2023-11-24 16:55:55 +01:00
<!doctype html>
2023-12-28 18:55:58 +01:00
< html lang = "en" dir = "ltr" class = "docs-wrapper plugin-docs plugin-id-algorithms docs-version-current docs-doc-page docs-doc-id-recursion/2023-08-17-pyramid-slide-down/pyramid-slide-down" data-has-hydrated = "false" >
2023-11-24 16:55:55 +01:00
< head >
< meta charset = "UTF-8" >
2024-07-11 23:59:04 +02:00
< meta name = "generator" content = "Docusaurus v3.0.0" >
2023-11-24 16:55:55 +01:00
< title data-rh = "true" > Introduction to dynamic programming | mf< / title > < meta data-rh = "true" name = "viewport" content = "width=device-width,initial-scale=1" > < meta data-rh = "true" name = "twitter:card" content = "summary_large_image" > < meta data-rh = "true" property = "og:url" content = "https://blog.mfocko.xyz/algorithms/recursion/pyramid-slide-down/" > < meta data-rh = "true" property = "og:locale" content = "en" > < meta data-rh = "true" name = "docusaurus_locale" content = "en" > < meta data-rh = "true" name = "docsearch:language" content = "en" > < meta data-rh = "true" name = "docusaurus_version" content = "current" > < meta data-rh = "true" name = "docusaurus_tag" content = "docs-algorithms-current" > < meta data-rh = "true" name = "docsearch:version" content = "current" > < meta data-rh = "true" name = "docsearch:docusaurus_tag" content = "docs-algorithms-current" > < meta data-rh = "true" property = "og:title" content = "Introduction to dynamic programming | mf" > < meta data-rh = "true" name = "description" content = "Solving a problem in different ways .
">< meta data-rh = "true" property = "og:description" content = "Solving a problem in different ways .
">< link data-rh = "true" rel = "icon" href = "/img/favicon.ico" > < link data-rh = "true" rel = "canonical" href = "https://blog.mfocko.xyz/algorithms/recursion/pyramid-slide-down/" > < link data-rh = "true" rel = "alternate" href = "https://blog.mfocko.xyz/algorithms/recursion/pyramid-slide-down/" hreflang = "en" > < link data-rh = "true" rel = "alternate" href = "https://blog.mfocko.xyz/algorithms/recursion/pyramid-slide-down/" hreflang = "x-default" > < link data-rh = "true" rel = "preconnect" href = "https://0VXRFPR4QF-dsn.algolia.net" crossorigin = "anonymous" > < link rel = "search" type = "application/opensearchdescription+xml" title = "mf" href = "/opensearch.xml" >
< link rel = "alternate" type = "application/rss+xml" href = "/blog/rss.xml" title = "mf RSS Feed" >
< link rel = "alternate" type = "application/atom+xml" href = "/blog/atom.xml" title = "mf Atom Feed" >
< link rel = "alternate" type = "application/json" href = "/blog/feed.json" title = "mf JSON Feed" >
2024-07-11 23:59:04 +02:00
