-2" name = "__codelineno-27-2" href = "#__codelineno-27-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span >
< a id = "__codelineno-27-3" name = "__codelineno-27-3" href = "#__codelineno-27-3" > < / a > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / 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-27-4" name = "__codelineno-27-4" href = "#__codelineno-27-4" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-27-5" name = "__codelineno-27-5" href = "#__codelineno-27-5" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [][]< / span >
< a id = "__codelineno-27-6" name = "__codelineno-27-6" href = "#__codelineno-27-6" > < / a > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-27-7" name = "__codelineno-27-7" href = "#__codelineno-27-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝< / span >
< a id = "__codelineno-27-8" name = "__codelineno-27-8" href = "#__codelineno-27-8" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 3< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-27-9" name = "__codelineno-27-9" href = "#__codelineno-27-9" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-27-10" name = "__codelineno-27-10" href = "#__codelineno-27-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-11" name = "__codelineno-27-11" href = "#__codelineno-27-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-27-12" name = "__codelineno-27-12" href = "#__codelineno-27-12" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-27-13" name = "__codelineno-27-13" href = "#__codelineno-27-13" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-27-14" name = "__codelineno-27-14" href = "#__codelineno-27-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-27-15" name = "__codelineno-27-15" href = "#__codelineno-27-15" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > ([...< / span > < span class = "nx" > path< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-27-16" name = "__codelineno-27-16" href = "#__codelineno-27-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-17" name = "__codelineno-27-17" href = "#__codelineno-27-17" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-27-18" name = "__codelineno-27-18" href = "#__codelineno-27-18" > < / a > < span class = "w" > < / span > < span class = "nx" > preOrder< / span > < span class = "p" > (< / span > < span class = "nx" > root< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-27-19" name = "__codelineno-27-19" href = "#__codelineno-27-19" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-27-20" name = "__codelineno-27-20" href = "#__codelineno-27-20" > < / a > < span class = "w" > < / span > < span class = "nx" > path< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-27-21" name = "__codelineno-27-21" href = "#__codelineno-27-21" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-28-1" name = "__codelineno-28-1" href = "#__codelineno-28-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > preOrder< / span > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-29-1" name = "__codelineno-29-1" href = "#__codelineno-29-1" > < / a > < span class = "cm" > /* 前序遍历：例题三 */< / span >
< a id = "__codelineno-29-2" name = "__codelineno-29-2" href = "#__codelineno-29-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-3" name = "__codelineno-29-3" href = "#__codelineno-29-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝< / span >
< a id = "__codelineno-29-4" name = "__codelineno-29-4" href = "#__codelineno-29-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 3< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-5" name = "__codelineno-29-5" href = "#__codelineno-29-5" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-29-6" name = "__codelineno-29-6" href = "#__codelineno-29-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-29-7" name = "__codelineno-29-7" href = "#__codelineno-29-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-29-8" name = "__codelineno-29-8" href = "#__codelineno-29-8" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > );< / span >
< a id = "__codelineno-29-9" name = "__codelineno-29-9" href = "#__codelineno-29-9" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 7< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-29-10" name = "__codelineno-29-10" href = "#__codelineno-29-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-29-11" name = "__codelineno-29-11" href = "#__codelineno-29-11" > < / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-29-12" name = "__codelineno-29-12" href = "#__codelineno-29-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-29-13" name = "__codelineno-29-13" href = "#__codelineno-29-13" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > );< / span >
< a id = "__codelineno-29-14" name = "__codelineno-29-14" href = "#__codelineno-29-14" > < / a > < span class = "w" > < / span > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-29-15" name = "__codelineno-29-15" href = "#__codelineno-29-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-29-16" name = "__codelineno-29-16" href = "#__codelineno-29-16" > < / a > < span class = "w" > < / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > RemoveAt< / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-29-17" name = "__codelineno-29-17" href = "#__codelineno-29-17" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-30-1" name = "__codelineno-30-1" href = "#__codelineno-30-1" > < / a > < span class = "cm" > /* 前序遍历：例题三 */< / span >
< a id = "__codelineno-30-2" name = "__codelineno-30-2" href = "#__codelineno-30-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?)< / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-3" name = "__codelineno-30-3" href = "#__codelineno-30-3" > < / a > < span class = "c1" > // 剪枝< / span >
< a id = "__codelineno-30-4" name = "__codelineno-30-4" href = "#__codelineno-30-4" > < / a > < span class = "k" > guard< / span > < span class = "kd" > let< / span > < span class = "nv" > root< / span > < span class = "p" > =< / span > < span class = "n" > root< / span > < span class = "p" > ,< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "o" > !=< / span > < span class = "mi" > 3< / span > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-5" name = "__codelineno-30-5" href = "#__codelineno-30-5" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-30-6" name = "__codelineno-30-6" href = "#__codelineno-30-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-30-7" name = "__codelineno-30-7" href = "#__codelineno-30-7" > < / a > < span class = "c1" > // 尝试< / span >
< a id = "__codelineno-30-8" name = "__codelineno-30-8" href = "#__codelineno-30-8" > < / a > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > )< / span >
< a id = "__codelineno-30-9" name = "__codelineno-30-9" href = "#__codelineno-30-9" > < / a > < span class = "k" > if< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "p" > ==< / span > < span class = "mi" > 7< / span > < span class = "p" > {< / span >
< a id = "__codelineno-30-10" name = "__codelineno-30-10" href = "#__codelineno-30-10" > < / a > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-30-11" name = "__codelineno-30-11" href = "#__codelineno-30-11" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > path< / span > < span class = "p" > )< / span >
< a id = "__codelineno-30-12" name = "__codelineno-30-12" href = "#__codelineno-30-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-30-13" name = "__codelineno-30-13" href = "#__codelineno-30-13" > < / a > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "kr" > left< / span > < span class = "p" > )< / span >
< a id = "__codelineno-30-14" name = "__codelineno-30-14" href = "#__codelineno-30-14" > < / a > < span class = "n" > preOrder< / span > < span class = "p" > (< / span > < span class = "n" > root< / span > < span class = "p" > :< / span > < span class = "n" > root< / span > < span class = "p" > .< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-30-15" name = "__codelineno-30-15" href = "#__codelineno-30-15" > < / a > < span class = "c1" > // 回退< / span >
< a id = "__codelineno-30-16" name = "__codelineno-30-16" href = "#__codelineno-30-16" > < / a > < span class = "n" > path< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-30-17" name = "__codelineno-30-17" href = "#__codelineno-30-17" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-31-1" name = "__codelineno-31-1" href = "#__codelineno-31-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > preOrder< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_compact.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-32-1" name = "__codelineno-32-1" href = "#__codelineno-32-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > preOrder< / span > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 剪枝是一个非常形象的名词。在搜索过程中，< strong > 我们利用约束条件“剪掉”了不满足约束条件的搜索分支< / strong > ，避免许多无意义的尝试，从而提升搜索效率。< / p >
< p > < img alt = "根据约束条件剪枝" src = "../backtracking_algorithm.assets/preorder_find_constrained_paths.png" / > < / p >
< p align = "center" > Fig. 根据约束条件剪枝 < / p >
2023-05-21 19:29:51 +08:00
< h2 id = "1213" > 12.1.3. 常用术语< a class = "headerlink" href = "#1213" title = "Permanent link" > ¶ < / a > < / h2 >
2023-04-16 04:55:58 +08:00
< p > 为了更清晰地分析算法问题，我们总结一下回溯算法中常用术语的含义，并对照例题三给出对应示例。< / p >
< table >
< thead >
< tr >
< th > 名词< / th >
< th > 定义< / th >
< th > 例题三< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > 解 Solution< / td >
< td > 解是满足问题特定条件的答案。回溯算法的目标是找到一个或多个满足条件的解< / td >
< td > 根节点到节点 < span class = "arithmatex" > \(7\)< / span > 的所有路径，且路径中不包含值为 < span class = "arithmatex" > \(3\)< / span > 的节点< / td >
< / tr >
< tr >
< td > 状态 State< / td >
< td > 状态表示问题在某一时刻的情况，包括已经做出的选择< / td >
< td > 当前已访问的节点路径，即 < code > path< / code > 节点列表< / td >
< / tr >
< tr >
< td > 约束条件 Constraint< / td >
< td > 约束条件是问题中限制解的可行性的条件，通常用于剪枝< / td >
< td > 要求路径中不能包含值为 < span class = "arithmatex" > \(3\)< / span > 的节点< / td >
< / tr >
< tr >
< td > 尝试 Attempt< / td >
< td > 尝试是在搜索过程中，根据当前状态和可用选择来探索解空间的过程。尝试包括做出选择，更新状态，检查是否为解< / td >
< td > 递归访问左（右）子节点，将节点添加进 < code > path< / code > ，判断节点的值是否为 < span class = "arithmatex" > \(7\)< / span > < / td >
< / tr >
< tr >
< td > 回退 Backtracking< / td >
< td > 回退指在搜索中遇到到不满足约束条件或无法继续搜索的状态时，撤销前面做出的选择，回到上一个状态< / td >
< td > 当越过叶结点、结束结点访问、遇到值为 < span class = "arithmatex" > \(3\)< / span > 的节点时终止搜索，函数返回< / td >
< / tr >
< tr >
< td > 剪枝 Pruning< / td >
< td > 剪枝是根据问题特性和约束条件避免无意义的搜索路径的方法，可提高搜索效率< / td >
< td > 当遇到值为 < span class = "arithmatex" > \(3\)< / span > 的节点时，则终止继续搜索< / td >
< / tr >
< / tbody >
< / table >
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > 解、状态、约束条件等术语是通用的，适用于回溯算法、动态规划、贪心算法等。< / p >
< / div >
2023-05-21 19:29:51 +08:00
< h2 id = "1214" > 12.1.4. 框架代码< a class = "headerlink" href = "#1214" title = "Permanent link" > ¶ < / a > < / h2 >
2023-04-16 04:55:58 +08:00
< p > 回溯算法可用于解决许多搜索问题、约束满足问题和组合优化问题。为提升代码通用性，我们希望将回溯算法的“尝试、回退、剪枝”的主体框架提炼出来。< / p >
< p > 设 < code > state< / code > 为问题的当前状态，< code > choices< / code > 表示当前状态下可以做出的选择，则可得到以下回溯算法的框架代码。< / p >
2023-06-02 02:38:32 +08:00
< div class = "tabbed-set tabbed-alternate" data-tabs = "5:11" > < input checked = "checked" id = "__tabbed_5_1" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_2" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_3" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_4" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_5" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_6" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_7" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_8" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_9" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_10" name = "__tabbed_5" type = "radio" / > < input id = "__tabbed_5_11" name = "__tabbed_5" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_5_1" > Java< / label > < label for = "__tabbed_5_2" > C++< / label > < label for = "__tabbed_5_3" > Python< / label > < label for = "__tabbed_5_4" > Go< / label > < label for = "__tabbed_5_5" > JavaScript< / label > < label for = "__tabbed_5_6" > TypeScript< / label > < label for = "__tabbed_5_7" > C< / label > < label for = "__tabbed_5_8" > C#< / label > < label for = "__tabbed_5_9" > Swift< / label > < label for = "__tabbed_5_10" > Zig< / label > < label for = "__tabbed_5_11" > Dart< / label > < / div >
2023-04-16 04:55:58 +08:00
< div class = "tabbed-content" >
< div class = "tabbed-block" >
