{"id":6985,"date":"2024-02-09T16:24:30","date_gmt":"2024-02-09T08:24:30","guid":{"rendered":"https:\/\/zyrastory.com\/?p=6985"},"modified":"2024-02-09T16:24:31","modified_gmt":"2024-02-09T08:24:31","slug":"leetcode-119-pascals-triangle-ii-solution-and-explanation-en","status":"publish","type":"post","link":"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-119-pascals-triangle-ii-solution-and-explanation-en\/","title":{"rendered":"LeetCode #119 Pascal&#8217;s Triangle II Solution &#038; Explanation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_65 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >\u5167\u5bb9\u76ee\u9304<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-119-pascals-triangle-ii-solution-and-explanation-en\/#leetcode-problem\" title=\"LeetCode Problem\">LeetCode Problem<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-119-pascals-triangle-ii-solution-and-explanation-en\/#solution\" title=\"Solution\">Solution<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-119-pascals-triangle-ii-solution-and-explanation-en\/#c-solution\" title=\"C# Solution\">C# Solution<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-119-pascals-triangle-ii-solution-and-explanation-en\/#java-solution\" title=\"Java Solution\">Java Solution<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-119-pascals-triangle-ii-solution-and-explanation-en\/#conclusion\" title=\"Conclusion\">Conclusion<\/a><\/li><\/ul><\/nav><\/div>\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"leetcode-problem\"><\/span><strong>LeetCode Problem<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Given an integer\u00a0<strong>rowIndex<\/strong>, return the\u00a0rowIndex<sup>th<\/sup>\u00a0(<strong>0-indexed<\/strong>) row of the\u00a0<strong>Pascal&#8217;s triangle<\/strong>.<\/p>\n\n\n\n<p>In&nbsp;<strong>Pascal&#8217;s triangle<\/strong>, each number is the sum of the two numbers directly above it as shown:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"240\" src=\"https:\/\/zyrastory.com\/wp-content\/uploads\/2024\/02\/PascalTriangleAnimated2.gif\" alt=\"\" class=\"wp-image-6986\" style=\"width:346px;height:auto\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"384\" height=\"581\" src=\"https:\/\/zyrastory.com\/wp-content\/uploads\/2024\/02\/119_Examples_Constraints.webp\" alt=\"\" class=\"wp-image-6988\" srcset=\"https:\/\/zyrastory.com\/wp-content\/uploads\/2024\/02\/119_Examples_Constraints.webp 384w, https:\/\/zyrastory.com\/wp-content\/uploads\/2024\/02\/119_Examples_Constraints-198x300.webp 198w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/figure>\n\n\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>Follow up:<\/strong>\u00a0Could you optimize your algorithm to use only\u00a0<strong>O(rowIndex)<\/strong>\u00a0extra space?<\/p>\n\n\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"solution\"><\/span><strong>Solution<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In this problem, we can refer to the solution of <a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-118-pascals-triangle-solution-explanation\/\" target=\"_blank\" rel=\"noreferrer noopener\">LeetCode #118 Pascal&#8217;s Triangle<\/a>. The only difference is that this problem only requires returning a specific row instead of the entire triangle.<\/p>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"c-solution\"><\/span><strong>C# Solution<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p><strong>Solution1<\/strong><\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism undefined-numbers lang-csharp\" data-lang=\"C#\"><code>public class Solution {\n    public IList&lt;int&gt; GetRow(int rowIndex) {\n        List&lt;int&gt; res = new List&lt;int&gt;();\n        \n        res.Add(1);  \/\/ the first line\n        \n        for (int i = 1; i &lt;= rowIndex; i++) {\n            for (int j = i - 1; j &gt;= 1; j--) {\n                res[j] += res[j - 1];\n            }\n            res.Add(1);\n        }\n        \n        return res;\n    }\n}<\/code><\/pre><\/div>\n\n\n\n<p>The loop <strong><em>for (int j = i &#8211; 1; j >= 1; j&#8211;)<\/em><\/strong> iterates from the end of the row towards the second element. This direction is chosen to prevent altering the values needed for further computations.<\/p>\n\n\n\n<p>This way, we can use just one row for storage, without requiring any additional space.<\/p>\n\n\n\n<div style=\"height:45px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"java-solution\"><\/span><strong>Java Solution<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p><strong>Solution1<\/strong><\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism undefined-numbers lang-java\" data-lang=\"Java\"><code>class Solution {\n    public List&lt;Integer&gt; getRow(int rowIndex) {\n        List&lt;Integer&gt; res = new ArrayList&lt;Integer&gt;();\n        \n        res.add(1);  \/\/ the first line\n        \n        for (int i = 1; i &lt;= rowIndex; i++) {\n            for (int j = i - 1; j &gt;= 1; j--) {\n                res.set(j,res.get(j) + res.get(j - 1));\n            }\n            res.add(1);\n        }\n        \n        return res;\n    }\n}<\/code><\/pre><\/div>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"tw-target-text\"><span class=\"ez-toc-section\" id=\"conclusion\"><\/span><strong>Conclusion<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div style=\"height:45px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-medium-font-size\">\ud83e\udde1<strong>If my solution helps, that is my honor!