{"id":30645,"date":"2023-01-16T04:56:11","date_gmt":"2023-01-15T23:26:11","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-why-i-am-getting-time-limit-exceeded-closed\/"},"modified":"2023-01-16T04:56:11","modified_gmt":"2023-01-15T23:26:11","slug":"solved-why-i-am-getting-time-limit-exceeded-closed","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-why-i-am-getting-time-limit-exceeded-closed\/","title":{"rendered":"[Solved] Why I am getting Time Limit Exceeded? [closed]"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-35137858\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"35137858\" data-parentid=\"35106692\" data-score=\"0\" 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<blockquote>\n<p>Why I am getting Time Limit Exceeded?<\/p>\n<\/blockquote>\n<p>Consider this triangle (ignore the numbers):<\/p>\n<pre><code>1\n2 3\n<\/code><\/pre>\n<p>There are 2 possible paths to take here. Let&#8217;s add a row:<\/p>\n<pre><code>1\n2 3\n4 5 6\n<\/code><\/pre>\n<p>The <code>4<\/code> can only be reached via a path that ends directly above, the <code>5<\/code> has two paths which can reach it, the <code>6<\/code> can only be reached from the path previously ending left above of it. We now have 4 possible paths. Another row:<\/p>\n<pre><code>1\n2 3\n4 5 6\n7 8 9 0\n<\/code><\/pre>\n<p>That&#8217;s 8 possible paths. Do you see a pattern? Let&#8217;s describe the path straight down to <code>7<\/code>, starting from <code>1<\/code>:<\/p>\n<pre><code>D = DOWN\nR = DOWN AND RIGHT\n\nDDD\n<\/code><\/pre>\n<p>The (single) path to <code>0<\/code>:<\/p>\n<pre><code>RRR\n<\/code><\/pre>\n<p>Since in each step you go down one row, you can only chose between the two possibilities <code>number of rows - 1<\/code> times, thus giving you:<\/p>\n<pre><code>2^(number of rows - 1) possible paths\n<\/code><\/pre>\n<p>With 100 rows, that&#8217;s <strong>alot<\/strong>. Your code tries to compute each of these paths separately. Assuming computing 1 path takes 1 nanosecond (which would be blazing fast) computing them all would take more than <code>2 * 10^16<\/code> <strong>years<\/strong>. Well, &#8230;<\/p>\n<blockquote>\n<p>Time Limit Exceeded<\/p>\n<\/blockquote>\n<p>So you now know that you cannot just compute every possible path and take the maximum. The main issue is the following:<\/p>\n<pre><code>1\n2 3\n4 5 6\n<\/code><\/pre>\n<p>One path to the <code>5<\/code> is <code>1 + 3 + 5<\/code>, the path to the <code>6<\/code> is <code>1 + 3 + 6<\/code>. Your code computes each path separately, thus <code>1 + 3<\/code> will be computed twice. If you save that result, you&#8217;ll get rid of most of the unnecessary computations.<\/p>\n<p>How could you store such results? Well, <code>1 + 3<\/code> is the computation of the path arriving at <code>3<\/code>, so store it there. What if a number (say <code>5<\/code>) can be reached by multiple paths?<\/p>\n<p><code>5<\/code> could be reached via <code>1 + 2 + 5<\/code> or <code>1 + 3 + 5<\/code>.<\/p>\n<p>Any path going through the <code>5<\/code> will give a higher result if it wen&#8217;t through the <code>3<\/code> first, so only remember this path (and ignore the path through the <code>2<\/code>, it&#8217;s useless now).<\/p>\n<p>So, as an algorithm:<\/p>\n<p>For each row, starting at row 1 (not the first, but the second): For each entry: Calculate the maximum of the entries left above (if available) and directly above (if available) and store the result + the entry&#8217;s value as new value for the entry. Then, find the maximum of the last row.<\/p>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\">1<\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved Why I am getting Time Limit Exceeded? [closed] <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] Why I am getting Time Limit Exceeded? Consider this triangle (ignore the numbers): 1 2 3 There are 2 possible paths to take here. Let&#8217;s add a row: 1 2 3 4 5 6 The 4 can only be reached via a path that ends directly above, the 5 has two paths which can &#8230; <a title=\"[Solved] Why I am getting Time Limit Exceeded? [closed]\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-why-i-am-getting-time-limit-exceeded-closed\/\" aria-label=\"More on [Solved] Why I am getting Time Limit Exceeded? [closed]\">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":[324],"class_list":["post-30645","post","type-post","status-publish","format-standard","hentry","category-solved","tag-c"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] Why I am getting Time Limit Exceeded? [closed] - 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-why-i-am-getting-time-limit-exceeded-closed\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] Why I am getting Time Limit Exceeded? 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