2023-05-10 19:38:29 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-33-1" name = "__codelineno-33-1" href = "#__codelineno-33-1" > < / a > < span class = "cm" > /* 回溯算法框架 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-33-2" name = "__codelineno-33-2" href = "#__codelineno-33-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > State< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Choice< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > State< / 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 >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-33-3" name = "__codelineno-33-3" href = "#__codelineno-33-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断是否为解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-33-4" name = "__codelineno-33-4" href = "#__codelineno-33-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-33-5" name = "__codelineno-33-5" href = "#__codelineno-33-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-33-6" name = "__codelineno-33-6" href = "#__codelineno-33-6" > < / a > < span class = "w" > < / span > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-33-7" name = "__codelineno-33-7" href = "#__codelineno-33-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-33-8" name = "__codelineno-33-8" href = "#__codelineno-33-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-9" name = "__codelineno-33-9" href = "#__codelineno-33-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-33-10" name = "__codelineno-33-10" href = "#__codelineno-33-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Choice< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-33-11" name = "__codelineno-33-11" href = "#__codelineno-33-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：判断选择是否合法< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-33-12" name = "__codelineno-33-12" href = "#__codelineno-33-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-33-13" name = "__codelineno-33-13" href = "#__codelineno-33-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-33-14" name = "__codelineno-33-14" href = "#__codelineno-33-14" > < / a > < span class = "w" > < / span > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-33-15" name = "__codelineno-33-15" href = "#__codelineno-33-15" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-33-16" name = "__codelineno-33-16" href = "#__codelineno-33-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-33-17" name = "__codelineno-33-17" href = "#__codelineno-33-17" > < / a > < span class = "w" > < / span > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-33-18" name = "__codelineno-33-18" href = "#__codelineno-33-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-19" name = "__codelineno-33-19" href = "#__codelineno-33-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-20" name = "__codelineno-33-20" href = "#__codelineno-33-20" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-10 19:38:29 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-34-1" name = "__codelineno-34-1" href = "#__codelineno-34-1" > < / a > < span class = "cm" > /* 回溯算法框架 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-34-2" name = "__codelineno-34-2" href = "#__codelineno-34-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > State< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > Choice< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > State< / span > < span class = "w" > < / 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 >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-34-3" name = "__codelineno-34-3" href = "#__codelineno-34-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断是否为解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-34-4" name = "__codelineno-34-4" href = "#__codelineno-34-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-34-5" name = "__codelineno-34-5" href = "#__codelineno-34-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-34-6" name = "__codelineno-34-6" href = "#__codelineno-34-6" > < / a > < span class = "w" > < / span > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-34-7" name = "__codelineno-34-7" href = "#__codelineno-34-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-34-8" name = "__codelineno-34-8" href = "#__codelineno-34-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-9" name = "__codelineno-34-9" href = "#__codelineno-34-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-34-10" name = "__codelineno-34-10" href = "#__codelineno-34-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Choice< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-34-11" name = "__codelineno-34-11" href = "#__codelineno-34-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：判断选择是否合法< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-34-12" name = "__codelineno-34-12" href = "#__codelineno-34-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-34-13" name = "__codelineno-34-13" href = "#__codelineno-34-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-34-14" name = "__codelineno-34-14" href = "#__codelineno-34-14" > < / a > < span class = "w" > < / span > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-34-15" name = "__codelineno-34-15" href = "#__codelineno-34-15" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-34-16" name = "__codelineno-34-16" href = "#__codelineno-34-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-34-17" name = "__codelineno-34-17" href = "#__codelineno-34-17" > < / a > < span class = "w" > < / span > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-34-18" name = "__codelineno-34-18" href = "#__codelineno-34-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-19" name = "__codelineno-34-19" href = "#__codelineno-34-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-20" name = "__codelineno-34-20" href = "#__codelineno-34-20" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-35-1" name = "__codelineno-35-1" href = "#__codelineno-35-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "n" > State< / span > < span class = "p" > ,< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > choice< / span > < span class = "p" > ],< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > state< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "kc" > None< / span > < span class = "p" > :< / span >
< a id = "__codelineno-35-2" name = "__codelineno-35-2" href = "#__codelineno-35-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 回溯算法框架" " " < / span >
< a id = "__codelineno-35-3" name = "__codelineno-35-3" href = "#__codelineno-35-3" > < / a > < span class = "c1" > # 判断是否为解< / span >
< a id = "__codelineno-35-4" name = "__codelineno-35-4" href = "#__codelineno-35-4" > < / a > < span class = "k" > if< / span > < span class = "n" > is_solution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-35-5" name = "__codelineno-35-5" href = "#__codelineno-35-5" > < / a > < span class = "c1" > # 记录解< / span >
< a id = "__codelineno-35-6" name = "__codelineno-35-6" href = "#__codelineno-35-6" > < / a > < span class = "n" > record_solution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-35-7" name = "__codelineno-35-7" href = "#__codelineno-35-7" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-35-8" name = "__codelineno-35-8" href = "#__codelineno-35-8" > < / a > < span class = "c1" > # 遍历所有选择< / span >
< a id = "__codelineno-35-9" name = "__codelineno-35-9" href = "#__codelineno-35-9" > < / a > < span class = "k" > for< / span > < span class = "n" > choice< / span > < span class = "ow" > in< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span >
< a id = "__codelineno-35-10" name = "__codelineno-35-10" href = "#__codelineno-35-10" > < / a > < span class = "c1" > # 剪枝：判断选择是否合法< / span >
< a id = "__codelineno-35-11" name = "__codelineno-35-11" href = "#__codelineno-35-11" > < / a > < span class = "k" > if< / span > < span class = "n" > is_valid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-35-12" name = "__codelineno-35-12" href = "#__codelineno-35-12" > < / a > < span class = "c1" > # 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-35-13" name = "__codelineno-35-13" href = "#__codelineno-35-13" > < / a > < span class = "n" > make_choice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-35-14" name = "__codelineno-35-14" href = "#__codelineno-35-14" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-35-15" name = "__codelineno-35-15" href = "#__codelineno-35-15" > < / a > < span class = "c1" > # 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-35-16" name = "__codelineno-35-16" href = "#__codelineno-35-16" > < / a > < span class = "n" > undo_choice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-10 19:38:29 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-36-1" name = "__codelineno-36-1" href = "#__codelineno-36-1" > < / a > < span class = "cm" > /* 回溯算法框架 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-36-2" name = "__codelineno-36-2" href = "#__codelineno-36-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > State< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "nx" > Choice< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "nx" > State< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-36-3" name = "__codelineno-36-3" href = "#__codelineno-36-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断是否为解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-36-4" name = "__codelineno-36-4" href = "#__codelineno-36-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > isSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-36-5" name = "__codelineno-36-5" href = "#__codelineno-36-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-36-6" name = "__codelineno-36-6" href = "#__codelineno-36-6" > < / a > < span class = "w" > < / span > < span class = "nx" > recordSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-36-7" name = "__codelineno-36-7" href = "#__codelineno-36-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-36-8" name = "__codelineno-36-8" href = "#__codelineno-36-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-9" name = "__codelineno-36-9" href = "#__codelineno-36-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-36-10" name = "__codelineno-36-10" href = "#__codelineno-36-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-36-11" name = "__codelineno-36-11" href = "#__codelineno-36-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：判断选择是否合法< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-36-12" name = "__codelineno-36-12" href = "#__codelineno-36-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > isValid< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-36-13" name = "__codelineno-36-13" href = "#__codelineno-36-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-36-14" name = "__codelineno-36-14" href = "#__codelineno-36-14" > < / a > < span class = "w" > < / span > < span class = "nx" > makeChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-36-15" name = "__codelineno-36-15" href = "#__codelineno-36-15" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-36-16" name = "__codelineno-36-16" href = "#__codelineno-36-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-36-17" name = "__codelineno-36-17" href = "#__codelineno-36-17" > < / a > < span class = "w" > < / span > < span class = "nx" > undoChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-36-18" name = "__codelineno-36-18" href = "#__codelineno-36-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-19" name = "__codelineno-36-19" href = "#__codelineno-36-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-20" name = "__codelineno-36-20" href = "#__codelineno-36-20" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-10 19:38:29 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-37-1" name = "__codelineno-37-1" href = "#__codelineno-37-1" > < / a > < span class = "cm" > /* 回溯算法框架 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-37-2" name = "__codelineno-37-2" href = "#__codelineno-37-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-37-3" name = "__codelineno-37-3" href = "#__codelineno-37-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断是否为解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-37-4" name = "__codelineno-37-4" href = "#__codelineno-37-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > isSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-37-5" name = "__codelineno-37-5" href = "#__codelineno-37-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-37-6" name = "__codelineno-37-6" href = "#__codelineno-37-6" > < / a > < span class = "w" > < / span > < span class = "nx" > recordSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-37-7" name = "__codelineno-37-7" href = "#__codelineno-37-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-37-8" name = "__codelineno-37-8" href = "#__codelineno-37-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-9" name = "__codelineno-37-9" href = "#__codelineno-37-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-37-10" name = "__codelineno-37-10" href = "#__codelineno-37-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-37-11" name = "__codelineno-37-11" href = "#__codelineno-37-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：判断选择是否合法< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-37-12" name = "__codelineno-37-12" href = "#__codelineno-37-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > isValid< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-37-13" name = "__codelineno-37-13" href = "#__codelineno-37-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-37-14" name = "__codelineno-37-14" href = "#__codelineno-37-14" > < / a > < span class = "w" > < / span > < span class = "nx" > makeChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-37-15" name = "__codelineno-37-15" href = "#__codelineno-37-15" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-37-16" name = "__codelineno-37-16" href = "#__codelineno-37-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-37-17" name = "__codelineno-37-17" href = "#__codelineno-37-17" > < / a > < span class = "w" > < / span > < span class = "nx" > undoChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-37-18" name = "__codelineno-37-18" href = "#__codelineno-37-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-19" name = "__codelineno-37-19" href = "#__codelineno-37-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-20" name = "__codelineno-37-20" href = "#__codelineno-37-20" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-05-10 19:38:29 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-38-1" name = "__codelineno-38-1" href = "#__codelineno-38-1" > < / a > < span class = "cm" > /* 回溯算法框架 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-38-2" name = "__codelineno-38-2" href = "#__codelineno-38-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > State< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > Choice< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > State< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-3" name = "__codelineno-38-3" href = "#__codelineno-38-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断是否为解< / span >
< a id = "__codelineno-38-4" name = "__codelineno-38-4" href = "#__codelineno-38-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > isSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-5" name = "__codelineno-38-5" href = "#__codelineno-38-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-38-6" name = "__codelineno-38-6" href = "#__codelineno-38-6" > < / a > < span class = "w" > < / span > < span class = "nx" > recordSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-38-7" name = "__codelineno-38-7" href = "#__codelineno-38-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-38-8" name = "__codelineno-38-8" href = "#__codelineno-38-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-38-9" name = "__codelineno-38-9" href = "#__codelineno-38-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-38-10" name = "__codelineno-38-10" href = "#__codelineno-38-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-11" name = "__codelineno-38-11" href = "#__codelineno-38-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：判断选择是否合法< / span >
