2023-12-22 00:01:12 +08:00
<!doctype html>
< html lang = "en" class = "no-js" >
< head >
< meta charset = "utf-8" >
< meta name = "viewport" content = "width=device-width,initial-scale=1" >
< meta name = "description" content = "Data Structures and Algorithms Crash Course with Animated Illustrations and Off-the-Shelf Code" >
2024-02-07 21:39:15 +08:00
< meta name = "author" content = "krahets" >
2023-12-22 00:01:12 +08:00
< link rel = "canonical" href = "https://www.hello-algo.com/en/chapter_introduction/" >
< link rel = "prev" href = "../chapter_preface/summary/" >
< link rel = "next" href = "algorithms_are_everywhere/" >
< link rel = "icon" href = "../assets/images/favicon.png" >
2024-01-25 21:09:11 +08:00
< meta name = "generator" content = "mkdocs-1.5.3, mkdocs-material-9.5.5" >
2023-12-22 00:01:12 +08:00
2024-04-06 03:02:26 +08:00
< title > Chapter 1. < / title >
2023-12-22 00:01:12 +08:00
< link rel = "stylesheet" href = "../assets/stylesheets/main.50c56a3b.min.css" >
< link rel = "stylesheet" href = "../assets/stylesheets/palette.06af60db.min.css" >
< link rel = "preconnect" href = "https://fonts.gstatic.com" crossorigin >
2024-01-12 01:01:43 +08:00
< link rel = "stylesheet" href = "https://fonts.googleapis.com/css?family=Roboto:300,300i,400,400i,700,700i%7CRoboto+Mono:400,400i,700,700i&display=fallback" >
< style > : root { --md-text-font : "Roboto" ; --md-code-font : "Roboto Mono" } < / style >
2023-12-22 00:01:12 +08:00
< 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 >
< link href = "../assets/stylesheets/glightbox.min.css" rel = "stylesheet" / > < style >
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
< / style > < script src = "../assets/javascripts/glightbox.min.js" > < / script > < / head >
2024-02-08 03:34:53 +08:00
< body dir = "ltr" data-md-color-scheme = "default" data-md-color-primary = "white" data-md-color-accent = "teal" >
2023-12-22 00:01:12 +08:00
< 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" >
2023-12-22 04:04:47 +08:00
< a href = "#chapter-1-introduction-to-algorithms" class = "md-skip" >
2023-12-22 00:01:12 +08:00
Skip to content
< / a >
< / div >
< div data-md-component = "announce" >
2024-02-23 17:03:55 +08:00
< aside class = "md-banner" >
< div class = "md-banner__inner md-grid md-typeset" >
< button class = "md-banner__button md-icon" aria-label = "Don't show this again" >
< 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 >
2024-02-23 17:59:37 +08:00
< div class = "banner-svg" >
< svg xmlns = "http://www.w3.org/2000/svg"
viewBox="0 0 512 512"><!-- !Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2024 Fonticons, Inc. -->
< path
d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
< / svg >
2024-04-06 04:00:51 +08:00
< span > The paper book (Chinese version) published. Please visit < a href = "/chapter_paperbook/" > this link< / a > for more details.< / span >
2024-02-23 17:59:37 +08:00
< / div >
2024-02-23 17:03:55 +08:00
< / div >
< script > var content , el = document . querySelector ( "[data-md-component=announce]" ) ; el && ( content = el . querySelector ( ".md-typeset" ) , _ _md _hash ( content . innerHTML ) === _ _md _get ( "__announce" ) && ( el . hidden = ! 0 ) ) < / script >
< / aside >
2023-12-22 00:01:12 +08:00
< / div >
< header class = "md-header md-header--shadow" data-md-component = "header" >
< nav class = "md-header__inner md-grid" aria-label = "Header" >
< a href = ".." title = "Hello Algo" class = "md-header__button md-logo" aria-label = "Hello Algo" data-md-component = "logo" >
< img src = "../assets/images/logo.svg" 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 Algo
< / span >
< / div >
< div class = "md-header__topic" data-md-component = "header-topic" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 1. Introduction to algorithms
2023-12-22 00:01:12 +08:00
< / span >
< / div >
< / div >
< / div >
< form class = "md-header__option" data-md-component = "palette" >
2024-02-08 03:34:53 +08:00
< input class = "md-option" data-md-color-media = "" data-md-color-scheme = "default" data-md-color-primary = "white" data-md-color-accent = "teal" aria-label = "Dark mode" type = "radio" name = "__palette" id = "__palette_0" >
2023-12-22 00:01:12 +08:00
2024-02-08 03:34:53 +08:00
< label class = "md-header__button md-icon" title = "Dark mode" for = "__palette_1" hidden >
2023-12-22 00:01:12 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z" / > < / svg >
< / label >
2024-02-08 03:34:53 +08:00
< input class = "md-option" data-md-color-media = "" data-md-color-scheme = "slate" data-md-color-primary = "black" data-md-color-accent = "teal" aria-label = "Light mode" type = "radio" name = "__palette" id = "__palette_1" >
2023-12-22 00:01:12 +08:00
2024-02-08 03:34:53 +08:00
< label class = "md-header__button md-icon" title = "Light mode" for = "__palette_0" hidden >
2023-12-22 00:01:12 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z" / > < / svg >
< / label >
< / form >
< script > var media , input , key , value , palette = _ _md _get ( "__palette" ) ; if ( palette && palette . color ) { "(prefers-color-scheme)" === palette . color . media && ( media = matchMedia ( "(prefers-color-scheme: light)" ) , input = document . querySelector ( media . matches ? "[data-md-color-media='(prefers-color-scheme: light)']" : "[data-md-color-media='(prefers-color-scheme: dark)']" ) , palette . color . media = input . getAttribute ( "data-md-color-media" ) , palette . color . scheme = input . getAttribute ( "data-md-color-scheme" ) , palette . color . primary = input . getAttribute ( "data-md-color-primary" ) , palette . color . accent = input . getAttribute ( "data-md-color-accent" ) ) ; for ( [ key , value ] of Object . entries ( palette . color ) ) document . body . setAttribute ( "data-md-color-" + key , value ) } < / script >
