mirror of
https://github.com/mfocko/blog.git
synced 2024-12-23 12:51:30 +01:00
53 lines
No EOL
67 KiB
HTML
53 lines
No EOL
67 KiB
HTML
<!doctype html>
|
||
<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">
|
||
<head>
|
||
<meta charset="UTF-8">
|
||
<meta name="generator" content="Docusaurus v3.1.1">
|
||
<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">
|
||
|
||
|
||
|
||
<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.525e8c38.css">
|
||
<script src="/assets/js/runtime~main.a26bb3ef.js" defer="defer"></script>
|
||
<script src="/assets/js/main.7af15fef.js" defer="defer"></script>
|
||
</head>
|
||
<body class="navigation-with-keyboard">
|
||
<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-2.9418 2.9419-7.7115 2.9419-10.6533 0-2.9419-2.9418-2.9419-7.7115 0-10.6533 2.9418-2.9419 7.7115-2.9419 10.6533 0 2.9419 2.9418 2.9419 7.7115 0 10.6533z" stroke="currentColor" fill="none" fill-rule="evenodd" stroke-linecap="round" stroke-linejoin="round"></path></svg><span class="DocSearch-Button-Placeholder">Search</span></span><span class="DocSearch-Button-Keys"></span></button></div></div></div><div role="presentation" class="navbar-sidebar__backdrop"></div></nav><div id="__docusaurus_skipToContent_fallback" class="main-wrapper mainWrapper_z2l0"><div class="docsWrapper_hBAB"><button aria-label="Scroll back to top" class="clean-btn theme-back-to-top-button backToTopButton_sjWU" type="button"></button><div class="docRoot_UBD9"><aside class="theme-doc-sidebar-container docSidebarContainer_YfHR"><div class="sidebarViewport_aRkj"><div class="sidebar_njMd"><nav aria-label="Docs sidebar" class="menu thin-scrollbar menu_SIkG"><ul class="theme-doc-sidebar-menu menu__list"><li class="theme-doc-sidebar-item-link theme-doc-sidebar-item-link-level-1 menu__list-item"><a class="menu__link" href="/algorithms/">Introduction</a></li><li class="theme-doc-sidebar-item-category theme-doc-sidebar-item-category-level-1 menu__list-item menu__list-item--collapsed"><div class="menu__list-item-collapsible"><a class="menu__link menu__link--sublist" aria-expanded="false" href="/algorithms/category/algorithms-and-correctness/">Algorithms and Correctness</a><button aria-label="Expand sidebar category 'Algorithms and Correctness'" type="button" class="clean-btn menu__caret"></button></div></li><li class="theme-doc-sidebar-item-category theme-doc-sidebar-item-category-level-1 menu__list-item menu__list-item--collapsed"><div class="menu__list-item-collapsible"><a class="menu__link menu__link--sublist" aria-expanded="false" href="/algorithms/category/asymptotic-notation-and-time-complexity/">Asymptotic Notation and Time Complexity</a><button aria-label="Expand sidebar category 'Asymptotic Notation and Time Complexity'" type="button" class="clean-btn menu__caret"></button></div></li><li class="theme-doc-sidebar-item-category theme-doc-sidebar-item-category-level-1 menu__list-item"><div class="menu__list-item-collapsible"><a class="menu__link menu__link--sublist menu__link--active" aria-expanded="true" href="/algorithms/category/recursion/">Recursion</a><button aria-label="Collapse sidebar category 'Recursion'" type="button" class="clean-btn menu__caret"></button></div><ul style="display:block;overflow:visible;height:auto" class="menu__list"><li class="theme-doc-sidebar-item-category theme-doc-sidebar-item-category-level-2 menu__list-item menu__list-item--collapsed"><div class="menu__list-item-collapsible"><a class="menu__link menu__link--sublist" aria-expanded="false" tabindex="0" href="/algorithms/recursion/karel/">Recursion and backtracking with Robot Karel</a><button aria-label="Expand sidebar category 'Recursion and backtracking with Robot Karel'" type="button" class="clean-btn menu__caret"></button></div></li><li class="theme-doc-sidebar-item-category theme-doc-sidebar-item-category-level-2 menu__list-item"><div class="menu__list-item-collapsible menu__list-item-collapsible--active"><a class="menu__link menu__link--sublist menu__link--active" aria-current="page" aria-expanded="true" tabindex="0" href="/algorithms/recursion/pyramid-slide-down/">Introduction to dynamic programming</a><button aria-label="Collapse sidebar category 'Introduction to dynamic programming'" type="button" class="clean-btn menu__caret"></button></div><ul style="display:block;overflow:visible;height:auto" class="menu__list"><li class="theme-doc-sidebar-item-link theme-doc-sidebar-item-link-level-3 menu__list-item"><a class="menu__link" tabindex="0" href="/algorithms/recursion/pyramid-slide-down/naive/">Naïve solution</a></li><li class="theme-doc-sidebar-item-link theme-doc-sidebar-item-link-level-3 menu__list-item"><a class="menu__link" tabindex="0" href="/algorithms/recursion/pyramid-slide-down/greedy/">Greedy solution</a></li><li class="theme-doc-sidebar-item-link theme-doc-sidebar-item-link-level-3 menu__list-item"><a class="menu__link" tabindex="0" href="/algorithms/recursion/pyramid-slide-down/top-down-dp/">Top-down DP solution</a></li><li class="theme-doc-sidebar-item-link theme-doc-sidebar-item-link-level-3 menu__list-item"><a class="menu__link" tabindex="0" href="/algorithms/recursion/pyramid-slide-down/bottom-up-dp/">Bottom-up DP solution</a></li></ul></li></ul></li><li class="theme-doc-sidebar-item-category theme-doc-sidebar-item-category-level-1 menu__list-item menu__list-item--collapsed"><div class="menu__list-item-collapsible"><a class="menu__link menu__link--sublist" aria-expanded="false" href="/algorithms/category/red-black-trees/">Red-Black Trees</a><button aria-label="Expand sidebar category 'Red-Black Trees'" type="button" class="clean-btn menu__caret"></button></div></li><li class="theme-doc-sidebar-item-category theme-doc-sidebar-item-category-level-1 menu__list-item menu__list-item--collapsed"><div class="menu__list-item-collapsible"><a class="menu__link menu__link--sublist" aria-expanded="false" href="/algorithms/category/graphs/">Graphs</a><button aria-label="Expand sidebar category 'Graphs'" type="button" class="clean-btn menu__caret"></button></div></li><li class="theme-doc-sidebar-item-category theme-doc-sidebar-item-category-level-1 menu__list-item menu__list-item--collapsed"><div class="menu__list-item-collapsible"><a class="menu__link menu__link--sublist" aria-expanded="false" href="/algorithms/category/paths-in-graphs/">Paths in Graphs</a><button aria-label="Expand sidebar category 'Paths in Graphs'" type="button" class="clean-btn menu__caret"></button></div></li><li class="theme-doc-sidebar-item-category theme-doc-sidebar-item-category-level-1 menu__list-item menu__list-item--collapsed"><div class="menu__list-item-collapsible"><a class="menu__link menu__link--sublist" aria-expanded="false" href="/algorithms/category/hash-tables/">Hash