< a id = "__codelineno-38-12" name = "__codelineno-38-12" href = "#__codelineno-38-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > isValid< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-38-13" name = "__codelineno-38-13" href = "#__codelineno-38-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-38-14" name = "__codelineno-38-14" href = "#__codelineno-38-14" > < / a > < span class = "w" > < / span > < span class = "nx" > makeChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-38-15" name = "__codelineno-38-15" href = "#__codelineno-38-15" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-38-16" name = "__codelineno-38-16" href = "#__codelineno-38-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-38-17" name = "__codelineno-38-17" href = "#__codelineno-38-17" > < / a > < span class = "w" > < / span > < span class = "nx" > undoChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-38-18" name = "__codelineno-38-18" href = "#__codelineno-38-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-38-19" name = "__codelineno-38-19" href = "#__codelineno-38-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-38-20" name = "__codelineno-38-20" href = "#__codelineno-38-20" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-39-1" name = "__codelineno-39-1" href = "#__codelineno-39-1" > < / a > < span class = "cm" > /* 回溯算法框架 */< / span >
< a id = "__codelineno-39-2" name = "__codelineno-39-2" href = "#__codelineno-39-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > State< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Choice< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > numChoices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > State< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > numRes< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-39-3" name = "__codelineno-39-3" href = "#__codelineno-39-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断是否为解< / span >
< a id = "__codelineno-39-4" name = "__codelineno-39-4" href = "#__codelineno-39-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-39-5" name = "__codelineno-39-5" href = "#__codelineno-39-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-39-6" name = "__codelineno-39-6" href = "#__codelineno-39-6" > < / a > < span class = "w" > < / span > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > numRes< / span > < span class = "p" > );< / span >
< a id = "__codelineno-39-7" name = "__codelineno-39-7" href = "#__codelineno-39-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-39-8" name = "__codelineno-39-8" href = "#__codelineno-39-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-9" name = "__codelineno-39-9" href = "#__codelineno-39-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-39-10" name = "__codelineno-39-10" href = "#__codelineno-39-10" > < / 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" > numChoices< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-39-11" name = "__codelineno-39-11" href = "#__codelineno-39-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：判断选择是否合法< / span >
< a id = "__codelineno-39-12" name = "__codelineno-39-12" href = "#__codelineno-39-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-39-13" name = "__codelineno-39-13" href = "#__codelineno-39-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-39-14" name = "__codelineno-39-14" href = "#__codelineno-39-14" > < / a > < span class = "w" > < / span > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-39-15" name = "__codelineno-39-15" href = "#__codelineno-39-15" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > numChoices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > numRes< / span > < span class = "p" > );< / span >
< a id = "__codelineno-39-16" name = "__codelineno-39-16" href = "#__codelineno-39-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-39-17" name = "__codelineno-39-17" href = "#__codelineno-39-17" > < / a > < span class = "w" > < / span > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > choices< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-39-18" name = "__codelineno-39-18" href = "#__codelineno-39-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-19" name = "__codelineno-39-19" href = "#__codelineno-39-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-39-20" name = "__codelineno-39-20" href = "#__codelineno-39-20" > < / a > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-40-1" name = "__codelineno-40-1" href = "#__codelineno-40-1" > < / a > < span class = "cm" > /* 回溯算法框架 */< / span >
< a id = "__codelineno-40-2" name = "__codelineno-40-2" href = "#__codelineno-40-2" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > State< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Choice< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > State< / 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-40-3" name = "__codelineno-40-3" href = "#__codelineno-40-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断是否为解< / span >
< a id = "__codelineno-40-4" name = "__codelineno-40-4" href = "#__codelineno-40-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-40-5" name = "__codelineno-40-5" href = "#__codelineno-40-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-40-6" name = "__codelineno-40-6" href = "#__codelineno-40-6" > < / a > < span class = "w" > < / span > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-40-7" name = "__codelineno-40-7" href = "#__codelineno-40-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-40-8" name = "__codelineno-40-8" href = "#__codelineno-40-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-40-9" name = "__codelineno-40-9" href = "#__codelineno-40-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-40-10" name = "__codelineno-40-10" href = "#__codelineno-40-10" > < / a > < span class = "w" > < / span > < span class = "k" > foreach< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Choice< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-40-11" name = "__codelineno-40-11" href = "#__codelineno-40-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：判断选择是否合法< / span >
< a id = "__codelineno-40-12" name = "__codelineno-40-12" href = "#__codelineno-40-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-40-13" name = "__codelineno-40-13" href = "#__codelineno-40-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-40-14" name = "__codelineno-40-14" href = "#__codelineno-40-14" > < / a > < span class = "w" > < / span > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-40-15" name = "__codelineno-40-15" href = "#__codelineno-40-15" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-40-16" name = "__codelineno-40-16" href = "#__codelineno-40-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-40-17" name = "__codelineno-40-17" href = "#__codelineno-40-17" > < / a > < span class = "w" > < / span > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-40-18" name = "__codelineno-40-18" href = "#__codelineno-40-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-40-19" name = "__codelineno-40-19" href = "#__codelineno-40-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-40-20" name = "__codelineno-40-20" href = "#__codelineno-40-20" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-41-1" name = "__codelineno-41-1" href = "#__codelineno-41-1" > < / a > < span class = "cm" > /* 回溯算法框架 */< / span >
< a id = "__codelineno-41-2" name = "__codelineno-41-2" href = "#__codelineno-41-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "n" > State< / span > < span class = "p" > ,< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > Choice< / 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 = "n" > State< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-3" name = "__codelineno-41-3" href = "#__codelineno-41-3" > < / a > < span class = "c1" > // 判断是否为解< / span >
< a id = "__codelineno-41-4" name = "__codelineno-41-4" href = "#__codelineno-41-4" > < / a > < span class = "k" > if< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-5" name = "__codelineno-41-5" href = "#__codelineno-41-5" > < / a > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-41-6" name = "__codelineno-41-6" href = "#__codelineno-41-6" > < / a > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "n" > state< / 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-41-7" name = "__codelineno-41-7" href = "#__codelineno-41-7" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-41-8" name = "__codelineno-41-8" href = "#__codelineno-41-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-41-9" name = "__codelineno-41-9" href = "#__codelineno-41-9" > < / a > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-41-10" name = "__codelineno-41-10" href = "#__codelineno-41-10" > < / a > < span class = "k" > for< / span > < span class = "n" > choice< / span > < span class = "k" > in< / span > < span class = "n" > choices< / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-11" name = "__codelineno-41-11" href = "#__codelineno-41-11" > < / a > < span class = "c1" > // 剪枝：判断选择是否合法< / span >
< a id = "__codelineno-41-12" name = "__codelineno-41-12" href = "#__codelineno-41-12" > < / a > < span class = "k" > if< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-41-13" name = "__codelineno-41-13" href = "#__codelineno-41-13" > < / a > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-41-14" name = "__codelineno-41-14" href = "#__codelineno-41-14" > < / a > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-41-15" name = "__codelineno-41-15" href = "#__codelineno-41-15" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "n" > choices< / 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-41-16" name = "__codelineno-41-16" href = "#__codelineno-41-16" > < / a > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-41-17" name = "__codelineno-41-17" href = "#__codelineno-41-17" > < / a > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-41-18" name = "__codelineno-41-18" href = "#__codelineno-41-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-41-19" name = "__codelineno-41-19" href = "#__codelineno-41-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-41-20" name = "__codelineno-41-20" href = "#__codelineno-41-20" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-42-1" name = "__codelineno-42-1" href = "#__codelineno-42-1" > < / a >
2023-05-10 19:38:29 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 15:07:41 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-43-1" name = "__codelineno-43-1" href = "#__codelineno-43-1" > < / a > < span class = "cm" > /* 回溯算法框架 */< / span >
< a id = "__codelineno-43-2" name = "__codelineno-43-2" href = "#__codelineno-43-2" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > State< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Choice< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > State< / 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-43-3" name = "__codelineno-43-3" href = "#__codelineno-43-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判断是否为解< / span >
< a id = "__codelineno-43-4" name = "__codelineno-43-4" href = "#__codelineno-43-4" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-43-5" name = "__codelineno-43-5" href = "#__codelineno-43-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-43-6" name = "__codelineno-43-6" href = "#__codelineno-43-6" > < / a > < span class = "w" > < / span > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-43-7" name = "__codelineno-43-7" href = "#__codelineno-43-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-43-8" name = "__codelineno-43-8" href = "#__codelineno-43-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-9" name = "__codelineno-43-9" href = "#__codelineno-43-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-43-10" name = "__codelineno-43-10" href = "#__codelineno-43-10" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > Choice< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-43-11" name = "__codelineno-43-11" href = "#__codelineno-43-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：判断选择是否合法< / span >
< a id = "__codelineno-43-12" name = "__codelineno-43-12" href = "#__codelineno-43-12" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-43-13" name = "__codelineno-43-13" href = "#__codelineno-43-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-43-14" name = "__codelineno-43-14" href = "#__codelineno-43-14" > < / a > < span class = "w" > < / span > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-43-15" name = "__codelineno-43-15" href = "#__codelineno-43-15" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-43-16" name = "__codelineno-43-16" href = "#__codelineno-43-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-43-17" name = "__codelineno-43-17" href = "#__codelineno-43-17" > < / a > < span class = "w" > < / span > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-43-18" name = "__codelineno-43-18" href = "#__codelineno-43-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-19" name = "__codelineno-43-19" href = "#__codelineno-43-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-43-20" name = "__codelineno-43-20" href = "#__codelineno-43-20" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< / code > < / pre > < / div >
< / div >
2023-06-02 02:38:32 +08:00
< / div >
< / div >
< p > 下面，我们尝试基于此框架来解决例题三。在例题三中，状态 < code > state< / code > 是节点遍历路径，选择 < code > choices< / code > 是当前节点的左子节点和右子节点，结果 < code > res< / code > 是路径列表，实现代码如下所示。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "6:11" > < input checked = "checked" id = "__tabbed_6_1" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_2" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_3" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_4" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_5" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_6" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_7" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_8" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_9" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_10" name = "__tabbed_6" type = "radio" / > < input id = "__tabbed_6_11" name = "__tabbed_6" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_6_1" > Java< / label > < label for = "__tabbed_6_2" > C++< / label > < label for = "__tabbed_6_3" > Python< / label > < label for = "__tabbed_6_4" > Go< / label > < label for = "__tabbed_6_5" > JavaScript< / label > < label for = "__tabbed_6_6" > TypeScript< / label > < label for = "__tabbed_6_7" > C< / label > < label for = "__tabbed_6_8" > C#< / label > < label for = "__tabbed_6_9" > Swift< / label > < label for = "__tabbed_6_10" > Zig< / label > < label for = "__tabbed_6_11" > Dart< / label > < / div >
