{"id":2860,"date":"2018-05-28T12:07:46","date_gmt":"2018-05-28T19:07:46","guid":{"rendered":"http:\/\/zxi.mytechroad.com\/blog\/?p=2860"},"modified":"2018-05-29T23:29:24","modified_gmt":"2018-05-30T06:29:24","slug":"leetcode-516-longest-palindromic-subsequence","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/dynamic-programming\/leetcode-516-longest-palindromic-subsequence\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 516. Longest Palindromic Subsequence"},"content":{"rendered":"<p><iframe loading=\"lazy\" title=\"\u82b1\u82b1\u9171 LeetCode 516. Longest Palindromic Subsequence - \u5237\u9898\u627e\u5de5\u4f5c EP192\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/OZX1nqaQ_9M?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<h1><strong>Problem<\/strong><\/h1>\n<p>\u9898\u76ee\u5927\u610f\uff1a\u627e\u51fa\u6700\u957f\u56de\u6587\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\u3002<\/p>\n<p><a href=\"https:\/\/leetcode.com\/problems\/longest-palindromic-subsequence\/description\/\">https:\/\/leetcode.com\/problems\/longest-palindromic-subsequence\/description\/<\/a><\/p>\n<p>Given a string s, find the longest palindromic subsequence&#8217;s length in s. You may assume that the maximum length of s is 1000.<\/p>\n<p><b>Example 1:<\/b><br \/>\nInput:<\/p>\n<pre class=\"crayon:false\">\"bbbab\"\r\n<\/pre>\n<p>Output:<\/p>\n<pre class=\"crayon:false\">4\r\n<\/pre>\n<p>One possible longest palindromic subsequence is &#8220;bbbb&#8221;.<\/p>\n<p><b>Example 2:<\/b><br \/>\nInput:<\/p>\n<pre class=\"crayon:false\">\"cbbd\"\r\n<\/pre>\n<p>Output:<\/p>\n<pre class=\"crayon:false\">2\r\n<\/pre>\n<p>One possible longest palindromic subsequence is &#8220;bb&#8221;.<\/p>\n<h1><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2866\" src=\"http:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2018\/05\/516-ep192.png\" alt=\"\" width=\"960\" height=\"540\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2018\/05\/516-ep192.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2018\/05\/516-ep192-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2018\/05\/516-ep192-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/h1>\n<h1><strong>Solution: DP<\/strong><\/h1>\n<p>Time complexity: O(n^2)<\/p>\n<p>Space complexity: O(n^2)<\/p>\n<p>C++<\/p>\n<pre class=\"lang:default decode:true \">\/\/ Author: Huahua\r\n\/\/ Running time: 102 ms\r\nclass Solution {\r\npublic:\r\n  int longestPalindromeSubseq(string s) {\r\n    const int n = s.length();\r\n    vector&lt;vector&lt;int&gt;&gt; dp(n, vector&lt;int&gt;(n, 0));\r\n    for (int l = 1; l &lt;= n; ++l)\r\n      for (int i = 0; i &lt;= n - l; ++i) {\r\n        int j = i + l - 1;\r\n        if (i == j) {\r\n          dp[i][j] = 1;\r\n          continue;\r\n        }\r\n        dp[i][j] = max(dp[i + 1][j], dp[i][j - 1]);\r\n        if (s[i] == s[j])\r\n          dp[i][j] = dp[i + 1][j - 1] + 2;\r\n      }\r\n    return dp[0][n - 1];\r\n  }\r\n};<\/pre>\n<p>Time complexity: O(n^2)<\/p>\n<p>Space complexity: O(n)<\/p>\n<p>C++<\/p>\n<pre class=\"lang:default decode:true \">\/\/ Author: Huahua\r\n\/\/ Running time: 28 ms\r\nclass Solution {\r\npublic:\r\n  int longestPalindromeSubseq(string s) {\r\n    const int n = s.length();\r\n    vector&lt;int&gt; dp0(n); \/\/ sols of len = l\r\n    vector&lt;int&gt; dp1(n); \/\/ sols of len = l - 1\r\n    vector&lt;int&gt; dp2(n); \/\/ sols of len = l - 2\r\n    for (int l = 1; l &lt;= n; ++l) {    \r\n      for (int i = 0; i &lt;= n - l; ++i) {\r\n        int j = i + l - 1;\r\n        if (i == j) {\r\n          dp0[i] = 1;\r\n          continue;\r\n        }\r\n        if (s[i] == s[j])\r\n          dp0[i] = dp2[i + 1] + 2;\r\n        else\r\n          dp0[i] = max(dp1[i + 1], dp1[i]);\r\n      }\r\n      dp0.swap(dp1);\r\n      dp2.swap(dp0);\r\n    }\r\n    return dp1[0];\r\n  }\r\n};<\/pre>\n<p>Python3<\/p>\n<pre class=\"lang:default decode:true \">\"\"\"\r\nAuthor: Huahua\r\nRunning time: 1276 ms\r\n\"\"\"\r\nclass Solution:\r\n  def longestPalindromeSubseq(self, s):\r\n    n = len(s)\r\n    dp0 = [0] * n\r\n    dp1 = [1] * n\r\n    dp2 = [0] * n\r\n    for l in range(2, n + 1):\r\n      for i in range(0, n - l + 1):        \r\n        j = i + l - 1\r\n        if s[i] == s[j]:\r\n          dp0[i] = dp2[i + 1] + 2\r\n        else:\r\n          dp0[i] = max(dp1[i + 1], dp1[i])      \r\n      dp0, dp1, dp2 = dp2, dp0, dp1\r\n    return dp1[0]\r\n<\/pre>\n<p>C#<\/p>\n<pre class=\"lang:default decode:true \">\/\/ Author: Huahua\r\n\/\/ Running time: 116 ms (beats 100%)\r\npublic class Solution {\r\n  public int LongestPalindromeSubseq(string s) {\r\n    var n = s.Length; \r\n    var dp0 = new int[n];\r\n    var dp1 = new int[n];\r\n    var dp2 = new int[n];\r\n    \r\n    for (var l = 1; l &lt;= n; ++l) {\r\n      for (var i = 0; i &lt;= n - l; ++i) {\r\n        int j = i + l - 1;\r\n        if (i == j) {\r\n          dp0[i] = 1;\r\n          continue;\r\n        }\r\n        if (s[i] == s[j])\r\n          dp0[i] = dp2[i + 1] + 2;\r\n        else\r\n          dp0[i] = Math.Max(dp1[i], dp1[i + 1]);\r\n      }\r\n      var tmp = dp2;\r\n      dp2 = dp1;\r\n      dp1 = dp0;\r\n      dp0 = tmp;\r\n    }\r\n    return dp1[0];\r\n  }\r\n}<\/pre>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem \u9898\u76ee\u5927\u610f\uff1a\u627e\u51fa\u6700\u957f\u56de\u6587\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\u3002 https:\/\/leetcode.com\/problems\/longest-palindromic-subsequence\/description\/ Given a string s, find the longest palindromic subsequence&#8217;s length in s. You may assume that the maximum length of s is&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46,47],"tags":[18,95,229],"class_list":["post-2860","post","type-post","status-publish","format-standard","hentry","category-dynamic-programming","category-string","tag-dp","tag-palindrome","tag-subsequence","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/2860","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/comments?post=2860"}],"version-history":[{"count":8,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/2860\/revisions"}],"predecessor-version":[{"id":2874,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/2860\/revisions\/2874"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=2860"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=2860"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=2860"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}