{"id":33159,"date":"2023-02-05T00:20:35","date_gmt":"2023-02-04T18:50:35","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/"},"modified":"2023-02-05T00:20:35","modified_gmt":"2023-02-04T18:50:35","slug":"solved-time-complexity-of-recursion-function","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/","title":{"rendered":"[Solved] time complexity of recursion function"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-47839478\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"47839478\" data-parentid=\"47826732\" data-score=\"4\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>We have:<br \/>\n<br \/> 1 : if statement<br \/>\n<br \/> 3 : * operator<br \/>\n<br \/> 3 : function statement<br \/>\n<br \/> Totally: 7<\/p>\n<p>So we have: <\/p>\n<pre><code>T(n)=t(n-1) + t(n-2) + t(n-3) + 7\nT(99)=1\nT(98)=1\n...\nT(1)=1\n<\/code><\/pre>\n<p>Then to <strong>reduce<\/strong> <code>T(n)<\/code>, we have <code>T(n-3)&lt;T(n-2)&lt;T(n-1)<\/code>   therefore:<\/p>\n<pre><code>T(n) &lt;= T(n-1)+T(n-1)+T(n-1) + 7\nT(n) &lt;= 3T(n-1) + 7\n<\/code><\/pre>\n<p>So we can solve <code>T(n) = 3T(n-1) + 7<\/code> (in big numbers <code>T(n-1)<\/code> is almost equal <code>T(n-2)<\/code> and &#8230; )<\/p>\n<p>Then we can calculate <code>T(n)<\/code> by following approach:<\/p>\n<pre><code>T(n) = 3.T(n-1) + 7\n     =3.(3.T(n-2)+7) + 7     = 3^2.T(n-2) + 7.(3^1 + 3^0)\n     =3^2.(3.T(n-3)+7) + ... = 3^3.T(n-3) + 7.(3^2 + 3^1 + 3^0)\n                             = 3^4.T(n-4) + 7.(3^4 + 3^2 + 3^1 + 3^0)\n     ...\n     =3^(n-99).T(n-(n-99)) + 7.(3^(n-98) + 3^(n-97) + ...+ 3^1 + 3^0)\n     =3^(n-99) + 7.(3^(n-98) + 3^(n-97) + ...+ 3^1 + 3^0)\n<\/code><\/pre>\n<p>So consider that <code>1 + 3 + 3^2 ...+3^(n-1) = 3^n - 1\/2<\/code><\/p>\n<p>Therefore we reached:<\/p>\n<pre><code>T(n) = 3^(n-99) + 7.(3^(n-99) + 1\/2) = 8.3^(n-99) - 7\/2\n     = 8\/(3^99) . 3^n -7\/2 \n<\/code><\/pre>\n<p><strong>Finally<\/strong>: Big O is <code>O(3^n)<\/code><\/p>\n<p>If you just have <code>T(1)=1<\/code>, the answer is the same.<\/p>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\">0<\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved time complexity of recursion function <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] We have: 1 : if statement 3 : * operator 3 : function statement Totally: 7 So we have: T(n)=t(n-1) + t(n-2) + t(n-3) + 7 T(99)=1 T(98)=1 &#8230; T(1)=1 Then to reduce T(n), we have T(n-3)&lt;T(n-2)&lt;T(n-1) therefore: T(n) &lt;= T(n-1)+T(n-1)+T(n-1) + 7 T(n) &lt;= 3T(n-1) + 7 So we can solve T(n) = &#8230; <a title=\"[Solved] time complexity of recursion function\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/\" aria-label=\"More on [Solved] time complexity of recursion function\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[457,612],"class_list":["post-33159","post","type-post","status-publish","format-standard","hentry","category-solved","tag-algorithm","tag-big-o"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>[Solved] time complexity of recursion function - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] time complexity of recursion function - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] We have: 1 : if statement 3 : * operator 3 : function statement Totally: 7 So we have: T(n)=t(n-1) + t(n-2) + t(n-3) + 7 T(99)=1 T(98)=1 ... T(1)=1 Then to reduce T(n), we have T(n-3)&lt;T(n-2)&lt;T(n-1) therefore: T(n) &lt;= T(n-1)+T(n-1)+T(n-1) + 7 T(n) &lt;= 3T(n-1) + 7 So we can solve T(n) = ... Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/\" \/>\n<meta property=\"og:site_name\" content=\"JassWeb\" \/>\n<meta property=\"article:published_time\" content=\"2023-02-04T18:50:35+00:00\" \/>\n<meta name=\"author\" content=\"Kirat\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Kirat\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/jassweb.com\\\/solved\\\/solved-time-complexity-of-recursion-function\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/jassweb.com\\\/solved\\\/solved-time-complexity-of-recursion-function\\\/\"},\"author\":{\"name\":\"Kirat\",\"@id\":\"https:\\\/\\\/jassweb.com\\\/solved\\\/#\\\/schema\\\/person\\\/65c9c7b7958150c0dc8371fa35dd7c31\"},\"headline\":\"[Solved] time complexity of recursion function\",\"datePublished\":\"2023-02-04T18:50:35+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/jassweb.com\\\/solved\\\/solved-time-complexity-of-recursion-function\\\/\"},\"wordCount\":68,\"publisher\":{\"@id\":\"https:\\\/\\\/jassweb.com\\\/solved\\\/#organization\"},\"keywords\":[\"algorithm\",\"big-o\"],\"articleSection\":[\"Solved\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/jassweb.com\\\/solved\\\/solved-time-complexity-of-recursion-function\\\/\",\"url\":\"https:\\\/\\\/jassweb.com\\\/solved\\\/solved-time-complexity-of-recursion-function\\\/\",\"name\":\"[Solved] time