< div class = "tabbed-content" >
2023-05-10 19:38:29 +08:00
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-44-1" name = "__codelineno-44-1" href = "#__codelineno-44-1" > < / a > < span class = "cm" > /* 判断当前状态是否为解 */< / span >
< a id = "__codelineno-44-2" name = "__codelineno-44-2" href = "#__codelineno-44-2" > < / a > < span class = "kt" > boolean< / span > < span class = "w" > < / span > < span class = "nf" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-44-3" name = "__codelineno-44-3" href = "#__codelineno-44-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > isEmpty< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > get< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ).< / span > < span class = "na" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > ;< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-4" name = "__codelineno-44-4" href = "#__codelineno-44-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-44-5" name = "__codelineno-44-5" href = "#__codelineno-44-5" > < / a >
< a id = "__codelineno-44-6" name = "__codelineno-44-6" href = "#__codelineno-44-6" > < / a > < span class = "cm" > /* 记录解 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-7" name = "__codelineno-44-7" href = "#__codelineno-44-7" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / 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-44-8" name = "__codelineno-44-8" href = "#__codelineno-44-8" > < / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ));< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-9" name = "__codelineno-44-9" href = "#__codelineno-44-9" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-44-10" name = "__codelineno-44-10" href = "#__codelineno-44-10" > < / a >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-11" name = "__codelineno-44-11" href = "#__codelineno-44-11" > < / a > < span class = "cm" > /* 判断在当前状态下，该选择是否合法 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-12" name = "__codelineno-44-12" href = "#__codelineno-44-12" > < / a > < span class = "kt" > boolean< / span > < span class = "w" > < / span > < span class = "nf" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-44-13" name = "__codelineno-44-13" href = "#__codelineno-44-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > .< / span > < span class = "na" > val< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > ;< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-14" name = "__codelineno-44-14" href = "#__codelineno-44-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-44-15" name = "__codelineno-44-15" href = "#__codelineno-44-15" > < / a >
< a id = "__codelineno-44-16" name = "__codelineno-44-16" href = "#__codelineno-44-16" > < / a > < span class = "cm" > /* 更新状态 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-17" name = "__codelineno-44-17" href = "#__codelineno-44-17" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-44-18" name = "__codelineno-44-18" href = "#__codelineno-44-18" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-19" name = "__codelineno-44-19" href = "#__codelineno-44-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-44-20" name = "__codelineno-44-20" href = "#__codelineno-44-20" > < / a >
< a id = "__codelineno-44-21" name = "__codelineno-44-21" href = "#__codelineno-44-21" > < / a > < span class = "cm" > /* 恢复状态 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-22" name = "__codelineno-44-22" href = "#__codelineno-44-22" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-44-23" name = "__codelineno-44-23" href = "#__codelineno-44-23" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > remove< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "na" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-24" name = "__codelineno-44-24" href = "#__codelineno-44-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-44-25" name = "__codelineno-44-25" href = "#__codelineno-44-25" > < / a >
< a id = "__codelineno-44-26" name = "__codelineno-44-26" href = "#__codelineno-44-26" > < / a > < span class = "cm" > /* 回溯算法：例题三 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-27" name = "__codelineno-44-27" href = "#__codelineno-44-27" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / 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 >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-28" name = "__codelineno-44-28" href = "#__codelineno-44-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 检查是否为解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-29" name = "__codelineno-44-29" href = "#__codelineno-44-29" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-30" name = "__codelineno-44-30" href = "#__codelineno-44-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-31" name = "__codelineno-44-31" href = "#__codelineno-44-31" > < / a > < span class = "w" > < / span > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-32" name = "__codelineno-44-32" href = "#__codelineno-44-32" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-44-33" name = "__codelineno-44-33" href = "#__codelineno-44-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-44-34" name = "__codelineno-44-34" href = "#__codelineno-44-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-35" name = "__codelineno-44-35" href = "#__codelineno-44-35" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-36" name = "__codelineno-44-36" href = "#__codelineno-44-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：检查选择是否合法< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-37" name = "__codelineno-44-37" href = "#__codelineno-44-37" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-38" name = "__codelineno-44-38" href = "#__codelineno-44-38" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-39" name = "__codelineno-44-39" href = "#__codelineno-44-39" > < / a > < span class = "w" > < / span > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-40" name = "__codelineno-44-40" href = "#__codelineno-44-40" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-41" name = "__codelineno-44-41" href = "#__codelineno-44-41" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Arrays< / span > < span class = "p" > .< / span > < span class = "na" > asList< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > .< / span > < span class = "na" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > .< / span > < span class = "na" > right< / span > < span class = "p" > ),< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-42" name = "__codelineno-44-42" href = "#__codelineno-44-42" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-44-43" name = "__codelineno-44-43" href = "#__codelineno-44-43" > < / a > < span class = "w" > < / span > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-44-44" name = "__codelineno-44-44" href = "#__codelineno-44-44" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-44-45" name = "__codelineno-44-45" href = "#__codelineno-44-45" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-44-46" name = "__codelineno-44-46" href = "#__codelineno-44-46" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-45-1" name = "__codelineno-45-1" href = "#__codelineno-45-1" > < / a > < span class = "cm" > /* 判断当前状态是否为解 */< / span >
< a id = "__codelineno-45-2" name = "__codelineno-45-2" href = "#__codelineno-45-2" > < / a > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "nf" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-3" name = "__codelineno-45-3" href = "#__codelineno-45-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > empty< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > back< / span > < span class = "p" > ()< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span > < span class = "p" > ;< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-45-4" name = "__codelineno-45-4" href = "#__codelineno-45-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-45-5" name = "__codelineno-45-5" href = "#__codelineno-45-5" > < / a >
< a id = "__codelineno-45-6" name = "__codelineno-45-6" href = "#__codelineno-45-6" > < / a > < span class = "cm" > /* 记录解 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-45-7" name = "__codelineno-45-7" href = "#__codelineno-45-7" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / 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-45-8" name = "__codelineno-45-8" href = "#__codelineno-45-8" > < / a > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-45-9" name = "__codelineno-45-9" href = "#__codelineno-45-9" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-45-10" name = "__codelineno-45-10" href = "#__codelineno-45-10" > < / a >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-45-11" name = "__codelineno-45-11" href = "#__codelineno-45-11" > < / a > < span class = "cm" > /* 判断在当前状态下，该选择是否合法 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-45-12" name = "__codelineno-45-12" href = "#__codelineno-45-12" > < / a > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "nf" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-13" name = "__codelineno-45-13" href = "#__codelineno-45-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "k" > nullptr< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "o" > -> < / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > ;< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-45-14" name = "__codelineno-45-14" href = "#__codelineno-45-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-45-15" name = "__codelineno-45-15" href = "#__codelineno-45-15" > < / a >
< a id = "__codelineno-45-16" name = "__codelineno-45-16" href = "#__codelineno-45-16" > < / a > < span class = "cm" > /* 更新状态 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-45-17" name = "__codelineno-45-17" href = "#__codelineno-45-17" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-18" name = "__codelineno-45-18" href = "#__codelineno-45-18" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > push_back< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-45-19" name = "__codelineno-45-19" href = "#__codelineno-45-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-45-20" name = "__codelineno-45-20" href = "#__codelineno-45-20" > < / a >
< a id = "__codelineno-45-21" name = "__codelineno-45-21" href = "#__codelineno-45-21" > < / a > < span class = "cm" > /* 恢复状态 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-45-22" name = "__codelineno-45-22" href = "#__codelineno-45-22" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-23" name = "__codelineno-45-23" href = "#__codelineno-45-23" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > pop_back< / span > < span class = "p" > ();< / span >
2023-05-16 14:51:45 +08:00
< a id = "__codelineno-45-24" name = "__codelineno-45-24" href = "#__codelineno-45-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-45-25" name = "__codelineno-45-25" href = "#__codelineno-45-25" > < / a >
< a id = "__codelineno-45-26" name = "__codelineno-45-26" href = "#__codelineno-45-26" > < / a > < span class = "cm" > /* 回溯算法：例题三 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-45-27" name = "__codelineno-45-27" href = "#__codelineno-45-27" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / 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-45-28" name = "__codelineno-45-28" href = "#__codelineno-45-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 检查是否为解< / span >
< a id = "__codelineno-45-29" name = "__codelineno-45-29" href = "#__codelineno-45-29" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-30" name = "__codelineno-45-30" href = "#__codelineno-45-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-45-31" name = "__codelineno-45-31" href = "#__codelineno-45-31" > < / a > < span class = "w" > < / span > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-45-32" name = "__codelineno-45-32" href = "#__codelineno-45-32" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-45-33" name = "__codelineno-45-33" href = "#__codelineno-45-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-34" name = "__codelineno-45-34" href = "#__codelineno-45-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-45-35" name = "__codelineno-45-35" href = "#__codelineno-45-35" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-36" name = "__codelineno-45-36" href = "#__codelineno-45-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：检查选择是否合法< / span >
< a id = "__codelineno-45-37" name = "__codelineno-45-37" href = "#__codelineno-45-37" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-45-38" name = "__codelineno-45-38" href = "#__codelineno-45-38" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-45-39" name = "__codelineno-45-39" href = "#__codelineno-45-39" > < / a > < span class = "w" > < / span > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-45-40" name = "__codelineno-45-40" href = "#__codelineno-45-40" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-45-41" name = "__codelineno-45-41" href = "#__codelineno-45-41" > < / a > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "o" > *> < / span > < span class = "w" > < / span > < span class = "n" > nextChoices< / span > < span class = "p" > {< / span > < span class = "n" > choice< / span > < span class = "o" > -> < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "o" > -> < / span > < span class = "n" > right< / span > < span class = "p" > };< / span >
< a id = "__codelineno-45-42" name = "__codelineno-45-42" href = "#__codelineno-45-42" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nextChoices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-45-43" name = "__codelineno-45-43" href = "#__codelineno-45-43" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-45-44" name = "__codelineno-45-44" href = "#__codelineno-45-44" > < / a > < span class = "w" > < / span > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-45-45" name = "__codelineno-45-45" href = "#__codelineno-45-45" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-46" name = "__codelineno-45-46" href = "#__codelineno-45-46" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-45-47" name = "__codelineno-45-47" href = "#__codelineno-45-47" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-46-1" name = "__codelineno-46-1" href = "#__codelineno-46-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > is_solution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ])< / span > < span class = "o" > -> < / span > < span class = "nb" > bool< / span > < span class = "p" > :< / span >
