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_data_structure/classification_of_data_structure/" >
2023-12-27 00:48:07 +08:00
< link rel = "prev" href = "../" >
< link rel = "next" href = "../basic_data_types/" >
2023-12-22 00:01:12 +08:00
< 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 > 3.1 Classification of data structures - Hello Algo< / 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" >
2023-12-27 00:48:07 +08:00
< a href = "#31-classification-of-data-structures" 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 >
2024-04-11 20:03:24 +08:00
< span > Feel free to engage in Chinese-to-English translation and pull request review! Please visit < a href = "https://github.com/krahets/hello-algo/issues/914" > #914< / a > for 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
3.1 Classification of data structures
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 >
2024-04-11 20:03:24 +08:00
< li class = "md-nav__item md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_1" >
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_hello_algo/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z" / > < / svg >
< span class = "md-ellipsis" >
Before starting
< / span >
< / a >
< / 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 >
Before starting
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< / ul >
< / nav >
< / li >
2023-12-22 00:01:12 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_2" >
2023-12-22 00:01:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_preface/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z" / > < / svg >
< span class = "md-ellipsis" >
Chapter 0. Preface
< / span >
< / a >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_2" id = "__nav_2_label" tabindex = "0" >
2023-12-22 00:01:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +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" >
2023-12-22 00:01:12 +08:00
< 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--nested" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_3" >
2023-12-22 00:01:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_introduction/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
Chapter 1. Encounter with algorithms
2023-12-22 00:01:12 +08:00
< / span >
< / a >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_3" id = "__nav_3_label" tabindex = "0" >
2023-12-22 00:01:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +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" >
2023-12-22 00:01:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
2024-04-11 20:03:24 +08:00
Chapter 1. Encounter with 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 = "../../chapter_introduction/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 = "../../chapter_introduction/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 = "../../chapter_introduction/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" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_4" >
2023-12-22 00:01:12 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_computational_complexity/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 2. Complexity analysis
2023-12-22 00:01:12 +08:00
< / span >
< / a >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
2023-12-22 00:01:12 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +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" >
2023-12-22 00:01:12 +08:00
< 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--active md-nav__item--nested" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_5" checked >
2023-12-27 00:48:07 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "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 >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
2023-12-27 00:48:07 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +08:00
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_5_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_5" >
2023-12-27 00:48:07 +08:00
< 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 md-nav__item--active" >
< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
3.1 Classification of data structures
2023-12-27 00:48:07 +08:00
< / span >
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
< 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 >
< 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" >
< a href = "#311-logical-structure-linear-and-non-linear" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
3.1.1 Logical structure: linear and non-linear
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#312-physical-structure-contiguous-and-dispersed" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
3.1.2 Physical structure: contiguous and dispersed
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "../basic_data_types/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
3.2 Basic data types
2023-12-27 00:48:07 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../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 = "../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 = "../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" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
2023-12-27 00:48:07 +08:00
< 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 >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
2023-12-27 00:48:07 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +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" >
2023-12-27 00:48:07 +08:00
< 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" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