< div class = "md-header__option" >
< div class = "md-select" >
< button class = "md-header__button md-icon" aria-label = "Select language" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12.87 15.07-2.54-2.51.03-.03A17.52 17.52 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z" / > < / svg >
< / button >
< div class = "md-select__inner" >
< ul class = "md-select__list" >
< li class = "md-select__item" >
< a href = "/" hreflang = "zh" class = "md-select__link" >
2024-04-06 03:02:26 +08:00
简体中文
< / a >
< / li >
< li class = "md-select__item" >
< a href = "/zh-hant/" hreflang = "zh-Hant" class = "md-select__link" >
繁體中文
2023-12-22 00:01:12 +08:00
< / a >
< / li >
< li class = "md-select__item" >
< a href = "/en/" hreflang = "en" class = "md-select__link" >
English
< / a >
< / li >
< / ul >
< / div >
< / div >
< / div >
< 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 = "Search" placeholder = "Search" 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 = "Search" >
< a href = "javascript:void(0)" class = "md-search__icon md-icon" title = "Share" aria-label = "Share" 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 = "Clear" aria-label = "Clear" 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" >
Initializing search
< / 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 = "Go to repository" class = "md-source" data-md-component = "source" >
< div class = "md-source__icon md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg >
< / 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 = "Navigation" data-md-level = "0" >
< label class = "md-nav__title" for = "__drawer" >
< a href = ".." title = "Hello Algo" class = "md-nav__button md-logo" aria-label = "Hello Algo" data-md-component = "logo" >
< img src = "../assets/images/logo.svg" alt = "logo" >
< / a >
Hello Algo
< / label >
< div class = "md-nav__source" >
< a href = "https://github.com/krahets/hello-algo" title = "Go to repository" class = "md-source" data-md-component = "source" >
< div class = "md-source__icon md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg >
< / div >
< div class = "md-source__repository" >
krahets/hello-algo
< / div >
< / a >
< / div >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_1" >
< div class = "md-nav__link md-nav__container" >
< a href = "../chapter_preface/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z" / > < / svg >
< span class = "md-ellipsis" >
Chapter 0. Preface
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_1" id = "__nav_1_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_1_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_1" >
< span class = "md-nav__icon md-icon" > < / span >
Chapter 0. Preface
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../chapter_preface/about_the_book/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
0.1 About this book
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_preface/suggestions/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
0.2 How to read
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_preface/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
0.3 Summary
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--active md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_2" checked >
< div class = "md-nav__link md-nav__container" >
< a href = "./" class = "md-nav__link md-nav__link--active" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 1. Introduction to algorithms
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< label class = "md-nav__link md-nav__link--active" for = "__nav_2" id = "__nav_2_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_2_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_2" >
< span class = "md-nav__icon md-icon" > < / span >
2024-04-06 03:02:26 +08:00
Chapter 1. Introduction to algorithms
2023-12-22 00:01:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "algorithms_are_everywhere/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
1.1 Algorithms are everywhere
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "what_is_dsa/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
1.2 What is an algorithm
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
1.3 Summary
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_3" >
< div class = "md-nav__link md-nav__container" >
< a href = "../chapter_computational_complexity/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 2. Complexity analysis
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_3" id = "__nav_3_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_3_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_3" >
< span class = "md-nav__icon md-icon" > < / span >
2024-04-06 03:02:26 +08:00
Chapter 2. Complexity analysis
2023-12-22 00:01:12 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../chapter_computational_complexity/performance_evaluation/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
2.1 Algorithm efficiency assessment