< a id = "__codelineno-46-2" name = "__codelineno-46-2" href = "#__codelineno-46-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 判断当前状态是否为解" " " < / span >
< a id = "__codelineno-46-3" name = "__codelineno-46-3" href = "#__codelineno-46-3" > < / a > < span class = "k" > return< / span > < span class = "n" > state< / span > < span class = "ow" > and< / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "o" > ==< / span > < span class = "mi" > 7< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-46-4" name = "__codelineno-46-4" href = "#__codelineno-46-4" > < / a >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-46-5" name = "__codelineno-46-5" href = "#__codelineno-46-5" > < / a > < span class = "k" > def< / span > < span class = "nf" > record_solution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ]]):< / span >
< a id = "__codelineno-46-6" name = "__codelineno-46-6" href = "#__codelineno-46-6" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 记录解" " " < / span >
< a id = "__codelineno-46-7" name = "__codelineno-46-7" href = "#__codelineno-46-7" > < / a > < span class = "n" > res< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "nb" > list< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ))< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-46-8" name = "__codelineno-46-8" href = "#__codelineno-46-8" > < / a >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-46-9" name = "__codelineno-46-9" href = "#__codelineno-46-9" > < / a > < span class = "k" > def< / span > < span class = "nf" > is_valid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > bool< / span > < span class = "p" > :< / span >
< a id = "__codelineno-46-10" name = "__codelineno-46-10" href = "#__codelineno-46-10" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 判断在当前状态下，该选择是否合法" " " < / span >
< a id = "__codelineno-46-11" name = "__codelineno-46-11" href = "#__codelineno-46-11" > < / a > < span class = "k" > return< / span > < span class = "n" > choice< / span > < span class = "ow" > is< / span > < span class = "ow" > not< / span > < span class = "kc" > None< / span > < span class = "ow" > and< / span > < span class = "n" > choice< / span > < span class = "o" > .< / span > < span class = "n" > val< / span > < span class = "o" > !=< / span > < span class = "mi" > 3< / span >
< a id = "__codelineno-46-12" name = "__codelineno-46-12" href = "#__codelineno-46-12" > < / a >
< a id = "__codelineno-46-13" name = "__codelineno-46-13" href = "#__codelineno-46-13" > < / a > < span class = "k" > def< / span > < span class = "nf" > make_choice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-46-14" name = "__codelineno-46-14" href = "#__codelineno-46-14" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 更新状态" " " < / span >
< a id = "__codelineno-46-15" name = "__codelineno-46-15" href = "#__codelineno-46-15" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-46-16" name = "__codelineno-46-16" href = "#__codelineno-46-16" > < / a >
< a id = "__codelineno-46-17" name = "__codelineno-46-17" href = "#__codelineno-46-17" > < / a > < span class = "k" > def< / span > < span class = "nf" > undo_choice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-46-18" name = "__codelineno-46-18" href = "#__codelineno-46-18" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 恢复状态" " " < / span >
< a id = "__codelineno-46-19" name = "__codelineno-46-19" href = "#__codelineno-46-19" > < / a > < span class = "n" > state< / span > < span class = "o" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-46-20" name = "__codelineno-46-20" href = "#__codelineno-46-20" > < / a >
< a id = "__codelineno-46-21" name = "__codelineno-46-21" href = "#__codelineno-46-21" > < / a > < span class = "k" > def< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-46-22" name = "__codelineno-46-22" href = "#__codelineno-46-22" > < / a > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > res< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ]]< / span >
< a id = "__codelineno-46-23" name = "__codelineno-46-23" href = "#__codelineno-46-23" > < / a > < span class = "p" > ):< / span >
< a id = "__codelineno-46-24" name = "__codelineno-46-24" href = "#__codelineno-46-24" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 回溯算法：例题三" " " < / span >
< a id = "__codelineno-46-25" name = "__codelineno-46-25" href = "#__codelineno-46-25" > < / a > < span class = "c1" > # 检查是否为解< / span >
< a id = "__codelineno-46-26" name = "__codelineno-46-26" href = "#__codelineno-46-26" > < / a > < span class = "k" > if< / span > < span class = "n" > is_solution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-46-27" name = "__codelineno-46-27" href = "#__codelineno-46-27" > < / a > < span class = "c1" > # 记录解< / span >
< a id = "__codelineno-46-28" name = "__codelineno-46-28" href = "#__codelineno-46-28" > < / a > < span class = "n" > record_solution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-46-29" name = "__codelineno-46-29" href = "#__codelineno-46-29" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-46-30" name = "__codelineno-46-30" href = "#__codelineno-46-30" > < / a > < span class = "c1" > # 遍历所有选择< / span >
< a id = "__codelineno-46-31" name = "__codelineno-46-31" href = "#__codelineno-46-31" > < / a > < span class = "k" > for< / span > < span class = "n" > choice< / span > < span class = "ow" > in< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span >
< a id = "__codelineno-46-32" name = "__codelineno-46-32" href = "#__codelineno-46-32" > < / a > < span class = "c1" > # 剪枝：检查选择是否合法< / span >
< a id = "__codelineno-46-33" name = "__codelineno-46-33" href = "#__codelineno-46-33" > < / a > < span class = "k" > if< / span > < span class = "n" > is_valid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-46-34" name = "__codelineno-46-34" href = "#__codelineno-46-34" > < / a > < span class = "c1" > # 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-46-35" name = "__codelineno-46-35" href = "#__codelineno-46-35" > < / a > < span class = "n" > make_choice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-46-36" name = "__codelineno-46-36" href = "#__codelineno-46-36" > < / a > < span class = "c1" > # 进行下一轮选择< / span >
< a id = "__codelineno-46-37" name = "__codelineno-46-37" href = "#__codelineno-46-37" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "p" > [< / span > < span class = "n" > choice< / span > < span class = "o" > .< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "o" > .< / span > < span class = "n" > right< / span > < span class = "p" > ],< / span > < span class = "n" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-46-38" name = "__codelineno-46-38" href = "#__codelineno-46-38" > < / a > < span class = "c1" > # 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-46-39" name = "__codelineno-46-39" href = "#__codelineno-46-39" > < / a > < span class = "n" > undo_choice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
2023-05-10 19:38:29 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-47-1" name = "__codelineno-47-1" href = "#__codelineno-47-1" > < / a > < span class = "cm" > /* 判断当前状态是否为解 */< / span >
< a id = "__codelineno-47-2" name = "__codelineno-47-2" href = "#__codelineno-47-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > isSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-3" name = "__codelineno-47-3" href = "#__codelineno-47-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ].< / span > < span class = "nx" > Val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "mi" > 7< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-4" name = "__codelineno-47-4" href = "#__codelineno-47-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-47-5" name = "__codelineno-47-5" href = "#__codelineno-47-5" > < / a >
< a id = "__codelineno-47-6" name = "__codelineno-47-6" href = "#__codelineno-47-6" > < / a > < span class = "cm" > /* 记录解 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-7" name = "__codelineno-47-7" href = "#__codelineno-47-7" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > recordSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-8" name = "__codelineno-47-8" href = "#__codelineno-47-8" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > res< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-9" name = "__codelineno-47-9" href = "#__codelineno-47-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-47-10" name = "__codelineno-47-10" href = "#__codelineno-47-10" > < / a >
< a id = "__codelineno-47-11" name = "__codelineno-47-11" href = "#__codelineno-47-11" > < / a > < span class = "cm" > /* 判断在当前状态下，该选择是否合法 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-12" name = "__codelineno-47-12" href = "#__codelineno-47-12" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > isValid< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-13" name = "__codelineno-47-13" href = "#__codelineno-47-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "kc" > nil< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > .< / span > < span class = "nx" > Val< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-14" name = "__codelineno-47-14" href = "#__codelineno-47-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-47-15" name = "__codelineno-47-15" href = "#__codelineno-47-15" > < / a >
< a id = "__codelineno-47-16" name = "__codelineno-47-16" href = "#__codelineno-47-16" > < / a > < span class = "cm" > /* 更新状态 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-17" name = "__codelineno-47-17" href = "#__codelineno-47-17" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > makeChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-18" name = "__codelineno-47-18" href = "#__codelineno-47-18" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-19" name = "__codelineno-47-19" href = "#__codelineno-47-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-47-20" name = "__codelineno-47-20" href = "#__codelineno-47-20" > < / a >
< a id = "__codelineno-47-21" name = "__codelineno-47-21" href = "#__codelineno-47-21" > < / a > < span class = "cm" > /* 恢复状态 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-22" name = "__codelineno-47-22" href = "#__codelineno-47-22" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > undoChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-47-23" name = "__codelineno-47-23" href = "#__codelineno-47-23" > < / a > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )[:< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "o" > *< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-24" name = "__codelineno-47-24" href = "#__codelineno-47-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-47-25" name = "__codelineno-47-25" href = "#__codelineno-47-25" > < / a >
< a id = "__codelineno-47-26" name = "__codelineno-47-26" href = "#__codelineno-47-26" > < / a > < span class = "cm" > /* 回溯算法：例题三 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-27" name = "__codelineno-47-27" href = "#__codelineno-47-27" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > backtrackIII< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > []< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > [][]< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-28" name = "__codelineno-47-28" href = "#__codelineno-47-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 检查是否为解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-29" name = "__codelineno-47-29" href = "#__codelineno-47-29" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > isSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-30" name = "__codelineno-47-30" href = "#__codelineno-47-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-31" name = "__codelineno-47-31" href = "#__codelineno-47-31" > < / a > < span class = "w" > < / span > < span class = "nx" > recordSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-47-32" name = "__codelineno-47-32" href = "#__codelineno-47-32" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-33" name = "__codelineno-47-33" href = "#__codelineno-47-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-34" name = "__codelineno-47-34" href = "#__codelineno-47-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-35" name = "__codelineno-47-35" href = "#__codelineno-47-35" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > _< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "k" > range< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > choices< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-36" name = "__codelineno-47-36" href = "#__codelineno-47-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：检查选择是否合法< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-37" name = "__codelineno-47-37" href = "#__codelineno-47-37" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > isValid< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-38" name = "__codelineno-47-38" href = "#__codelineno-47-38" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-39" name = "__codelineno-47-39" href = "#__codelineno-47-39" > < / a > < span class = "w" > < / span > < span class = "nx" > makeChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-47-40" name = "__codelineno-47-40" href = "#__codelineno-47-40" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-47-41" name = "__codelineno-47-41" href = "#__codelineno-47-41" > < / a > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "o" > *< / span > < span class = "nx" > TreeNode< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-47-42" name = "__codelineno-47-42" href = "#__codelineno-47-42" > < / a > < span class = "w" > < / span > < span class = "nx" > temp< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nb" > append< / span > < span class = "p" > (< / span > < span class = "nx" > temp< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > .< / span > < span class = "nx" > Left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > .< / span > < span class = "nx" > Right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-47-43" name = "__codelineno-47-43" href = "#__codelineno-47-43" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrackIII< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > temp< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span >
