{"id":7095,"date":"2024-02-15T23:43:55","date_gmt":"2024-02-15T15:43:55","guid":{"rendered":"https:\/\/zyrastory.com\/?p=7095"},"modified":"2024-02-15T23:44:15","modified_gmt":"2024-02-15T15:44:15","slug":"leetcode-5-longest-palindromic-substring-solution-and-explanation-en","status":"publish","type":"post","link":"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-5-longest-palindromic-substring-solution-and-explanation-en\/","title":{"rendered":"LeetCode #5 Longest Palindromic Substring 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-5-longest-palindromic-substring-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-5-longest-palindromic-substring-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-5-longest-palindromic-substring-solution-and-explanation-en\/#c-solution\" title=\"C# Solution\">C# Solution<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-5-longest-palindromic-substring-solution-and-explanation-en\/#conclusion\" title=\"Conclusion\">Conclusion<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-5-longest-palindromic-substring-solution-and-explanation-en\/#similar-questions\" title=\"Similar Questions\">Similar Questions<\/a><\/li><\/ul><\/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 a string <strong>s<\/strong>, return <em>the longest<strong> palindromic substring<\/strong><\/em> in <strong>s<\/strong>.<\/p>\n\n\n\n<p>(A string is\u00a0<strong>palindromic<\/strong>\u00a0if it reads the same forward and backward.)<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"596\" height=\"568\" src=\"https:\/\/zyrastory.com\/wp-content\/uploads\/2024\/02\/5_Examples_Constraints.webp\" alt=\"\" class=\"wp-image-7097\" srcset=\"https:\/\/zyrastory.com\/wp-content\/uploads\/2024\/02\/5_Examples_Constraints.webp 596w, https:\/\/zyrastory.com\/wp-content\/uploads\/2024\/02\/5_Examples_Constraints-300x286.webp 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/figure>\n\n\n\n<div style=\"height:25px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\ud83d\udca1<strong>Hint&nbsp;1<\/strong><\/p>\n\n\n\n<p>How can we reuse a previously computed palindrome to compute a larger palindrome?<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\ud83d\udca1<strong>Hint&nbsp;2<\/strong><\/p>\n\n\n\n<p>If \u201caba\u201d is a palindrome, is \u201cxabax\u201d a palindrome? Similarly is \u201cxabay\u201d a palindrome?<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\ud83d\udca1<strong>Hint\u00a03<\/strong><\/p>\n\n\n\n<p>Complexity based hint:<br>If we use brute-force and check whether for every start and end position a substring is a palindrome we have O(n^2) start &#8211; end pairs and O(n) palindromic checks. Can we reduce the time for palindromic checks to O(1) by reusing some previous computation.<\/p>\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 apply dynamic programming to divide the problem.<\/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 string LongestPalindrome(string s) {\n        int n = s.Length;\n        bool[] dp = new bool[n];\n        \n        \/\/Initialize the answer. Since s.Length &gt;= 1, the first character itself is a palindrome substring.\n        int start = 0;\n        int maxLength = 1;\n\n        \/\/i indicates the start of the substring, while j indicates the end of the substring.\n        for (int i = n-1; i &gt;= 0; i--)\n        {\n            for (int j = n-1; j &gt;= i; j--) \n            {\n                dp[j] = s[i] == s[j] && (j - i &lt; 3 || dp[j - 1]); \n                if (dp[j] && j - i + 1 &gt; maxLength) \n                {\n                    maxLength = j - i + 1;\n                    start = i;\n                }\n            }\n        }\n\n        return s.Substring(start, maxLength);\n    }\n}<\/code><\/pre><\/div>\n\n\n\n<p><strong><em>dp[j] = s[i] == s[j] &amp;&amp; (j &#8211; i &lt; 3 || dp[j &#8211; 1]);<\/em><\/strong>   : there means two condition<\/p>\n\n\n\n<ol>\n<li><strong><em>j &#8211; i &lt; 3<\/em><\/strong>, means length equals to 1,2,3 and that means the substring is a palindrome\n<ul>\n<li>When the length is 2, both characters must be the same to form a palindrome. <\/li>\n\n\n\n<li>When the length is 3, the substring is a palindrome regardless of the character in the middle, because it&#8217;s the same as its mirror image.<\/li>\n\n\n\n<li>When the length is 1, it&#8217;s always a palindrome (a single character). <br><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong><em> dp[j &#8211; 1]<\/em><\/strong> == true\n<ul>\n<li>This condition checks whether the substring from index i+1 to j-1 is a palindrome. If it&#8217;s a palindrome, and the characters at indexes i and j are the same, then the entire substring from index i to j is a palindrome.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\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<p>I&#8217;ve encountered palindrome problems before, and they didn&#8217;t seem as challenging. <\/p>\n\n\n\n<p>However, this one appears to be more difficult&#8230;<\/p>\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\/longest-palindromic-substring\/\" target=\"_blank\" rel=\"noreferrer noopener\">Longest Palindromic Substring &#8211; LeetCode<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"similar-questions\"><\/span>Similar Questions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul>\n<li><a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-9-palindrome-number-solution-and-explanation-en\/\">LeetCode #9 Palindrome Number Solution &amp; Explanation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-125-valid-palindrome-solution-and-explanation-en\/\">LeetCode #125\u00a0Valid Palindrome Solution &amp; Explanation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/zyrastory.com\/en\/coding-en\/leetcode-en\/leetcode-2108-find-first-palindromic-string-in-the-array-solution-and-explanation-en\/\" target=\"_blank\" rel=\"noreferrer noopener\">LeetCode #2108 Find First Palindromic String in the Array 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-9-palindrome-number-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #9 Palindrome Number 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=\"2022-05-29T23:10:48+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2022-05-29\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-9-palindrome-number-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-387-first-unique-character-in-a-string-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #387\u00a0First Unique Character in a String 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=\"2022-08-20T10:22:10+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2022-08-20\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-387-first-unique-character-in-a-string-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-34-find-first-and-last-position-of-element-in-sorted-array-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #34\u00a0Find First and Last Position of Element in 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=\"2023-12-18T23:33:10+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2023-12-18\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-34-find-first-and-last-position-of-element-in-sorted-array-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-27-remove-element-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #27\u00a0Remove Element 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=\"2022-07-19T21:30:36+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2022-07-19\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-27-remove-element-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-455-assign-cookies-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #455 Assign Cookies 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=\"2024-01-30T22:35:42+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2024-01-30\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-455-assign-cookies-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-11-container-with-most-water-solution-and-explanation-en\/\" target=\"_self\" rel=\"bookmark noopener noreferrer\">LeetCode #11 Container With Most Water 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=\"2022-06-18T21:33:15+08:00\" class=\"uagb-post__date\">\n\t\t\t\t<span class=\"dashicons-calendar dashicons\"><\/span>\t\t\t\t\t2022-06-18\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-11-container-with-most-water-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>Finding the longest palindromic substring in a given string. 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