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_computational_complexity/iteration_and_recursion/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
2.2 Iteration and recursion
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_computational_complexity/time_complexity/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
2.3 Time complexity
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_computational_complexity/space_complexity/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
2.4 Space complexity
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_computational_complexity/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2.5 Summary
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-27 00:48:07 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_4" >
< div class = "md-nav__link md-nav__container" >
< a href = "../chapter_data_structure/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 3. Data structures
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_4_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
2024-04-06 03:02:26 +08:00
Chapter 3. Data structures
2023-12-27 00:48:07 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../chapter_data_structure/classification_of_data_structure/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
3.1 Classification of data structures
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_data_structure/basic_data_types/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
3.2 Fundamental data types
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_data_structure/number_encoding/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
3.3 Number encoding *
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_data_structure/character_encoding/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
3.4 Character encoding *
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_data_structure/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
3.5 Summary
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" >
< div class = "md-nav__link md-nav__container" >
< a href = "../chapter_array_and_linkedlist/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 4. Array and linked list
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_5_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
2024-04-06 03:02:26 +08:00
Chapter 4. Array and linked list
2023-12-27 00:48:07 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
< span class = "md-ellipsis" >
4.1 Array
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
4.2 Linked list
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
< span class = "md-ellipsis" >
4.3 List
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_array_and_linkedlist/ram_and_cache/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
4.4 Memory and cache
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
4.5 Summary
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2024-01-09 16:00:33 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
< div class = "md-nav__link md-nav__container" >
< a href = "../chapter_stack_and_queue/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 5. Stack and queue
2024-01-09 16:00:33 +08:00
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_6_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
2024-04-06 03:02:26 +08:00
Chapter 5. Stack and queue
2024-01-09 16:00:33 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../chapter_stack_and_queue/stack/" class = "md-nav__link" >
< span class = "md-ellipsis" >
5.1 Stack
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_stack_and_queue/queue/" class = "md-nav__link" >
< span class = "md-ellipsis" >
5.2 Queue
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_stack_and_queue/deque/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
5.3 Double-ended queue
2024-01-09 16:00:33 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_stack_and_queue/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
5.4 Summary
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2024-01-28 22:31:13 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
< div class = "md-nav__link md-nav__container" >
< a href = "../chapter_hashing/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 6. Hash table
2024-01-28 22:31:13 +08:00
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_7_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
2024-04-06 03:02:26 +08:00
Chapter 6. Hash table
2024-01-28 22:31:13 +08:00
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../chapter_hashing/hash_map/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
6.1 Hash table
2024-01-28 22:31:13 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_hashing/hash_collision/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
6.2 Hash collision
2024-01-28 22:31:13 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_hashing/hash_algorithm/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
6.3 Hash algorithm
2024-01-28 22:31:13 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_hashing/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
6.4 Summary
2024-04-02 19:00:08 +08:00
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
< div class = "md-nav__link md-nav__container" >
< a href = "../chapter_tree/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z" / > < / svg >
< span class = "md-ellipsis" >
Chapter 7. Tree
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
Chapter 7. Tree