<\/strong><\/p>\n\n\n\n<p>\ud83e\udde1<strong>You can support me by  sharing my posts, thanks a lot<\/strong><\/p>\n\n\n\n<p>\u2705<strong>If you got any problem about the explanation, please feel free to let me know<\/strong><\/p>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>The problem link :<\/strong> <a href=\"https:\/\/leetcode.com\/problems\/pascals-triangle-ii\/description\/\" target=\"_blank\" rel=\"noreferrer noopener\">Pascal&#8217;s Triangle II &#8211; LeetCode<\/a><\/p>\n\n\n\n<p><strong>Similar problem : <\/strong><\/p>\n\n\n\n<ul>\n<li><a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-118-pascals-triangle-solution-explanation\/\" target=\"_blank\" rel=\"noreferrer noopener\">LeetCode #118 Pascal&#8217;s Triangle Solution &amp; Explanation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-70-climbing-stairs-solution-and-explanation-en\/\" target=\"_blank\" rel=\"noreferrer noopener\">LeetCode #70 Climbing Stairs Solution &amp; Explanation<\/a><\/li>\n<\/ul>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>Some Random LeetCode posts<\/strong><\/p>\n\n\n\n\t\t\t<div class=\"wp-block-uagb-post-grid uagb-post-grid  uagb-post__image-position-top uagb-post__image-disabled uagb-block-f4bc3f3d     uagb-post__items uagb-post__columns-3 is-grid uagb-post__columns-tablet-2 uagb-post__columns-mobile-1 uagb-post__equal-height\" data-total=\"13\" style=\"\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-26-remove-duplicates-from-sorted-array-solution-explanation\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #26\u00a0Remove Duplicates from Sorted Array Solution &#038; Explanation<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t\t<time datetime=\"2022-07-18T16:34:48+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2022-07-18\t\t\t\t<\/time>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-26-remove-duplicates-from-sorted-array-solution-explanation\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read More<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-2279-maximum-bags-with-full-capacity-of-rocks-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode#2279 Maximum Bags With Full Capacity of Rocks<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t\t<time datetime=\"2022-05-22T17:35:01+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2022-05-22\t\t\t\t<\/time>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-2279-maximum-bags-with-full-capacity-of-rocks-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read More<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-53-maximum-subarray-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #53\u00a0Maximum Subarray Solution &#038; Explanation<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t\t<time datetime=\"2022-08-07T17:03:19+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2022-08-07\t\t\t\t<\/time>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-53-maximum-subarray-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read More<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-219-contains-duplicate-ii-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #219 Contains Duplicate II Solution &#038; Explanation<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t\t<time datetime=\"2023-09-22T22:13:57+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2023-09-22\t\t\t\t<\/time>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-219-contains-duplicate-ii-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read More<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-1700-number-of-students-unable-to-eat-lunch-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #1700 Number of Students Unable to Eat Lunch Solution &amp; Explanation<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t\t<time datetime=\"2024-04-09T22:07:16+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2024-04-09\t\t\t\t<\/time>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-1700-number-of-students-unable-to-eat-lunch-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read More<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<article class=\"uagb-post__inner-wrap\">\t\t\t\t\t\t\t\t<h4 class=\"uagb-post__title uagb-post__text\">\n\t\t\t\t<a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-290-word-pattern-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #290\u00a0Word Pattern Solution &#038; Explanation<\/a>\n\t\t\t<\/h4>\n\t\t\t\t\t\t<div class='uagb-post__text uagb-post-grid-byline'>\n\t\t\t\t\t\t\t\t<time datetime=\"2023-08-27T23:49:48+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2023-08-27\t\t\t\t<\/time>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"uagb-post__text uagb-post__cta wp-block-button\">\n\t\t\t\t<a class=\"wp-block-button__link uagb-text-link\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-290-word-pattern-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">Read More<\/a>\n\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<\/article>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"uagb-post-pagination-wrap\">\n\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t","protected":false},"excerpt":{"rendered":"<p>Return the specific row of a Pascal&#8217;s Triangle. 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