2024-01-09 16:00:33 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_stack_and_queue/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 5. Stack and queue
2024-01-09 16:00:33 +08:00
< / span >
< / a >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
2024-01-09 16:00:33 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +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" >
2024-01-09 16:00:33 +08:00
< 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" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
2024-01-28 22:31:13 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_hashing/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z" / > < / svg >
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 6. Hash table
2024-01-28 22:31:13 +08:00
< / span >
< / a >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
2024-01-28 22:31:13 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +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" >
2024-01-28 22:31:13 +08:00
< 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
< / span >
< / a >
< / li >
< / ul >
< / nav >
< / li >
2024-04-02 19:00:08 +08:00
< li class = "md-nav__item md-nav__item--nested" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
2024-04-02 19:00:08 +08:00
< 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 >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
2024-04-02 19:00:08 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +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" >
2024-04-02 19:00:08 +08:00
< 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" >
2024-04-11 20:03:24 +08:00
7.1 Binary tree
2024-04-02 19:00:08 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
7.2 Binary tree Traversal
2024-04-02 19:00:08 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
7.3 Array Representation of tree
2024-04-02 19:00:08 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
7.4 Binary Search tree
2024-04-02 19:00:08 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
7.5 AVL tree *
2024-04-02 19:00:08 +08:00
< / 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" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
2024-04-02 19:00:08 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_heap/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z" / > < / svg >
< span class = "md-ellipsis" >
Chapter 8. Heap
< / span >
< / a >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
2024-04-02 19:00:08 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +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" >
2024-04-02 19:00:08 +08:00
< 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" >
2024-04-11 20:03:24 +08:00
8.2 Building a heap
2024-04-02 19:00:08 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/top_k/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
8.3 Top-k problem
2024-04-02 19:00:08 +08:00
< / 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" >
2024-04-11 20:03:24 +08:00
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
2024-04-02 19:00:08 +08:00
< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_graph/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
< span class = "md-ellipsis" >
Chapter 9. Graph
< / span >
< / a >
2024-04-11 20:03:24 +08:00
< label class = "md-nav__link " for = "__nav_11" id = "__nav_11_label" tabindex = "0" >
2024-04-02 19:00:08 +08:00
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< / div >
2024-04-11 20:03:24 +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" >
2024-04-02 19:00:08 +08:00
< 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" >
2024-04-11 20:03:24 +08:00
9.2 Basic graph operations
2024-04-02 19:00:08 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
< span class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
9.3 Graph traversal
2024-04-02 19:00:08 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
< span class = "md-ellipsis" >
9.4 Summary
< / 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" >
2023-12-27 00:48:07 +08:00
< a href = "#311-logical-structure-linear-and-non-linear" class = "md-nav__link" >
2023-12-22 00:01:12 +08:00
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
3.1.1 Logical structure: linear and non-linear
2023-12-22 00:01:12 +08:00
< / span >
< / a >
< / li >
< li class = "md-nav__item" >
2023-12-27 00:48:07 +08:00
< a href = "#312-physical-structure-contiguous-and-dispersed" class = "md-nav__link" >
2023-12-22 00:01:12 +08:00
< span class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
3.1.2 Physical structure: contiguous and dispersed
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_data_structure/classification_of_data_structure.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 = "31-classification-of-data-structures" > 3.1 Classification of data structures< a class = "headerlink" href = "#31-classification-of-data-structures" title = "Permanent link" > ¶ < / a > < / h1 >
2024-01-02 15:16:59 +08:00
< p > Common data structures include arrays, linked lists, stacks, queues, hash tables, trees, heaps, and graphs. They can be classified into "logical structure" and "physical structure".< / p >
2024-04-06 03:02:26 +08:00
< h2 id = "311-logical-structure-linear-and-non-linear" > 3.1.1 Logical structure: linear and non-linear< a class = "headerlink" href = "#311-logical-structure-linear-and-non-linear" title = "Permanent link" > ¶ < / a > < / h2 >
2024-01-02 15:16:59 +08:00