< link rel = "stylesheet" href = "https://cdn.jsdelivr.net/npm/katex@0.13.24/dist/katex.min.css" integrity = "sha384-odtC+0UGzzFL/6PNoE8rX/SPcQDXBJ+uRepguP4QkPCm2LBxH3FA3y+fKSiJ+AmM" crossorigin = "anonymous" > < link rel = "stylesheet" href = "/assets/css/styles.b9f07789.css" >
< script src = "/assets/js/runtime~main.7784bcb4.js" defer = "defer" > < / script >
< script src = "/assets/js/main.93ba00d4.js" defer = "defer" > < / script >
2023-11-24 16:55:55 +01:00
< / head >
< body class = "navigation-with-keyboard" >
2024-01-03 15:14:53 +01:00
< script > ! function ( ) { function t ( t ) { document . documentElement . setAttribute ( "data-theme" , t ) } var e = function ( ) { try { return new URLSearchParams ( window . location . search ) . get ( "docusaurus-theme" ) } catch ( t ) { } } ( ) || function ( ) { try { return localStorage . getItem ( "theme" ) } catch ( t ) { } } ( ) ; t ( null !== e ? e : "light" ) } ( ) , function ( ) { try { const c = new URLSearchParams ( window . location . search ) . entries ( ) ; for ( var [ t , e ] of c ) if ( t . startsWith ( "docusaurus-data-" ) ) { var a = t . replace ( "docusaurus-data-" , "data-" ) ; document . documentElement . setAttribute ( a , e ) } } catch ( t ) { } } ( ) < / script > < div id = "__docusaurus" > < div role = "region" aria-label = "Skip to main content" > < a class = "skipToContent_fXgn" href = "#__docusaurus_skipToContent_fallback" > Skip to main content< / a > < / div > < nav aria-label = "Main" class = "navbar navbar--fixed-top" > < div class = "navbar__inner" > < div class = "navbar__items" > < button aria-label = "Toggle navigation bar" aria-expanded = "false" class = "navbar__toggle clean-btn" type = "button" > < svg width = "30" height = "30" viewBox = "0 0 30 30" aria-hidden = "true" > < path stroke = "currentColor" stroke-linecap = "round" stroke-miterlimit = "10" stroke-width = "2" d = "M4 7h22M4 15h22M4 23h22" > < / path > < / svg > < / button > < a class = "navbar__brand" href = "/" > < b class = "navbar__title text--truncate" > mf< / b > < / a > < div class = "navbar__item dropdown dropdown--hoverable" > < a href = "#" aria-haspopup = "true" aria-expanded = "false" role = "button" class = "navbar__link" > Additional FI MU materials< / a > < ul class = "dropdown__menu" > < li > < a aria-current = "page" class = "dropdown__link dropdown__link--active" href = "/algorithms/" > Algorithms< / a > < / li > < li > < a class = "dropdown__link" href = "/c/" > C< / a > < / li > < li > < a class = "dropdown__link" href = "/cpp/" > C++< / a > < / li > < / ul > < / div > < a class = "navbar__item navbar__link" href = "/contributions/" > Contributions< / a > < a class = "navbar__item navbar__link" href = "/talks/" > Talks< / a > < / div > < div class = "navbar__items navbar__items--right" > < a class = "navbar__item navbar__link" href = "/blog/" > Blog< / a > < div class = "toggle_vylO colorModeToggle_DEke" > < button class = "clean-btn toggleButton_gllP toggleButtonDisabled_aARS" type = "button" disabled = "" title = "Switch between dark and light mode (currently light mode)" aria-label = "Switch between dark and light mode (currently light mode)" aria-live = "polite" > < svg viewBox = "0 0 24 24" width = "24" height = "24" class = "lightToggleIcon_pyhR" > < path fill = "currentColor" d = "M12,9c1.65,0,3,1.35,3,3s-1.35,3-3,3s-3-1.35-3-3S10.35,9,12,9 M12,7c-2.76,0-5,2.24-5,5s2.24,5,5,5s5-2.24,5-5 S14.76,7,12,7L12,7z M2,13l2,0c0.55,0,1-0.45,1-1s-0.45-1-1-1l-2,0c-0.55,0-1,0.45-1,1S1.45,13,2,13z M20,13l2,0c0.55,0,1-0.45,1-1 s-0.45-1-1-1l-2,0c-0.55,0-1,0.45-1,1S19.45,13,20,13z M11,2v2c0,0.55,0.45,1,1,1s1-0.45,1-1V2c0-0.55-0.45-1-1-1S11,1.45,11,2z M11,20v2c0,0.55,0.45,1,1,1s1-0.45,1-1v-2c0-0.55-0.45-1-1-1C11.45,19,11,19.45,11,20z M5.99,4.58c-0.39-0.39-1.03-0.39-1.41,0 c-0.39,0.39-0.39,1.03,0,1.41l1.06,1.06c0.39,0.39,1.03,0.39,1.41,0s0.39-1.03,0-1.41L5.99,4.58z M18.36,16.95 c-0.39-0.39-1.03-0.39-1.41,0c-0.39,0.39-0.39,1.03,0,1.41l1.06,1.06c0.39,0.39,1.03,0.39,1.41,0c0.39-0.39,0.39-1.03,0-1.41 L18.36,16.95z M19.42,5.99c0.39-0.39,0.39-1.03,0-1.41c-0.39-0.39-1.03-0.39-1.41,0l-1.06,1.06c-0.39,0.39-0.39,1.03,0,1.41 s1.03,0.39,1.41,0L19.42,5.99z M7.05,18.36c0.39-0.39,0.39-1.03,0-1.41c-0.39-0.39-1.03-0.39-1.41,0l-1.06,1.06 c-0.39,0.39-0.39,1.03,0,1.41s1.03,0.39,1.41,0L7.05,18.36z" > < / path > < / svg > < svg viewBox = "0 0 24 24" width = "24" height = "24" class = "darkToggleIcon_wfgR" > < path fill = "currentColor" d = "M9.37,5.51C9.19,6.15,9.1,6.82,9.1,7.5c0,4.08,3.32,7.4,7.4,7.4c0.68,0,1.35-0.09,1.99-0.27C17.45,17.19,14.93,19,12,19 c-3.86,0-7-3.14-7-7C5,9.07,6.81,6.55,9.37,5.51z M12,3c-4.97,0-9,4.03-9,9s4.03,9,9,9s9-4.03,9-9c0-0.46-0.04-0.92-0.1-1.36 c-0.98,1.37-2.58,2.26-4.4,2.26c-2.98,0-5.4-2.42-5.4-5.4c0-1.81,0.89-3.42,2.26-4.4C12.92,3.04,12.46,3,12,3L12,3z" > < / path > < / svg > < / button > < / div > < div class = "navbarSearchContainer_Bca1" > < button type = "button" class = "DocSearch DocSearch-Button" aria-label = "Search" > < span class = "DocSearch-Button-Container" > < svg width = "20" height = "20" class = "DocSearch-Search-Icon" viewBox = "0 0 20 20" > < path d = "M14.386 14 . 386l4 . 0877 4 . 0877-4 . 0877-4 . 0877c-2 .
2023-11-24 16:55:55 +01:00
< h2 class = "anchor anchorWithStickyNavbar_LWe7" id = "problem" > Problem< a href = "#problem" class = "hash-link" aria-label = "Direct link to Problem" title = "Direct link to Problem" > < / a > < / h2 >
< p > The problem we are going to solve is one of < em > CodeWars< / em > katas and is called
< a href = "https://www.codewars.com/kata/551f23362ff852e2ab000037" target = "_blank" rel = "noopener noreferrer" > Pyramid Slide Down< / a > .< / p >
< p > We are given a 2D array of integers and we are to find the < em > slide down< / em > .