< a id = "__codelineno-47-44" name = "__codelineno-47-44" href = "#__codelineno-47-44" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-47-45" name = "__codelineno-47-45" href = "#__codelineno-47-45" > < / a > < span class = "w" > < / span > < span class = "nx" > undoChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-47-46" name = "__codelineno-47-46" href = "#__codelineno-47-46" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-47" name = "__codelineno-47-47" href = "#__codelineno-47-47" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-47-48" name = "__codelineno-47-48" href = "#__codelineno-47-48" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-48-1" name = "__codelineno-48-1" href = "#__codelineno-48-1" > < / a > < span class = "cm" > /* 判断当前状态是否为解 */< / span >
< a id = "__codelineno-48-2" name = "__codelineno-48-2" href = "#__codelineno-48-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > isSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-3" name = "__codelineno-48-3" href = "#__codelineno-48-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > ;< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-48-4" name = "__codelineno-48-4" href = "#__codelineno-48-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-5" name = "__codelineno-48-5" href = "#__codelineno-48-5" > < / a >
< a id = "__codelineno-48-6" name = "__codelineno-48-6" href = "#__codelineno-48-6" > < / a > < span class = "cm" > /* 记录解 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-48-7" name = "__codelineno-48-7" href = "#__codelineno-48-7" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > recordSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-8" name = "__codelineno-48-8" href = "#__codelineno-48-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > ([...< / span > < span class = "nx" > state< / span > < span class = "p" > ]);< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-48-9" name = "__codelineno-48-9" href = "#__codelineno-48-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-10" name = "__codelineno-48-10" href = "#__codelineno-48-10" > < / a >
< a id = "__codelineno-48-11" name = "__codelineno-48-11" href = "#__codelineno-48-11" > < / a > < span class = "cm" > /* 判断在当前状态下，该选择是否合法 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-48-12" name = "__codelineno-48-12" href = "#__codelineno-48-12" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > isValid< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-13" name = "__codelineno-48-13" href = "#__codelineno-48-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > !==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > !==< / span > < span class = "w" > < / span > < span class = "mf" > 3< / span > < span class = "p" > ;< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-48-14" name = "__codelineno-48-14" href = "#__codelineno-48-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-15" name = "__codelineno-48-15" href = "#__codelineno-48-15" > < / a >
< a id = "__codelineno-48-16" name = "__codelineno-48-16" href = "#__codelineno-48-16" > < / a > < span class = "cm" > /* 更新状态 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-48-17" name = "__codelineno-48-17" href = "#__codelineno-48-17" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > makeChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-18" name = "__codelineno-48-18" href = "#__codelineno-48-18" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-48-19" name = "__codelineno-48-19" href = "#__codelineno-48-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-20" name = "__codelineno-48-20" href = "#__codelineno-48-20" > < / a >
< a id = "__codelineno-48-21" name = "__codelineno-48-21" href = "#__codelineno-48-21" > < / a > < span class = "cm" > /* 恢复状态 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-48-22" name = "__codelineno-48-22" href = "#__codelineno-48-22" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > undoChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-23" name = "__codelineno-48-23" href = "#__codelineno-48-23" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-48-24" name = "__codelineno-48-24" href = "#__codelineno-48-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-48-25" name = "__codelineno-48-25" href = "#__codelineno-48-25" > < / a >
< a id = "__codelineno-48-26" name = "__codelineno-48-26" href = "#__codelineno-48-26" > < / a > < span class = "cm" > /* 回溯算法：例题三 */< / span >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-48-27" name = "__codelineno-48-27" href = "#__codelineno-48-27" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-28" name = "__codelineno-48-28" href = "#__codelineno-48-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 检查是否为解< / span >
< a id = "__codelineno-48-29" name = "__codelineno-48-29" href = "#__codelineno-48-29" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > isSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-30" name = "__codelineno-48-30" href = "#__codelineno-48-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-48-31" name = "__codelineno-48-31" href = "#__codelineno-48-31" > < / a > < span class = "w" > < / span > < span class = "nx" > recordSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-48-32" name = "__codelineno-48-32" href = "#__codelineno-48-32" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-48-33" name = "__codelineno-48-33" href = "#__codelineno-48-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-48-34" name = "__codelineno-48-34" href = "#__codelineno-48-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-48-35" name = "__codelineno-48-35" href = "#__codelineno-48-35" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-36" name = "__codelineno-48-36" href = "#__codelineno-48-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：检查选择是否合法< / span >
< a id = "__codelineno-48-37" name = "__codelineno-48-37" href = "#__codelineno-48-37" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > isValid< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-48-38" name = "__codelineno-48-38" href = "#__codelineno-48-38" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-48-39" name = "__codelineno-48-39" href = "#__codelineno-48-39" > < / a > < span class = "w" > < / span > < span class = "nx" > makeChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-48-40" name = "__codelineno-48-40" href = "#__codelineno-48-40" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-48-41" name = "__codelineno-48-41" href = "#__codelineno-48-41" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "nx" > choice< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-48-42" name = "__codelineno-48-42" href = "#__codelineno-48-42" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-48-43" name = "__codelineno-48-43" href = "#__codelineno-48-43" > < / a > < span class = "w" > < / span > < span class = "nx" > undoChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-48-44" name = "__codelineno-48-44" href = "#__codelineno-48-44" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-48-45" name = "__codelineno-48-45" href = "#__codelineno-48-45" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-48-46" name = "__codelineno-48-46" href = "#__codelineno-48-46" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-06-02 02:38:32 +08:00
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-49-1" name = "__codelineno-49-1" href = "#__codelineno-49-1" > < / a > < span class = "cm" > /* 判断当前状态是否为解 */< / span >
< a id = "__codelineno-49-2" name = "__codelineno-49-2" href = "#__codelineno-49-2" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > isSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-3" name = "__codelineno-49-3" href = "#__codelineno-49-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > [< / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > length< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "mf" > 7< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-4" name = "__codelineno-49-4" href = "#__codelineno-49-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-49-5" name = "__codelineno-49-5" href = "#__codelineno-49-5" > < / a >
< a id = "__codelineno-49-6" name = "__codelineno-49-6" href = "#__codelineno-49-6" > < / a > < span class = "cm" > /* 记录解 */< / span >
< a id = "__codelineno-49-7" name = "__codelineno-49-7" href = "#__codelineno-49-7" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > recordSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [][])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-8" name = "__codelineno-49-8" href = "#__codelineno-49-8" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > ([...< / span > < span class = "nx" > state< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-49-9" name = "__codelineno-49-9" href = "#__codelineno-49-9" > < / a > < span class = "p" > }< / span >
2023-05-10 19:38:29 +08:00
< a id = "__codelineno-49-10" name = "__codelineno-49-10" href = "#__codelineno-49-10" > < / a >
2023-06-02 02:38:32 +08:00
< a id = "__codelineno-49-11" name = "__codelineno-49-11" href = "#__codelineno-49-11" > < / a > < span class = "cm" > /* 判断在当前状态下，该选择是否合法 */< / span >
< a id = "__codelineno-49-12" name = "__codelineno-49-12" href = "#__codelineno-49-12" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > isValid< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > boolean< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-13" name = "__codelineno-49-13" href = "#__codelineno-49-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "o" > !==< / span > < span class = "w" > < / span > < span class = "kc" > null< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > .< / span > < span class = "nx" > val< / span > < span class = "w" > < / span > < span class = "o" > !==< / span > < span class = "w" > < / span > < span class = "mf" > 3< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-14" name = "__codelineno-49-14" href = "#__codelineno-49-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-49-15" name = "__codelineno-49-15" href = "#__codelineno-49-15" > < / a >
< a id = "__codelineno-49-16" name = "__codelineno-49-16" href = "#__codelineno-49-16" > < / a > < span class = "cm" > /* 更新状态 */< / span >
< a id = "__codelineno-49-17" name = "__codelineno-49-17" href = "#__codelineno-49-17" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > makeChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-18" name = "__codelineno-49-18" href = "#__codelineno-49-18" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > push< / span > < span class = "p" > (< / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-19" name = "__codelineno-49-19" href = "#__codelineno-49-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-49-20" name = "__codelineno-49-20" href = "#__codelineno-49-20" > < / a >
< a id = "__codelineno-49-21" name = "__codelineno-49-21" href = "#__codelineno-49-21" > < / a > < span class = "cm" > /* 恢复状态 */< / span >
< a id = "__codelineno-49-22" name = "__codelineno-49-22" href = "#__codelineno-49-22" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > undoChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [])< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-23" name = "__codelineno-49-23" href = "#__codelineno-49-23" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "p" > .< / span > < span class = "nx" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-49-24" name = "__codelineno-49-24" href = "#__codelineno-49-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-49-25" name = "__codelineno-49-25" href = "#__codelineno-49-25" > < / a >
< a id = "__codelineno-49-26" name = "__codelineno-49-26" href = "#__codelineno-49-26" > < / a > < span class = "cm" > /* 回溯算法：例题三 */< / span >
< a id = "__codelineno-49-27" name = "__codelineno-49-27" href = "#__codelineno-49-27" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span >
< a id = "__codelineno-49-28" name = "__codelineno-49-28" href = "#__codelineno-49-28" > < / a > < span class = "w" > < / span > < span class = "nx" > state< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-49-29" name = "__codelineno-49-29" href = "#__codelineno-49-29" > < / a > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [],< / span >
< a id = "__codelineno-49-30" name = "__codelineno-49-30" href = "#__codelineno-49-30" > < / a > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > TreeNode< / span > < span class = "p" > [][]< / span >
< a id = "__codelineno-49-31" name = "__codelineno-49-31" href = "#__codelineno-49-31" > < / a > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-32" name = "__codelineno-49-32" href = "#__codelineno-49-32" > < / a > < span class = "w" > < / span > < span class = "c1" > // 检查是否为解< / span >
< a id = "__codelineno-49-33" name = "__codelineno-49-33" href = "#__codelineno-49-33" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > isSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-34" name = "__codelineno-49-34" href = "#__codelineno-49-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-49-35" name = "__codelineno-49-35" href = "#__codelineno-49-35" > < / a > < span class = "w" > < / span > < span class = "nx" > recordSolution< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-36" name = "__codelineno-49-36" href = "#__codelineno-49-36" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-49-37" name = "__codelineno-49-37" href = "#__codelineno-49-37" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-49-38" name = "__codelineno-49-38" href = "#__codelineno-49-38" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-49-39" name = "__codelineno-49-39" href = "#__codelineno-49-39" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > const< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "w" > < / span > < span class = "k" > of< / span > < span class = "w" > < / span > < span class = "nx" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-40" name = "__codelineno-49-40" href = "#__codelineno-49-40" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：检查选择是否合法< / span >