complexity of recursion function - 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JassWeb","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/","og_locale":"en_US","og_type":"article","og_title":"[Solved] time complexity of recursion function - JassWeb","og_description":"[ad_1] We have: 1 : if statement 3 : * operator 3 : function statement Totally: 7 So we have: T(n)=t(n-1) + t(n-2) + t(n-3) + 7 T(99)=1 T(98)=1 ... T(1)=1 Then to reduce T(n), we have T(n-3)&lt;T(n-2)&lt;T(n-1) therefore: T(n) &lt;= T(n-1)+T(n-1)+T(n-1) + 7 T(n) &lt;= 3T(n-1) + 7 So we can solve T(n) = ... Read more","og_url":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/","og_site_name":"JassWeb","article_published_time":"2023-02-04T18:50:35+00:00","author":"Kirat","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Kirat","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/#article","isPartOf":{"@id":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/"},"author":{"name":"Kirat","@id":"https:\/\/jassweb.com\/solved\/#\/schema\/person\/65c9c7b7958150c0dc8371fa35dd7c31"},"headline":"[Solved] time complexity of recursion function","datePublished":"2023-02-04T18:50:35+00:00","mainEntityOfPage":{"@id":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/"},"wordCount":68,"publisher":{"@id":"https:\/\/jassweb.com\/solved\/#organization"},"keywords":["algorithm","big-o"],"articleSection":["Solved"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/","url":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/","name":"[Solved] time complexity of recursion function - JassWeb","isPartOf":{"@id":"https:\/\/jassweb.com\/solved\/#website"},"datePublished":"2023-02-04T18:50:35+00:00","breadcrumb":{"@id":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/jassweb.com\/solved\/solved-time-complexity-of-recursion-function\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/jassweb.com\/solved\/"},{"@type":"ListItem","position":2,"name":"[Solved] time complexity of recursion function"}]},{"@type":"WebSite","@id":"https:\/\/jassweb.com\/solved\/#website","url":"https:\/\/jassweb.com\/solved\/","name":"JassWeb","description":"Build High-quality Websites","publisher":{"@id":"https:\/\/jassweb.com\/solved\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/jassweb.com\/solved\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/jassweb.com\/solved\/#organization","name":"Jass Web","url":"https:\/\/jassweb.com\/solved\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/jassweb.com\/solved\/#\/schema\/logo\/image\/","url":"https:\/\/jassweb.com\/wp-content\/uploads\/2021\/02\/jass-website-logo-1.png","contentUrl":"https:\/\/jassweb.com\/wp-content\/uploads\/2021\/02\/jass-website-logo-1.png","width":693,"height":132,"caption":"Jass Web"},"image":{"@id":"https:\/\/jassweb.com\/solved\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/jassweb.com\/solved\/#\/schema\/person\/65c9c7b7958150c0dc8371fa35dd7c31","name":"Kirat","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/jassweb.com\/solved\/wp-content\/litespeed\/avatar\/1261af3c9451399fa1336d28b98ea3bb.jpg?ver=1777008400","url":"https:\/\/jassweb.com\/solved\/wp-content\/litespeed\/avatar\/1261af3c9451399fa1336d28b98ea3bb.jpg?ver=1777008400","contentUrl":"https:\/\/jassweb.com\/solved\/wp-content\/litespeed\/avatar\/1261af3c9451399fa1336d28b98ea3bb.jpg?ver=1777008400","caption":"Kirat"},"sameAs":["http:\/\/jassweb.com"],"url":"https:\/\/jassweb.com\/solved\/author\/jaspritsinghghumangmail-com\/"}]}},"_links":{"self":[{"href":"https:\/\/jassweb.com\/solved\/wp-json\/wp\/v2\/posts\/33159","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jassweb.com\/solved\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jassweb.com\/solved\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jassweb.com\/solved\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jassweb.com\/solved\/wp-json\/wp\/v2\/comments?post=33159"}],"version-history":[{"count":0,"href":"https:\/\/jassweb.com\/solved\/wp-json\/wp\/v2\/posts\/33159\/revisions"}],"wp:attachment":[{"href":"https:\/\/jassweb.com\/solved\/wp-json\/wp\/v2\/media?parent=33159"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jassweb.com\/solved\/wp-json\/wp\/v2\/categories?post=33159"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jassweb.com\/solved\/wp-json\/wp\/v2\/tags?post=33159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}