Tables</a><button aria-label="Expand sidebar category 'Hash Tables'" type="button" class="clean-btn menu__caret"></button></div></li></ul></nav><button type="button" title="Collapse sidebar" aria-label="Collapse sidebar" class="button button--secondary button--outline collapseSidebarButton_PEFL"><svg width="20" height="20" aria-hidden="true" class="collapseSidebarButtonIcon_kv0_"><g fill="#7a7a7a"><path d="M9.992 10.023c0 .2-.062.399-.172.547l-4.996 7.492a.982.982 0 01-.828.454H1c-.55 0-1-.453-1-1 0-.2.059-.403.168-.551l4.629-6.942L.168 3.078A.939.939 0 010 2.528c0-.548.45-.997 1-.997h2.996c.352 0 .649.18.828.45L9.82 9.472c.11.148.172.347.172.55zm0 0"></path><path d="M19.98 10.023c0 .2-.058.399-.168.547l-4.996 7.492a.987.987 0 01-.828.454h-3c-.547 0-.996-.453-.996-1 0-.2.059-.403.168-.551l4.625-6.942-4.625-6.945a.939.939 0 01-.168-.55 1 1 0 01.996-.997h3c.348 0 .649.18.828.45l4.996 7.492c.11.148.168.347.168.55zm0 0"></path></g></svg></button></div></div></aside><main class="docMainContainer_TBSr"><div class="container padding-top--md padding-bottom--lg"><div class="row"><div class="col docItemCol_VOVn"><div class="docItemContainer_Djhp"><article><nav class="theme-doc-breadcrumbs breadcrumbsContainer_Z_bl" aria-label="Breadcrumbs"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><li class="breadcrumbs__item"><a aria-label="Home page" class="breadcrumbs__link" href="/"><svg viewBox="0 0 24 24" class="breadcrumbHomeIcon_YNFT"><path d="M10 19v-5h4v5c0 .55.45 1 1 1h3c.55 0 1-.45 1-1v-7h1.7c.46 0 .68-.57.33-.87L12.67 3.6c-.38-.34-.96-.34-1.34 0l-8.36 7.53c-.34.3-.13.87.33.87H5v7c0 .55.45 1 1 1h3c.55 0 1-.45 1-1z" fill="currentColor"></path></svg></a></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item"><a class="breadcrumbs__link" itemprop="item" href="/algorithms/category/recursion/"><span itemprop="name">Recursion</span></a><meta itemprop="position" content="1"></li><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="breadcrumbs__link" itemprop="name">Introduction to dynamic programming</span><meta itemprop="position" content="2"></li></ul></nav><div class="tocCollapsible_ETCw theme-doc-toc-mobile tocMobile_ITEo"><button type="button" class="clean-btn tocCollapsibleButton_TO0P">On this page</button></div><div class="theme-doc-markdown markdown"><header><h1>Introduction to dynamic programming</h1></header><p>In this series we will try to solve one problem in different ways.</p>
|
||
<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>
|
||
<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>
|
||
<p>This pyramid has following slide down:</p>
|
||
<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>
|
||
<p>And its value is <code>23</code>.</p>
|
||
<p>We can also have a look at a <em>bigger</em> example:</p>
|
||
<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>
|
||
<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>
|
||
<div class="theme-admonition theme-admonition-caution 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
|
||
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>
|
||
<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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">7</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%)">4</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">2</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%)">4</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%)">6</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">8</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%)">5</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%)">9</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 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 punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">==</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">23</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">?</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"passed"</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"failed"</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" style="display:inline-block"></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 #2: "</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%)">75</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">95</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%)">64</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">17</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%)">47</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%)">82</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">18</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%)">35</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%)">87</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%)">10</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">20</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%)">4</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%)">82</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%)">47</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%)">65</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">19</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%)">1</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%)">23</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%)">75</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 punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">34</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">88</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%)">2</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%)">77</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%)">73</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%)">7</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%)">63</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%)">67</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">99</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%)">65</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%)">4</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%)">28</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%)">6</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%)">16</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%)">70</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%)">92</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">41</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%)">41</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%)">26</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%)">56</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%)">83</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%)">40</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