< a id = "__codelineno-49-41" name = "__codelineno-49-41" href = "#__codelineno-49-41" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > isValid< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-49-42" name = "__codelineno-49-42" href = "#__codelineno-49-42" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-49-43" name = "__codelineno-49-43" href = "#__codelineno-49-43" > < / a > < span class = "w" > < / span > < span class = "nx" > makeChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-44" name = "__codelineno-49-44" href = "#__codelineno-49-44" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-49-45" name = "__codelineno-49-45" href = "#__codelineno-49-45" > < / a > < span class = "w" > < / span > < span class = "nx" > backtrack< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "nx" > choice< / span > < span class = "p" > .< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > choice< / span > < span class = "p" > .< / span > < span class = "nx" > right< / span > < span class = "p" > ],< / span > < span class = "w" > < / span > < span class = "nx" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-46" name = "__codelineno-49-46" href = "#__codelineno-49-46" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-49-47" name = "__codelineno-49-47" href = "#__codelineno-49-47" > < / a > < span class = "w" > < / span > < span class = "nx" > undoChoice< / span > < span class = "p" > (< / span > < span class = "nx" > state< / span > < span class = "p" > );< / span >
< a id = "__codelineno-49-48" name = "__codelineno-49-48" href = "#__codelineno-49-48" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-49-49" name = "__codelineno-49-49" href = "#__codelineno-49-49" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-49-50" name = "__codelineno-49-50" href = "#__codelineno-49-50" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-50-1" name = "__codelineno-50-1" href = "#__codelineno-50-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > isSolution< / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-2" name = "__codelineno-50-2" href = "#__codelineno-50-2" > < / a >
< a id = "__codelineno-50-3" name = "__codelineno-50-3" href = "#__codelineno-50-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > recordSolution< / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-4" name = "__codelineno-50-4" href = "#__codelineno-50-4" > < / a >
< a id = "__codelineno-50-5" name = "__codelineno-50-5" href = "#__codelineno-50-5" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > isValid< / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-6" name = "__codelineno-50-6" href = "#__codelineno-50-6" > < / a >
< a id = "__codelineno-50-7" name = "__codelineno-50-7" href = "#__codelineno-50-7" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > makeChoice< / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-8" name = "__codelineno-50-8" href = "#__codelineno-50-8" > < / a >
< a id = "__codelineno-50-9" name = "__codelineno-50-9" href = "#__codelineno-50-9" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > undoChoice< / span > < span class = "p" > }< / span >
< a id = "__codelineno-50-10" name = "__codelineno-50-10" href = "#__codelineno-50-10" > < / a >
< a id = "__codelineno-50-11" name = "__codelineno-50-11" href = "#__codelineno-50-11" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > backtrack< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-51-1" name = "__codelineno-51-1" href = "#__codelineno-51-1" > < / a > < span class = "cm" > /* 判断当前状态是否为解 */< / span >
< a id = "__codelineno-51-2" name = "__codelineno-51-2" href = "#__codelineno-51-2" > < / a > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "nf" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-3" name = "__codelineno-51-3" href = "#__codelineno-51-3" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > [< / span > < span class = "o" > ^< / span > < span class = "m" > 1< / span > < span class = "p" > ].< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 7< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-51-4" name = "__codelineno-51-4" href = "#__codelineno-51-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-51-5" name = "__codelineno-51-5" href = "#__codelineno-51-5" > < / a >
< a id = "__codelineno-51-6" name = "__codelineno-51-6" href = "#__codelineno-51-6" > < / a > < span class = "cm" > /* 记录解 */< / span >
< a id = "__codelineno-51-7" name = "__codelineno-51-7" href = "#__codelineno-51-7" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / 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-51-8" name = "__codelineno-51-8" href = "#__codelineno-51-8" > < / 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 = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-51-9" name = "__codelineno-51-9" href = "#__codelineno-51-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-51-10" name = "__codelineno-51-10" href = "#__codelineno-51-10" > < / a >
< a id = "__codelineno-51-11" name = "__codelineno-51-11" href = "#__codelineno-51-11" > < / a > < span class = "cm" > /* 判断在当前状态下，该选择是否合法 */< / span >
< a id = "__codelineno-51-12" name = "__codelineno-51-12" href = "#__codelineno-51-12" > < / a > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "nf" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-13" name = "__codelineno-51-13" href = "#__codelineno-51-13" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "k" > null< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > .< / span > < span class = "n" > val< / span > < span class = "w" > < / span > < span class = "o" > !=< / span > < span class = "w" > < / span > < span class = "m" > 3< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-51-14" name = "__codelineno-51-14" href = "#__codelineno-51-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-51-15" name = "__codelineno-51-15" href = "#__codelineno-51-15" > < / a >
< a id = "__codelineno-51-16" name = "__codelineno-51-16" href = "#__codelineno-51-16" > < / a > < span class = "cm" > /* 更新状态 */< / span >
< a id = "__codelineno-51-17" name = "__codelineno-51-17" href = "#__codelineno-51-17" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-18" name = "__codelineno-51-18" href = "#__codelineno-51-18" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Add< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-19" name = "__codelineno-51-19" href = "#__codelineno-51-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-51-20" name = "__codelineno-51-20" href = "#__codelineno-51-20" > < / a >
< a id = "__codelineno-51-21" name = "__codelineno-51-21" href = "#__codelineno-51-21" > < / a > < span class = "cm" > /* 恢复状态 */< / span >
< a id = "__codelineno-51-22" name = "__codelineno-51-22" href = "#__codelineno-51-22" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-23" name = "__codelineno-51-23" href = "#__codelineno-51-23" > < / a > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > RemoveAt< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > Count< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-24" name = "__codelineno-51-24" href = "#__codelineno-51-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-51-25" name = "__codelineno-51-25" href = "#__codelineno-51-25" > < / a >
< a id = "__codelineno-51-26" name = "__codelineno-51-26" href = "#__codelineno-51-26" > < / a > < span class = "cm" > /* 回溯算法：例题三 */< / span >
< a id = "__codelineno-51-27" name = "__codelineno-51-27" href = "#__codelineno-51-27" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > TreeNode< / 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-51-28" name = "__codelineno-51-28" href = "#__codelineno-51-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 检查是否为解< / span >
< a id = "__codelineno-51-29" name = "__codelineno-51-29" href = "#__codelineno-51-29" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-30" name = "__codelineno-51-30" href = "#__codelineno-51-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 记录解< / span >
< a id = "__codelineno-51-31" name = "__codelineno-51-31" href = "#__codelineno-51-31" > < / a > < span class = "w" > < / span > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-32" name = "__codelineno-51-32" href = "#__codelineno-51-32" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-51-33" name = "__codelineno-51-33" href = "#__codelineno-51-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-51-34" name = "__codelineno-51-34" href = "#__codelineno-51-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-51-35" name = "__codelineno-51-35" href = "#__codelineno-51-35" > < / a > < span class = "w" > < / span > < span class = "k" > foreach< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > TreeNode< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > choices< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-36" name = "__codelineno-51-36" href = "#__codelineno-51-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 剪枝：检查选择是否合法< / span >
< a id = "__codelineno-51-37" name = "__codelineno-51-37" href = "#__codelineno-51-37" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > ))< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-51-38" name = "__codelineno-51-38" href = "#__codelineno-51-38" > < / a > < span class = "w" > < / span > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-51-39" name = "__codelineno-51-39" href = "#__codelineno-51-39" > < / a > < span class = "w" > < / span > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-40" name = "__codelineno-51-40" href = "#__codelineno-51-40" > < / a > < span class = "w" > < / span > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-51-41" name = "__codelineno-51-41" href = "#__codelineno-51-41" > < / a > < span class = "w" > < / span > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / 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 = "n" > TreeNode< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > .< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > .< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "p" > },< / span > < span class = "w" > < / span > < span class = "n" > res< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-42" name = "__codelineno-51-42" href = "#__codelineno-51-42" > < / a > < span class = "w" > < / span > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-51-43" name = "__codelineno-51-43" href = "#__codelineno-51-43" > < / a > < span class = "w" > < / span > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > choice< / span > < span class = "p" > );< / span >
< a id = "__codelineno-51-44" name = "__codelineno-51-44" href = "#__codelineno-51-44" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-51-45" name = "__codelineno-51-45" href = "#__codelineno-51-45" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-51-46" name = "__codelineno-51-46" href = "#__codelineno-51-46" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-52-1" name = "__codelineno-52-1" href = "#__codelineno-52-1" > < / a > < span class = "cm" > /* 判断当前状态是否为解 */< / span >
< a id = "__codelineno-52-2" name = "__codelineno-52-2" href = "#__codelineno-52-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ])< / span > < span class = "p" > -> < / span > < span class = "nb" > Bool< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-3" name = "__codelineno-52-3" href = "#__codelineno-52-3" > < / a > < span class = "o" > !< / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "bp" > isEmpty< / span > < span class = "o" > & & < / span > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "bp" > last< / span > < span class = "p" > !.< / span > < span class = "n" > val< / span > < span class = "p" > ==< / span > < span class = "mi" > 7< / span >
< a id = "__codelineno-52-4" name = "__codelineno-52-4" href = "#__codelineno-52-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-5" name = "__codelineno-52-5" href = "#__codelineno-52-5" > < / a >
< a id = "__codelineno-52-6" name = "__codelineno-52-6" href = "#__codelineno-52-6" > < / a > < span class = "cm" > /* 记录解 */< / span >
< a id = "__codelineno-52-7" name = "__codelineno-52-7" href = "#__codelineno-52-7" > < / a > < span class = "kd" > func< / span > < span class = "nf" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / 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 = "n" > TreeNode< / span > < span class = "p" > ]])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-8" name = "__codelineno-52-8" href = "#__codelineno-52-8" > < / a > < span class = "n" > res< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-9" name = "__codelineno-52-9" href = "#__codelineno-52-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-10" name = "__codelineno-52-10" href = "#__codelineno-52-10" > < / a >
< a id = "__codelineno-52-11" name = "__codelineno-52-11" href = "#__codelineno-52-11" > < / a > < span class = "cm" > /* 判断在当前状态下，该选择是否合法 */< / span >
< a id = "__codelineno-52-12" name = "__codelineno-52-12" href = "#__codelineno-52-12" > < / a > < span class = "kd" > func< / span > < span class = "nf" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ?)< / span > < span class = "p" > -> < / span > < span class = "nb" > Bool< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-13" name = "__codelineno-52-13" href = "#__codelineno-52-13" > < / a > < span class = "n" > choice< / span > < span class = "o" > !=< / span > < span class = "kc" > nil< / span > < span class = "o" > & & < / span > < span class = "n" > choice< / span > < span class = "p" > !.< / span > < span class = "n" > val< / span > < span class = "o" > !=< / span > < span class = "mi" > 3< / span >
< a id = "__codelineno-52-14" name = "__codelineno-52-14" href = "#__codelineno-52-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-15" name = "__codelineno-52-15" href = "#__codelineno-52-15" > < / a >
< a id = "__codelineno-52-16" name = "__codelineno-52-16" href = "#__codelineno-52-16" > < / a > < span class = "cm" > /* 更新状态 */< / span >