< em > Slide down< / em > is a maximum sum of consecutive numbers from the top to the bottom.< / p >
< p > Let' s have a look at few examples. Consider the following pyramid:< / p >
2024-02-04 13:54:29 +01:00
< div class = "codeBlockContainer_Ckt0 theme-code-block" style = "--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-text codeBlock_bY9V thin-scrollbar" style = "background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 3< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 7 4< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 2 4 6< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 8 5 9 3< / span > < br > < / span > < / code > < / pre > < div class = "buttonGroup__atx" > < button type = "button" aria-label = "Copy code to clipboard" title = "Copy" class = "clean-btn" > < span class = "copyButtonIcons_eSgA" aria-hidden = "true" > < svg viewBox = "0 0 24 24" class = "copyButtonIcon_y97N" > < path fill = "currentColor" d = "M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z" > < / path > < / svg > < svg viewBox = "0 0 24 24" class = "copyButtonSuccessIcon_LjdS" > < path fill = "currentColor" d = "M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z" > < / path > < / svg > < / span > < / button > < / div > < / div > < / div >
2023-11-24 16:55:55 +01:00
< p > This pyramid has following slide down:< / p >
2024-02-04 13:54:29 +01:00
< div class = "codeBlockContainer_Ckt0 theme-code-block" style = "--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-text codeBlock_bY9V thin-scrollbar" style = "background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > *3< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > *7 4< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 2 *4 6< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 8 5 *9 3< / span > < br > < / span > < / code > < / pre > < div class = "buttonGroup__atx" > < button type = "button" aria-label = "Copy code to clipboard" title = "Copy" class = "clean-btn" > < span class = "copyButtonIcons_eSgA" aria-hidden = "true" > < svg viewBox = "0 0 24 24" class = "copyButtonIcon_y97N" > < path fill = "currentColor" d = "M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z" > < / path > < / svg > < svg viewBox = "0 0 24 24" class = "copyButtonSuccessIcon_LjdS" > < path fill = "currentColor" d = "M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z" > < / path > < / svg > < / span > < / button > < / div > < / div > < / div >
2023-11-24 16:55:55 +01:00
< p > And its value is < code > 23< / code > .< / p >
< p > We can also have a look at a < em > bigger< / em > example:< / p >
2024-02-04 13:54:29 +01:00
< div class = "codeBlockContainer_Ckt0 theme-code-block" style = "--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-text codeBlock_bY9V thin-scrollbar" style = "background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 75< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 95 64< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 17 47 82< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 18 35 87 10< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 20 4 82 47 65< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 19 1 23 3 34< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 88 2 77 73 7 63 67< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 99 65 4 28 6 16 70 92< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 41 41 26 56 83 40 80 70 33< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 41 48 72 33 47 32 37 16 94 29< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 53 71 44 65 25 43 91 52 97 51 14< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 70 11 33 28 77 73 17 78 39 68 17 57< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 91 71 52 38 17 14 91 43 58 50 27 29 48< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 63 66 4 68 89 53 67 30 73 16 69 87 40 31< / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > 4 62 98 27 23 9 70 98 73 93 38 53 60 4 23< / span > < br > < / span > < / code > < / pre > < div class = "buttonGroup__atx" > < button type = "button" aria-label = "Copy code to clipboard" title = "Copy" class = "clean-btn" > < span class = "copyButtonIcons_eSgA" aria-hidden = "true" > < svg viewBox = "0 0 24 24" class = "copyButtonIcon_y97N" > < path fill = "currentColor" d = "M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z" > < / path > < / svg > < svg viewBox = "0 0 24 24" class = "copyButtonSuccessIcon_LjdS" > < path fill = "currentColor" d = "M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z" > < / path > < / svg > < / span > < / button > < / div > < / div > < / div >
2023-11-24 16:55:55 +01:00
< p > Slide down in this case is equal to < code > 1074< / code > .< / p >
< h2 class = "anchor anchorWithStickyNavbar_LWe7" id = "solving-the-problem" > Solving the problem< a href = "#solving-the-problem" class = "hash-link" aria-label = "Direct link to Solving the problem" title = "Direct link to Solving the problem" > < / a > < / h2 >