< p > < strong > The logical structures reveal the logical relationships between data elements< / strong > . In arrays and linked lists, data are arranged in a specific sequence, demonstrating the linear relationship between data; while in trees, data are arranged hierarchically from the top down, showing the derived relationship between "ancestors" and "descendants"; and graphs are composed of nodes and edges, reflecting the intricate network relationship.< / p >
< p > As shown in the Figure 3-1 , logical structures can be divided into two major categories: "linear" and "non-linear". Linear structures are more intuitive, indicating data is arranged linearly in logical relationships; non-linear structures, conversely, are arranged non-linearly.< / p >
2023-12-22 00:01:12 +08:00
< ul >
2024-04-06 03:02:26 +08:00
< li > < strong > Linear data structures< / strong > : Arrays, Linked Lists, Stacks, Queues, Hash Tables.< / li >
< li > < strong > Non-linear data structures< / strong > : Trees, Heaps, Graphs, Hash Tables.< / li >
2023-12-22 00:01:12 +08:00
< / ul >
2024-04-06 03:02:26 +08:00
< p > < a class = "glightbox" href = "../classification_of_data_structure.assets/classification_logic_structure.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Linear and non-linear data structures" class = "animation-figure" src = "../classification_of_data_structure.assets/classification_logic_structure.png" / > < / a > < / p >
< p align = "center" > Figure 3-1 Linear and non-linear data structures < / p >
2023-12-27 00:48:07 +08:00
< p > Non-linear data structures can be further divided into tree structures and network structures.< / p >
2023-12-22 00:01:12 +08:00
< ul >
2024-04-06 03:02:26 +08:00
< li > < strong > Linear structures< / strong > : Arrays, linked lists, queues, stacks, and hash tables, where elements have a one-to-one sequential relationship.< / li >
< li > < strong > Tree structures< / strong > : Trees, Heaps, Hash Tables, where elements have a one-to-many relationship.< / li >
< li > < strong > Network structures< / strong > : Graphs, where elements have a many-to-many relationships.< / li >
2023-12-22 00:01:12 +08:00
< / ul >
2024-04-06 03:02:26 +08:00
< h2 id = "312-physical-structure-contiguous-and-dispersed" > 3.1.2 Physical structure: contiguous and dispersed< a class = "headerlink" href = "#312-physical-structure-contiguous-and-dispersed" title = "Permanent link" > ¶ < / a > < / h2 >
2024-01-02 15:16:59 +08:00
< p > < strong > During the execution of an algorithm, the data being processed is stored in memory< / strong > . The Figure 3-2 shows a computer memory stick where each black square is a physical memory space. We can think of memory as a vast Excel spreadsheet, with each cell capable of storing a certain amount of data.< / p >
< p > < strong > The system accesses the data at the target location by means of a memory address< / strong > . As shown in the Figure 3-2 , the computer assigns a unique identifier to each cell in the table according to specific rules, ensuring that each memory space has a unique memory address. With these addresses, the program can access the data stored in memory.< / p >
2024-04-06 03:02:26 +08:00
< p > < a class = "glightbox" href = "../classification_of_data_structure.assets/computer_memory_location.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Memory stick, memory spaces, memory addresses" class = "animation-figure" src = "../classification_of_data_structure.assets/computer_memory_location.png" / > < / a > < / p >
< p align = "center" > Figure 3-2 Memory stick, memory spaces, memory addresses < / p >
2023-12-27 00:48:07 +08:00
2023-12-22 00:01:12 +08:00
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
2023-12-27 00:48:07 +08:00
< p > It's worth noting that comparing memory to an Excel spreadsheet is a simplified analogy. The actual working mechanism of memory is more complex, involving concepts like address space, memory management, cache mechanisms, virtual memory, and physical memory.< / p >
2023-12-22 00:01:12 +08:00
< / div >
2024-01-02 15:16:59 +08:00
< p > Memory is a shared resource for all programs. When a block of memory is occupied by one program, it cannot be simultaneously used by other programs. < strong > Therefore, considering memory resources is crucial in designing data structures and algorithms< / strong > . For instance, the algorithm's peak memory usage should not exceed the remaining free memory of the system; if there is a lack of contiguous memory blocks, then the data structure chosen must be able to be stored in non-contiguous memory blocks.< / p >
< p > As illustrated in the Figure 3-3 , < strong > the physical structure reflects the way data is stored in computer memory< / strong > and it can be divided into contiguous space storage (arrays) and non-contiguous space storage (linked lists). The two types of physical structures exhibit complementary characteristics in terms of time efficiency and space efficiency.< / p >
2024-04-06 03:02:26 +08:00
< p > < a class = "glightbox" href = "../classification_of_data_structure.assets/classification_phisical_structure.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Contiguous space storage and dispersed space storage" class = "animation-figure" src = "../classification_of_data_structure.assets/classification_phisical_structure.png" / > < / a > < / p >
< p align = "center" > Figure 3-3 Contiguous space storage and dispersed space storage < / p >
2023-12-27 00:48:07 +08:00
2024-01-02 15:16:59 +08:00
< p > < strong > It is worth noting that all data structures are implemented based on arrays, linked lists, or a combination of both< / strong > . For example, stacks and queues can be implemented using either arrays or linked lists; while implementations of hash tables may involve both arrays and linked lists.