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../chapter_tree/binary_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.1 Binary Tree
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.2 Binary Tree Traversal
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.3 Array Representation of Tree
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_tree/binary_search_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.4 Binary Search Tree
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_tree/avl_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.5 AVL Tree *
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_tree/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
7.6 Summary
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
< div class = "md-nav__link md-nav__container" >
< a href = "../chapter_heap/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z" / > < / svg >
< span class = "md-ellipsis" >
Chapter 8. Heap
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_9_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_9" >
< span class = "md-nav__icon md-icon" > < / span >
Chapter 8. Heap
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../chapter_heap/heap/" class = "md-nav__link" >
< span class = "md-ellipsis" >
8.1 Heap
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_heap/build_heap/" class = "md-nav__link" >
< span class = "md-ellipsis" >
8.2 Building a Heap
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_heap/top_k/" class = "md-nav__link" >
< span class = "md-ellipsis" >
8.3 Top-k Problem
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_heap/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
8.4 Summary
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
< div class = "md-nav__link md-nav__container" >
< a href = "../chapter_graph/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
< span class = "md-ellipsis" >
Chapter 9. Graph
< / span >
< / a >
< label class = "md-nav__link " for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
Chapter 9. Graph
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../chapter_graph/graph/" class = "md-nav__link" >
< span class = "md-ellipsis" >
9.1 Graph
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_graph/graph_operations/" class = "md-nav__link" >
< span class = "md-ellipsis" >
9.2 Basic Graph Operations
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_graph/graph_traversal/" class = "md-nav__link" >
< span class = "md-ellipsis" >
9.3 Graph Traversal
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../chapter_graph/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
9.4 Summary
2024-01-28 22:31:13 +08:00
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2023-12-22 00:01:12 +08:00
< / 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 = "Table of contents" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
Table of contents
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
2023-12-29 00:57:27 +08:00
< a href = "#chapter-contents" class = "md-nav__link" >
2023-12-22 00:01:12 +08:00
< span class = "md-ellipsis" >
2024-04-07 02:41:57 +08:00
Chapter contents
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-content" data-md-component = "content" >
< article class = "md-content__inner md-typeset" >
<!-- Tags -->
<!-- Actions -->
<!-- Actions -->
<!-- Edit button -->
< a
2024-03-23 03:04:36 +08:00
href="https://github.com/krahets/hello-algo/tree/main/en/docs/chapter_introduction/index.md"
2023-12-22 00:01:12 +08:00
title="Edit this page"
class="md-content__button md-icon"
>
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 512 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z" / > < / svg >
< / a >
<!-- View button -->
<!-- Page content -->
2024-04-06 03:02:26 +08:00
< h1 id = "chapter-1-introduction-to-algorithms" > Chapter 1. Introduction to algorithms< a class = "headerlink" href = "#chapter-1-introduction-to-algorithms" title = "Permanent link" > ¶ < / a > < / h1 >
< p > < a class = "glightbox" href = "../assets/covers/chapter_introduction.jpg" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Introduction to algorithms" class = "cover-image" src = "../assets/covers/chapter_introduction.jpg" / > < / a > < / p >
2023-12-22 00:01:12 +08:00
< div class = "admonition abstract" >
< p class = "admonition-title" > Abstract< / p >
< p > A graceful maiden dances, intertwined with the data, her skirt swaying to the melody of algorithms.< / p >
< p > She invites you to a dance, follow her steps, and enter the world of algorithms full of logic and beauty.< / p >
< / div >
2024-04-07 02:41:57 +08:00
< h2 id = "chapter-contents" > Chapter contents< a class = "headerlink" href = "#chapter-contents" title = "Permanent link" > ¶ < / a > < / h2 >
2023-12-22 00:01:12 +08:00
< ul >
2024-04-07 02:41:57 +08:00
< li > < a href = "algorithms_are_everywhere/" > 1.1 Algorithms are everywhere< / a > < / li >
< li > < a href = "what_is_dsa/" > 1.2 What is an algorithm< / a > < / li >
< li > < a href = "summary/" > 1.3 Summary< / a > < / li >
2023-12-22 00:01:12 +08:00
< / ul >
<!-- Source file information -->
<!-- Was this page helpful? -->
<!-- Previous and next pages link -->
< nav
class="md-footer__inner md-grid"
aria-label="Footer"
>
<!-- Link to previous page -->
< a
href="../chapter_preface/summary/"
class="md-footer__link md-footer__link--prev"
aria-label="Previous: 0.3 Summary"
rel="prev"
>