2024-07-11 23:59:04 +02:00
< div class = "theme-admonition theme-admonition-warning admonition_xJq3 alert alert--warning" > < div class = "admonitionHeading_Gvgb" > < span class = "admonitionIcon_Rf37" > < svg viewBox = "0 0 16 16" > < path fill-rule = "evenodd" d = "M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z" > < / path > < / svg > < / span > caution< / div > < div class = "admonitionContent_BuS1" > < p > I will describe the following ways you can approach this problem and implement
2023-11-24 16:55:55 +01:00
them in < em > Java< / em > < sup > < a href = "#user-content-fn-1" id = "user-content-fnref-1" data-footnote-ref = "true" aria-describedby = "footnote-label" > 1< / a > < / sup > .< / p > < / div > < / div >
< p > For all of the following solutions I will be using basic < code > main< / code > function that
will output < code > true< / code > /< code > false< / code > based on the expected output of our algorithm. Any
other differences will lie only in the solutions of the problem. You can see the
< code > main< / code > here:< / p >
2024-02-04 13:54:29 +01:00
< div class = "language-java codeBlockContainer_Ckt0 theme-code-block" style = "--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-java codeBlock_bY9V thin-scrollbar" style = "background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token keyword" style = "color:hsl(301, 63%, 40%)" > public< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:hsl(301, 63%, 40%)" > static< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:hsl(301, 63%, 40%)" > void< / span > < span class = "token plain" > < / span > < span class = "token function" style = "color:hsl(221, 87%, 60%)" > main< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > (< / span > < span class = "token class-name" style = "color:hsl(35, 99%, 36%)" > String< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > [< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > ]< / span > < span class = "token plain" > args< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > )< / span > < span class = "token plain" > < / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > {< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > < / span > < span class = "token class-name" style = "color:hsl(35, 99%, 36%)" > System< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > .< / span > < span class = "token plain" > out< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > .< / span > < span class = "token function" style = "color:hsl(221, 87%, 60%)" > print< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > (< / span > < span class = "token string" style = "color:hsl(119, 34%, 47%)" > " Test #1: " < / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > )< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > ;< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > < / span > < span class = "token class-name" style = "color:hsl(35, 99%, 36%)" > System< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > .< / span > < span class = "token plain" > out< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > .< / span > < span class = "token function" style = "color:hsl(221, 87%, 60%)" > println< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > (< / span > < span class = "token function" style = "color:hsl(221, 87%, 60%)" > longestSlideDown< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > (< / span > < span class = "token keyword" style = "color:hsl(301, 63%, 40%)" > new< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:hsl(301, 63%, 40%)" > int< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > [< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > ]< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > [< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > ]< / span > < span class = "token plain" > < / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > {< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > < / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > {< / span > < span class = "token plain" > < / span > < span class = "token number" style = "color:hsl(35, 99%, 36%)" > 3< / span > < span class = "token plain" > < / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > }< / span > < span class = "token punctuation" style = "color:hsl(119, 34%, 47%)" > ,< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:hsl(230, 8%, 24%)" > < span class = "token plain" > < / span > < span class = "token punctuation" style = "color:hsl(119, 34 % , 47
2023-11-24 16:55:55 +01:00
< section data-footnotes = "true" class = "footnotes" > < h2 class = "anchor anchorWithStickyNavbar_LWe7 sr-only" id = "footnote-label" > Footnotes< a href = "#footnote-label" class = "hash-link" aria-label = "Direct link to Footnotes" title = "Direct link to Footnotes" > < / a > < / h2 >
< ol >