- < strong > Array-based implementations< / strong > : Stacks, Queues, Hash Tables, Trees, Heaps, Graphs, Matrices, Tensors (arrays with dimensions < span class = "arithmatex" > \(\geq 3\)< / span > ).
- < strong > Linked-list-based implementations< / strong > : Stacks, Queues, Hash Tables, Trees, Heaps, Graphs, etc.< / p >
2023-12-27 00:48:07 +08:00
< p > Data structures implemented based on arrays are also called “Static Data Structures,” meaning their length cannot be changed after initialization. Conversely, those based on linked lists are called “Dynamic Data Structures,” which can still adjust their size during program execution.< / p >
2023-12-22 00:01:12 +08:00
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
2024-01-02 15:16:59 +08:00
< p > If you find it challenging to comprehend the physical structure, it is recommended that you read the next chapter, "Arrays and Linked Lists," and revisit this section later.< / p >
2023-12-22 00:01:12 +08:00
< / div >
<!-- 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 -->
2023-12-27 00:48:07 +08:00
< a
href="../"
class="md-footer__link md-footer__link--prev"
2024-04-06 03:02:26 +08:00
aria-label="Previous: Chapter 3. & nbsp; Data structures"
2023-12-27 00:48:07 +08:00
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" >
2024-04-06 03:02:26 +08:00
Chapter 3. Data structures
2023-12-27 00:48:07 +08:00
< / div >
< / div >
< / a >
2023-12-22 00:01:12 +08:00
<!-- Link to next page -->
2023-12-27 00:48:07 +08:00
< a
href="../basic_data_types/"
class="md-footer__link md-footer__link--next"
2024-04-11 20:03:24 +08:00
aria-label="Next: 3.2 Basic data types"
2023-12-27 00:48:07 +08:00
rel="next"
>
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
Next
< / span >
< div class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
3.2 Basic data types
2023-12-27 00:48:07 +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 >
2023-12-22 00:01:12 +08:00
< / nav >
<!-- Comment system -->
2023-12-27 00:48:07 +08:00
< 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"
2023-12-27 00:48:07 +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 >
2023-12-22 00:01:12 +08:00
< / 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" >
2023-12-27 00:48:07 +08:00
< nav class = "md-footer__inner md-grid" aria-label = "Footer" >
2024-04-06 03:02:26 +08:00
< a href = "../" class = "md-footer__link md-footer__link--prev" aria-label = "Previous: Chapter 3. &nbsp; Data structures" >
2023-12-27 00:48:07 +08:00
< div class = "md-footer__button md-icon" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z" / > < / svg >
< / div >
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
Previous
< / span >
< div class = "md-ellipsis" >
2024-04-06 03:02:26 +08:00
Chapter 3. Data structures
2023-12-27 00:48:07 +08:00
< / div >
< / div >
< / a >
2024-04-11 20:03:24 +08:00
< a href = "../basic_data_types/" class = "md-footer__link md-footer__link--next" aria-label = "Next: 3.2 Basic data types" >
2023-12-27 00:48:07 +08:00
< div class = "md-footer__title" >
< span class = "md-footer__direction" >
Next
< / span >
< div class = "md-ellipsis" >
2024-04-11 20:03:24 +08:00
3.2 Basic data types
2023-12-27 00:48:07 +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 >
2023-12-22 00:01:12 +08:00
< div class = "md-footer-meta md-typeset" >
< div class = "md-footer-meta__inner md-grid" >
< div class = "md-copyright" >
< div class = "md-copyright__highlight" >
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 >