< a id = "__codelineno-52-17" name = "__codelineno-52-17" href = "#__codelineno-52-17" > < / a > < span class = "kd" > func< / span > < span class = "nf" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-18" name = "__codelineno-52-18" href = "#__codelineno-52-18" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-19" name = "__codelineno-52-19" href = "#__codelineno-52-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-20" name = "__codelineno-52-20" href = "#__codelineno-52-20" > < / a >
< a id = "__codelineno-52-21" name = "__codelineno-52-21" href = "#__codelineno-52-21" > < / a > < span class = "cm" > /* 恢复状态 */< / span >
< a id = "__codelineno-52-22" name = "__codelineno-52-22" href = "#__codelineno-52-22" > < / a > < span class = "kd" > func< / span > < span class = "nf" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > TreeNode< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-23" name = "__codelineno-52-23" href = "#__codelineno-52-23" > < / a > < span class = "n" > state< / span > < span class = "p" > .< / span > < span class = "bp" > removeLast< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-52-24" name = "__codelineno-52-24" href = "#__codelineno-52-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-25" name = "__codelineno-52-25" href = "#__codelineno-52-25" > < / a >
< a id = "__codelineno-52-26" name = "__codelineno-52-26" href = "#__codelineno-52-26" > < / a > < span class = "cm" > /* 回溯算法：例题三 */< / span >
< a id = "__codelineno-52-27" name = "__codelineno-52-27" href = "#__codelineno-52-27" > < / a > < span class = "kd" > func< / span > < span class = "nf" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / span > < span class = "p" > ],< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > TreeNode< / 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 = "n" > TreeNode< / span > < span class = "p" > ]])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-28" name = "__codelineno-52-28" href = "#__codelineno-52-28" > < / a > < span class = "c1" > // 检查是否为解< / span >
< a id = "__codelineno-52-29" name = "__codelineno-52-29" href = "#__codelineno-52-29" > < / a > < span class = "k" > if< / span > < span class = "n" > isSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "n" > state< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-30" name = "__codelineno-52-30" href = "#__codelineno-52-30" > < / a > < span class = "n" > recordSolution< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "n" > state< / 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-52-31" name = "__codelineno-52-31" href = "#__codelineno-52-31" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-52-32" name = "__codelineno-52-32" href = "#__codelineno-52-32" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-33" name = "__codelineno-52-33" href = "#__codelineno-52-33" > < / a > < span class = "c1" > // 遍历所有选择< / span >
< a id = "__codelineno-52-34" name = "__codelineno-52-34" href = "#__codelineno-52-34" > < / a > < span class = "k" > for< / span > < span class = "n" > choice< / span > < span class = "k" > in< / span > < span class = "n" > choices< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-35" name = "__codelineno-52-35" href = "#__codelineno-52-35" > < / a > < span class = "c1" > // 剪枝：检查选择是否合法< / span >
< a id = "__codelineno-52-36" name = "__codelineno-52-36" href = "#__codelineno-52-36" > < / a > < span class = "k" > if< / span > < span class = "n" > isValid< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-52-37" name = "__codelineno-52-37" href = "#__codelineno-52-37" > < / a > < span class = "c1" > // 尝试：做出选择，更新状态< / span >
< a id = "__codelineno-52-38" name = "__codelineno-52-38" href = "#__codelineno-52-38" > < / a > < span class = "n" > makeChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-39" name = "__codelineno-52-39" href = "#__codelineno-52-39" > < / a > < span class = "c1" > // 进行下一轮选择< / span >
< a id = "__codelineno-52-40" name = "__codelineno-52-40" href = "#__codelineno-52-40" > < / a > < span class = "n" > backtrack< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choices< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "n" > choice< / span > < span class = "p" > .< / span > < span class = "kr" > left< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > .< / span > < span class = "kr" > right< / span > < span class = "p" > ].< / span > < span class = "n" > compactMap< / span > < span class = "p" > {< / span > < span class = "nv" > $0< / 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-52-41" name = "__codelineno-52-41" href = "#__codelineno-52-41" > < / a > < span class = "c1" > // 回退：撤销选择，恢复到之前的状态< / span >
< a id = "__codelineno-52-42" name = "__codelineno-52-42" href = "#__codelineno-52-42" > < / a > < span class = "n" > undoChoice< / span > < span class = "p" > (< / span > < span class = "n" > state< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > state< / span > < span class = "p" > ,< / span > < span class = "n" > choice< / span > < span class = "p" > :< / span > < span class = "n" > choice< / span > < span class = "p" > )< / span >
< a id = "__codelineno-52-43" name = "__codelineno-52-43" href = "#__codelineno-52-43" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-44" name = "__codelineno-52-44" href = "#__codelineno-52-44" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-52-45" name = "__codelineno-52-45" href = "#__codelineno-52-45" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-53-1" name = "__codelineno-53-1" href = "#__codelineno-53-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > isSolution< / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-2" name = "__codelineno-53-2" href = "#__codelineno-53-2" > < / a >
< a id = "__codelineno-53-3" name = "__codelineno-53-3" href = "#__codelineno-53-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > recordSolution< / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-4" name = "__codelineno-53-4" href = "#__codelineno-53-4" > < / a >
< a id = "__codelineno-53-5" name = "__codelineno-53-5" href = "#__codelineno-53-5" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > isValid< / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-6" name = "__codelineno-53-6" href = "#__codelineno-53-6" > < / a >
< a id = "__codelineno-53-7" name = "__codelineno-53-7" href = "#__codelineno-53-7" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > makeChoice< / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-8" name = "__codelineno-53-8" href = "#__codelineno-53-8" > < / a >
< a id = "__codelineno-53-9" name = "__codelineno-53-9" href = "#__codelineno-53-9" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > undoChoice< / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-10" name = "__codelineno-53-10" href = "#__codelineno-53-10" > < / a >
< a id = "__codelineno-53-11" name = "__codelineno-53-11" href = "#__codelineno-53-11" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > backtrack< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > preorder_traversal_iii_template.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-54-1" name = "__codelineno-54-1" href = "#__codelineno-54-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > isSolution< / span > < span class = "p" > }< / span >
< a id = "__codelineno-54-2" name = "__codelineno-54-2" href = "#__codelineno-54-2" > < / a >
< a id = "__codelineno-54-3" name = "__codelineno-54-3" href = "#__codelineno-54-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > recordSolution< / span > < span class = "p" > }< / span >
< a id = "__codelineno-54-4" name = "__codelineno-54-4" href = "#__codelineno-54-4" > < / a >
< a id = "__codelineno-54-5" name = "__codelineno-54-5" href = "#__codelineno-54-5" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > isValid< / span > < span class = "p" > }< / span >
< a id = "__codelineno-54-6" name = "__codelineno-54-6" href = "#__codelineno-54-6" > < / a >
< a id = "__codelineno-54-7" name = "__codelineno-54-7" href = "#__codelineno-54-7" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > makeChoice< / span > < span class = "p" > }< / span >
< a id = "__codelineno-54-8" name = "__codelineno-54-8" href = "#__codelineno-54-8" > < / a >
< a id = "__codelineno-54-9" name = "__codelineno-54-9" href = "#__codelineno-54-9" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > undoChoice< / span > < span class = "p" > }< / span >
< a id = "__codelineno-54-10" name = "__codelineno-54-10" href = "#__codelineno-54-10" > < / a >
< a id = "__codelineno-54-11" name = "__codelineno-54-11" href = "#__codelineno-54-11" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > backtrack< / span > < span class = "p" > }< / span >
2023-04-16 04:55:58 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-05-10 19:38:29 +08:00
< p > 相较于基于前序遍历的实现代码，基于回溯算法框架的实现代码虽然显得啰嗦，但通用性更好。实际上，< strong > 所有回溯问题都可以在该框架下解决< / strong > 。我们需要根据具体问题来定义 < code > state< / code > 和 < code > choices< / code > ，并实现框架中的各个方法。< / p >
2023-07-11 19:21:38 +08:00
< h2 id = "1215" > 12.1.5. 优势与局限性< a class = "headerlink" href = "#1215" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 回溯算法本质上是一种深度优先搜索算法，它尝试所有可能的解决方案直到找到满足条件的解。这种方法的优势在于它能够找到所有可能的解决方案，而且在合理的剪枝操作下，具有很高的效率。< / p >
< p > 然而，在处理大规模或者复杂问题时，< strong > 回溯算法的运行效率可能难以接受< / strong > 。< / p >
< ul >
< li > 在最坏的情况下，回溯算法需要遍历解空间的所有可能解，所需时间很长。例如，求解 < span class = "arithmatex" > \(n\)< / span > 皇后问题的时间复杂度可以达到 < span class = "arithmatex" > \(O(n!)\)< / span > 。< / li >
< li > 在每一次递归调用时，都需要保存当前的状态（例如选择路径、用于剪枝的辅助变量等），对于深度很大的递归，空间需求可能会变得非常大。< / li >
< / ul >
< p > 即便如此，< strong > 回溯算法仍然是某些搜索问题和约束满足问题的最佳解决方案< / strong > 。对于这些问题，由于无法预测哪些选择可生成有效的解，因此我们必须对所有可能的选择进行遍历。在这种情况下，< strong > 关键是如何进行效率优化< / strong > ： < / p >
< ul >
< li > 上文介绍过的剪枝是一种常用的优化方法。它可以避免搜索那些肯定不会产生有效解的路径，从而节省时间和空间。< / li >
< li > 另一个常用的优化方法是加入「启发式搜索 Heuristic Search」策略， ， < / li >
< / ul >
< h2 id = "1216" > 12.1.6. 典型例题< a class = "headerlink" href = "#1216" title = "Permanent link" > ¶ < / a > < / h2 >
2023-04-16 04:55:58 +08:00
< p > < strong > 搜索问题< / strong > ：这类问题的目标是找到满足特定条件的解决方案。< / p >
< ul >
< li > 全排列问题：给定一个集合，求出其所有可能的排列组合。< / li >
< li > 子集和问题：给定一个集合和一个目标和，找到集合中所有和为目标和的子集。< / li >
< li > 汉诺塔问题：给定三个柱子和一系列大小不同的圆盘，要求将所有圆盘从一个柱子移动到另一个柱子，每次只能移动一个圆盘，且不能将大圆盘放在小圆盘上。< / li >
< / ul >
< p > < strong > 约束满足问题< / strong > ：这类问题的目标是找到满足所有约束条件的解。< / p >
< ul >
< li > < span class = "arithmatex" > \(n\)< / span > 皇后：在 < span class = "arithmatex" > \(n \times n\)< / span > 的棋盘上放置 < span class = "arithmatex" > \(n\)< / span > 个皇后，使得它们互不攻击。< / li >
< li > 数独：在 < span class = "arithmatex" > \(9 \times 9\)< / span > 的网格中填入数字 < span class = "arithmatex" > \(1\)< / span > ~ < span class = "arithmatex" > \(9\)< / span > ，使得每行、每列和每个 < span class = "arithmatex" > \(3 \times 3\)< / span > 子网格中的数字不重复。< / li >
< li > 图着色问题：给定一个无向图，用最少的颜色给图的每个顶点着色，使得相邻顶点颜色不同。< / li >
< / ul >
< p > < strong > 组合优化问题< / strong > ：这类问题的目标是在一个组合空间中找到满足某些条件的最优解。< / p >
< ul >
< li > 0-1 背包问题：给定一组物品和一个背包，每个物品有一定的价值和重量，要求在背包容量限制内，选择物品使得总价值最大。< / li >
< li > 旅行商问题：在一个图中，从一个点出发，访问所有其他点恰好一次后返回起点，求最短路径。< / li >
< li > 最大团问题：给定一个无向图，找到最大的完全子图，即子图中的任意两个顶点之间都有边相连。< / li >
< / ul >
2023-06-22 00:23:01 +08:00
< p > 请注意， < / p >
2023-04-16 04:55:58 +08:00
< 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"
2023-04-16 04:55:58 +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 >
2023-04-16 16:40:06 +08:00
< button type = "button" class = "md-top md-icon" data-md-component = "top" hidden >
2023-04-16 04:55:58 +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
2023-04-16 16:40:06 +08:00
< / button >
2023-04-16 04:55:58 +08:00
< / main >
< footer class = "md-footer" >
< nav class = "md-footer__inner md-grid" aria-label = "页脚" >
2023-06-02 01:35:09 +08:00
< a href = "../" class = "md-footer__link md-footer__link--prev" aria-label = "上一页: 12. &nbsp; 回溯" rel = "prev" >
2023-04-16 04:55:58 +08:00
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / div >
< div class = "md-footer__title" >
2023-04-16 16:40:06 +08:00
< span class = "md-footer__direction" >
上一页
< / span >
2023-04-16 04:55:58 +08:00
< div class = "md-ellipsis" >
2023-06-02 01:35:09 +08:00
12. 回溯
2023-04-16 04:55:58 +08:00
< / div >
< / div >
< / a >
2023-06-02 01:35:09 +08:00
< a href = "../permutations_problem/" class = "md-footer__link md-footer__link--next" aria-label = "下一页: 12.2. &nbsp; 全排列问题" rel = "next" >
2023-04-16 04:55:58 +08:00
< div class = "md-footer__title" >
2023-04-16 16:40:06 +08:00
< span class = "md-footer__direction" >
下一页
< / span >
2023-04-16 04:55:58 +08:00
< div class = "md-ellipsis" >
2023-06-02 01:35:09 +08:00
12.2. 全排列问题
2023-04-16 04:55:58 +08:00
< / div >
< / div >
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z" / > < / svg >
< / div >
< / a >
< / nav >
< 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" >
2023-04-16 16:40:06 +08:00
< 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 >
2023-04-16 04:55:58 +08:00
< / a >
< a href = "https://twitter.com/krahets" target = "_blank" rel = "noopener" title = "twitter.com" class = "md-social__link" >
2023-04-16 16:40:06 +08:00
< 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 >
2023-04-16 04:55:58 +08:00
< / a >
< a href = "https://leetcode.cn/u/jyd/" target = "_blank" rel = "noopener" title = "leetcode.cn" class = "md-social__link" >
2023-04-16 16:40:06 +08:00
< 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 >
2023-04-16 04:55:58 +08:00
< / a >
< / div >
< / div >
< / div >
< / footer >
< / div >
< div class = "md-dialog" data-md-component = "dialog" >
< div class = "md-dialog__inner md-typeset" > < / div >
< / div >
2023-06-30 04:49:34 +08:00
< script id = "__config" type = "application/json" > { "base" : "../.." , "features" : [ "content.action.edit" , "content.code.annotate" , "content.code.copy" , "content.tabs.link" , "content.tooltips" , "navigation.indexes" , "navigation.top" , "navigation.footer" , "navigation.tracking" , "search.highlight" , "search.share" , "search.suggest" , "toc.follow" ] , "search" : "../../assets/javascripts/workers/search.208ed371.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 >
2023-04-16 04:55:58 +08:00
2023-05-31 01:03:26 +08:00
< script src = "../../assets/javascripts/bundle.fac441b0.min.js" > < / script >
2023-04-16 04:55:58 +08:00
< script src = "../../javascripts/mathjax.js" > < / script >
< script src = "https://polyfill.io/v3/polyfill.min.js?features=es6" > < / script >
< script src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" > < / script >
< / body >
< / html >