< li id = "user-content-fn-1" >
< p > cause why not, right!? < a href = "#user-content-fnref-1" data-footnote-backref = "" aria-label = "Back to reference 1" class = "data-footnote-backref" > ↩< / a > < / p >
< / li >
< / ol >
2024-01-03 15:14:53 +01:00
< / section > < / div > < footer class = "theme-doc-footer docusaurus-mt-lg" > < div class = "theme-doc-footer-tags-row row margin-bottom--sm" > < div class = "col" > < b > Tags:< / b > < ul class = "tags_jXut padding--none margin-left--sm" > < li class = "tag_QGVx" > < a class = "tag_zVej tagRegular_sFm0" href = "/algorithms/tags/java/" > java< / a > < / li > < li class = "tag_QGVx" > < a class = "tag_zVej tagRegular_sFm0" href = "/algorithms/tags/recursion/" > recursion< / a > < / li > < li class = "tag_QGVx" > < a class = "tag_zVej tagRegular_sFm0" href = "/algorithms/tags/exponential/" > exponential< / a > < / li > < li class = "tag_QGVx" > < a class = "tag_zVej tagRegular_sFm0" href = "/algorithms/tags/greedy/" > greedy< / a > < / li > < li class = "tag_QGVx" > < a class = "tag_zVej tagRegular_sFm0" href = "/algorithms/tags/dynamic-programming/" > dynamic-programming< / a > < / li > < li class = "tag_QGVx" > < a class = "tag_zVej tagRegular_sFm0" href = "/algorithms/tags/top-down-dp/" > top-down-dp< / a > < / li > < li class = "tag_QGVx" > < a class = "tag_zVej tagRegular_sFm0" href = "/algorithms/tags/bottom-up-dp/" > bottom-up-dp< / a > < / li > < / ul > < / div > < / div > < div class = "theme-doc-footer-edit-meta-row row" > < div class = "col" > < a href = "https://github.com/mfocko/blog/tree/main/algorithms/04-recursion/2023-08-17-pyramid-slide-down/index.md" target = "_blank" rel = "noopener noreferrer" class = "theme-edit-this-page" > < svg fill = "currentColor" height = "20" width = "20" viewBox = "0 0 40 40" class = "iconEdit_Z9Sw" aria-hidden = "true" > < g > < path d = "m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z" > < / path > < / g > < / svg > Edit this page< / a > < / div > < div class = "col lastUpdated_vwxv" > < span class = "theme-last-updated" > Last updated<!-- --> on < b > < time datetime = "2023-08-17T00:00:00.000Z" > Aug 17, 2023< / time > < / b > < / span > < / div > < / div > < / footer > < / article > < nav class = "pagination-nav docusaurus-mt-lg" aria-label = "Docs pages" > < a class = "pagination-nav__link pagination-nav__link--prev" href = "/algorithms/recursion/karel/solution/" > < div class = "pagination-nav__sublabel" > Previous< / div > < div class = "pagination-nav__label" > Solution to the problem< / div > < / a > < a class = "pagination-nav__link pagination-nav__link--next" href = "/algorithms/recursion/pyramid-slide-down/naive/" > < div class = "pagination-nav__sublabel" > Next< / div > < div class = "pagination-nav__label" > Naïve solution< / div > < / a > < / nav > < / div > < / div > < div class = "col col--3" > < div class = "tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop" > < ul class = "table-of-contents table-of-contents__left-border" > < li > < a href = "#problem" class = "table-of-contents__link toc-highlight" > Problem< / a > < / li > < li > < a href = "#solving-the-problem" class = "table-of-contents__link toc-highlight" > Solving the problem< / a > < / li > < / ul > < / div > < / div > < / div > < / div > < / main > < / div > < / div > < / div > < footer class = "footer footer--dark" > < div class = "container container-fluid" > < div class = "row footer__links" > < div class = "col footer__col" > < div class = "footer__title" > Git< / div > < ul class = "footer__items clean-list" > < li class = "footer__item" > < a href = "https://github.com/mfocko" target = "_blank" rel = "noopener noreferrer" class = "footer__link-item" > GitHub< svg width = "13.5" height = "13.5" aria-hidden = "true" viewBox = "0 0 24 24" class = "iconExternalLink_nPIU" > < path fill = "currentColor" d = "M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z" > < / path > < / svg > < / a > < / li > < li class = "footer__item" > < a href = "https://gitlab.com/mfocko" target = "_blank" rel = "noopener noreferrer" class = "footer__link-item" > GitLab< svg width = "13.5" height = "13.5" aria-hidden = "true" viewBox = "0 0 24 24" class = "iconExternalLink_nPIU" > < path fill = "currentColor" d = "M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10.988l4.035 4-6.977 7.07 2.828 2.828 6.977-7.07 4.125 4.172v-11z" > < / path > < / svg > < / a > < / li > < li class = "footer__item" > < a href = "https://git.mfocko.xyz/mfocko" target = "_blank" rel = "noopener noreferrer" class = "footer__link-item" > Gitea (self-hosted)< svg width = "13.5" height = "13.5" aria-hidden = "true" viewBox = "0 0 24 24" class = "iconExternalLink_nPIU" > < path fill = "currentColor" d = "M21 13v10h-21v-19h12v2h-10v15h17v-8h2zm3-12h-10 . 988l4 . 035 4-6 . 977 7 . 07 2 . 828 2 . 828 6 . 977-7 . 07 4 . 125 4 . 172v
2023-11-24 16:55:55 +01:00
< / body >
< / html >