%)">80</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%)">70</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%)">33</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">41</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%)">48</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%)">72</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%)">33</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%)">47</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%)">32</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%)">37</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%)">16</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%)">94</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%)">29</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">53</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%)">71</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%)">44</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%)">65</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%)">25</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%)">43</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%)">91</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%)">52</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%)">97</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%)">51</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%)">14</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">70</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%)">11</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%)">33</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%)">28</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%)">77</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%)">73</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%)">17</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%)">78</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%)">39</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%)">68</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%)">17</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%)">57</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">91</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%)">71</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%)">52</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%)">38</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%)">17</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%)">14</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%)">91</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%)">43</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%)">58</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%)">50</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%)">27</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%)">29</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%)">48</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">63</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%)">66</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%)">4</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%)">68</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%)">89</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%)">53</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%)">67</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%)">30</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%)">73</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%)">16</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%)">69</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%)">87</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%)">40</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%)">31</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%)">{</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">4</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%)">62</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%)">98</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%)">27</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%)">23</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%)">9</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%)">70</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%)">98</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%)">73</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%)">93</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%)">38</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%)">53</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%)">60</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%)">4</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%)">23</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%)">}</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">==</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1074</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">?</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"passed"</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"failed"</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%)">}</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>
|
||
<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>
|
||
</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-11z"></path></svg></a></li></ul></div><div class="col footer__col"><div class="footer__title">Social #1</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://www.linkedin.com/in/mfocko/" target="_blank" rel="noopener noreferrer" class="footer__link-item">LinkedIn<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://fosstodon.org/@m4tt_314" target="_blank" rel="noopener noreferrer" class="footer__link-item">Fosstodon<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://hachyderm.io/@m4tt_314" target="_blank" rel="noopener noreferrer" class="footer__link-item">Hachyderm.io<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></ul></div><div class="col footer__col"><div class="footer__title">Social #2</div><ul class="footer__items clean-list"><li class="footer__item"><a href="https://twitter.com/m4tt_314" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitter<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://twitch.tv/m4tt_314" target="_blank" rel="noopener noreferrer" class="footer__link-item">Twitch<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://ko-fi.com/m4tt_314" target="_blank" rel="noopener noreferrer" class="footer__link-item">Ko-fi<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></ul></div></div><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2024 Matej Focko.</div></div></div></footer></div>
|
||
</body>
|
||
</html> |