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / div >
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
Previous
< / span >
< div class = "md-ellipsis" >
0.3 Summary
< / div >
< / div >
< / a >
<!-- Link to next page -->
< a
href="algorithms_are_everywhere/"
class="md-footer__link md-footer__link--next"
2024-04-06 03:02:26 +08:00
aria-label="Next: 1.1 Algorithms are everywhere"
2023-12-22 00:01:12 +08:00
rel="next"
>
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
Next
< / span >
< div class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
1.1 Algorithms are everywhere
2023-12-22 00:01:12 +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 >
<!-- Comment system -->
< h5 align = "center" id = "__comments" > Feel free to drop your insights, questions or suggestions< / h5 >
<!-- Insert generated snippet here -->
< script
src="https://giscus.app/client.js"
data-repo="krahets/hello-algo"
data-repo-id="R_kgDOIXtSqw"
data-category="Announcements"
data-category-id="DIC_kwDOIXtSq84CSZk_"
data-mapping="pathname"
data-strict="1"
data-reactions-enabled="1"
data-emit-metadata="0"
data-input-position="top"
2024-02-08 08:40:29 +08:00
data-theme="light"
2023-12-22 00:01:12 +08:00
data-lang="en"
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_dimmed" : "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_dimmed" : "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 >
< script > var target = document . getElementById ( location . hash . slice ( 1 ) ) ; target && target . name && ( target . checked = target . name . startsWith ( "__tabbed_" ) ) < / script >
< / div >
< button type = "button" class = "md-top md-icon" data-md-component = "top" hidden >
< 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 >
Back to top
< / button >
< / main >
< footer class = "md-footer" >
< nav class = "md-footer__inner md-grid" aria-label = "Footer" >
< a href = "../chapter_preface/summary/" class = "md-footer__link md-footer__link--prev" aria-label = "Previous: 0.3 Summary" >
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / div >
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
Previous
< / span >
< div class = "md-ellipsis" >
0.3 Summary
< / div >
< / div >
< / a >
2024-04-06 03:02:26 +08:00
< a href = "algorithms_are_everywhere/" class = "md-footer__link md-footer__link--next" aria-label = "Next: 1.1 Algorithms are everywhere" >
2023-12-22 00:01:12 +08:00
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
Next
< / span >
< div class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
1.1 Algorithms are everywhere
2023-12-22 00:01:12 +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" >
2024-04-03 04:41:32 +08:00
Copyright © 2022-2024 krahets< br > The website content is licensed under < a href = "https://creativecommons.org/licenses/by-nc-sa/4.0/" > CC BY-NC-SA 4.0< / a >
2023-12-22 00:01:12 +08:00
< / div >
< / div >
< div class = "md-social" >
< a href = "https://github.com/krahets" target = "_blank" rel = "noopener" title = "github.com" class = "md-social__link" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 496 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" / > < / svg >
< / a >
< a href = "https://twitter.com/krahets" target = "_blank" rel = "noopener" title = "twitter.com" class = "md-social__link" >
2024-04-03 15:44:14 +08:00
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 512 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M389.2 48h70.6L305.6 224.2 487 464H345L233.7 318.6 106.5 464H35.8l164.9-188.5L26.8 48h145.6l100.5 132.9L389.2 48zm-24.8 373.8h39.1L151.1 88h-42l255.3 333.8z" / > < / svg >
2023-12-22 00:01:12 +08:00
< / a >
< a href = "https://leetcode.cn/u/jyd/" target = "_blank" rel = "noopener" title = "leetcode.cn" class = "md-social__link" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 640 512" > <!-- ! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc. --> < path d = "M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3l89.3 89.4-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z" / > < / svg >
< / a >
< / div >
< / div >
< / div >
< / footer >
< / div >
< div class = "md-dialog" data-md-component = "dialog" >
< div class = "md-dialog__inner md-typeset" > < / div >
< / div >
2024-02-23 17:03:55 +08:00
< script id = "__config" type = "application/json" > { "base" : ".." , "features" : [ "announce.dismiss" , "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.b8dbb3d2.min.js" , "translations" : { "clipboard.copied" : "Copied to clipboard" , "clipboard.copy" : "Copy to clipboard" , "search.result.more.one" : "1 more on this page" , "search.result.more.other" : "# more on this page" , "search.result.none" : "No matching documents" , "search.result.one" : "1 matching document" , "search.result.other" : "# matching documents" , "search.result.placeholder" : "Type to start searching" , "search.result.term.missing" : "Missing" , "select.version" : "Select version" } } < / script >
2023-12-22 00:01:12 +08:00
2024-01-25 21:09:11 +08:00
< script src = "../assets/javascripts/bundle.c18c5fb9.min.js" > < / script >
2023-12-22 00:01:12 +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 >
< script > document $ . subscribe ( ( ) => { const lightbox = GLightbox ( { "touchNavigation" : true , "loop" : false , "zoomable" : true , "draggable" : false , "openEffect" : "zoom" , "closeEffect" : "zoom" , "slideEffect" : "none" } ) ; } ) < / script > < / body >
< / html >
