{"id":204,"date":"2022-03-02T16:51:51","date_gmt":"2022-03-02T08:51:51","guid":{"rendered":"http:\/\/nas.hepcloud.top:7000\/?p=204"},"modified":"2022-11-01T23:40:23","modified_gmt":"2022-11-01T15:40:23","slug":"5-%e6%9c%80%e9%95%bf%e5%9b%9e%e6%96%87%e5%ad%90%e4%b8%b2-2","status":"publish","type":"post","link":"http:\/\/www.huerpu.cc:7000\/?p=204","title":{"rendered":"5. \u6700\u957f\u56de\u6587\u5b50\u4e32"},"content":{"rendered":"<p><a href=\"http:\/\/www.huerpu.cc:2080\">\u4ee3\u7801\u4ed3\u5e93<\/a><\/p>\n<\/p>\n<p>\u7ed9\u4f60\u4e00\u4e2a\u5b57\u7b26\u4e32 s\uff0c\u627e\u5230 s \u4e2d\u6700\u957f\u7684\u56de\u6587\u5b50\u4e32\u3002<\/p>\n<p><strong>\u793a\u4f8b 1\uff1a<\/strong><\/p>\n<pre><code class=\"language-in\">\u8f93\u5165\uff1as = &quot;babad&quot;\n\u8f93\u51fa\uff1a&quot;bab&quot;\n\u89e3\u91ca\uff1a&quot;aba&quot; \u540c\u6837\u662f\u7b26\u5408\u9898\u610f\u7684\u7b54\u6848\u3002<\/code><\/pre>\n<p><strong>\u793a\u4f8b 2\uff1a<\/strong><\/p>\n<pre><code class=\"language-in\">\u8f93\u5165\uff1as = &quot;cbbd&quot;\n\u8f93\u51fa\uff1a&quot;bb&quot;<\/code><\/pre>\n<p><strong>\u63d0\u793a\uff1a<\/strong><\/p>\n<ul>\n<li>1 &lt;= s.length &lt;= 1000<\/li>\n<li>s \u4ec5\u7531\u6570\u5b57\u548c\u82f1\u6587\u5b57\u6bcd\u7ec4\u6210<\/li>\n<\/ul>\n<p><strong>\u5b50\u4e32<\/strong>\u548c<strong>\u5b50\u5e8f\u5217<\/strong>\u7684\u533a\u522b\u662f\uff0c<strong>\u5b50\u4e32<\/strong>\u4e00\u5b9a\u662f\u8fde\u7eed\u7684\uff0c\u800c<strong>\u5b50\u5e8f\u5217<\/strong>\u4e0d\u4e00\u5b9a\u662f\u8fde\u7eed\u7684\u3002<strong>\u56de\u6587\u5b50\u4e32<\/strong>\u5c31\u662f\u6b63\u7740\u770b\u548c\u53cd\u7740\u770b\u90fd\u4e00\u6837\u7684\u5b50\u4e32\u3002\u6bd4\u5982\u8bf4\u5b57\u7b26\u4e32 <code>aba<\/code> \u548c <code>abba<\/code> \u90fd\u662f\u56de\u6587\u4e32\uff0c\u56e0\u4e3a\u5b83\u4eec\u5bf9\u79f0\uff0c\u53cd\u8fc7\u6765\u8fd8\u662f\u548c\u672c\u8eab\u4e00\u6837\u3002<\/p>\n<h3>\u4e00\u3001\u66b4\u529b\u7834\u89e3<\/h3>\n<p>\u7528\u4e24\u4e2a\u53d8\u91cf<code>i<\/code>\u548c<code>j<\/code>\uff0c\u5224\u65ad\u5b57\u7b26\u4e32\u4ece<code>i<\/code>\u5230<code>j<\/code>\u7684\u5b50\u4e32\u662f\u5426\u4e3a\u56de\u6587\u4e32\uff0c\u627e\u51fa\u6700\u957f\u7684\u56de\u6587\u5b50\u4e32\u3002\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a <code>O(n\u00b3)<\/code>\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6<code>O(1)<\/code>\u3002<\/p>\n<pre><code class=\"language-java\">\/\/1.\u66b4\u529b\u7834\u89e3\n\/\/\u65f6\u95f4\u590d\u6742\u5ea6 O(N^3), \u7a7a\u95f4\u590d\u6742\u5ea6O(1)\npublic String longestPalindrome(String s) {\n    char[] charArr = s.toCharArray();\n    \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u5f00\u59cb\u4f4d\u7f6e\u548c\u957f\u5ea6\n    int start = 0, maxLen = 1;\n    for(int i = 0; i &lt; charArr.length - 1; i++){\n        for(int j = i + 1; j &lt; charArr.length; j++){\n            \/\/\u5224\u65adcharArr[i,...,j]\u662f\u5426\u4e3a\u56de\u6587\u5b50\u4e32\uff0c\u5e76\u4e14\u662f\u5426\u4e3a\u6700\u5927\u957f\u5ea6\n            if(maxLen &lt; j - i + 1 &amp;&amp; isPalindrome(charArr,i,j)){\n                start = i;\n                maxLen = j - i + 1;\n            }\n        }\n    }\n    return s.substring(start,start + maxLen);\n}\n\n\/**\n * \u9a8c\u8bc1charArr\u6570\u7ec4\u4ecefrom\u5230to\u662f\u5426\u4e3a\u56de\u6587\u4e32\n *\/\npublic boolean isPalindrome(char[] charArr,int from, int to){\n    while(from &lt; to){\n        if(charArr[from] != charArr[to]){\n            return false;\n        }\n        from++;\n        to--;\n    }\n    return true;\n}<\/code><\/pre>\n<h3>\u4e8c\u3001\u52a8\u6001\u89c4\u5212\uff0c\u4e8c\u7ef4\u6570\u7ec4: dp[i][j] \u8868\u793a s[i, &#8230; ,j] \u662f\u5426\u662f\u56de\u6587\u4e32<\/h3>\n<p>\u52a8\u6001\u89c4\u5212\u6700\u4e3b\u8981\u7684\u662fdp\u6570\u7ec4\u7684\u5b9a\u4e49\uff0c\u96be\u70b9\u5c31\u5728\u4e8e\u5bfb\u627e\u6b63\u786e\u7684\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u3002<\/p>\n<h4>1\u3001\u5b9a\u4e49\u72b6\u6001<\/h4>\n<p>\u5982\u679cs\u7684\u5b50\u4e32<code>s[i+1,\u2026,j-1]<\/code>\u7684\u72b6\u6001\u5df2\u77e5\uff0c\u90a3\u4e48\u6211\u4eec\u5f88\u5bb9\u6613\u6839\u636e<code>s[i]<\/code>\u548c<code>s[j]<\/code>\u6765\u63a8\u51fa<code>s[i,\u2026,j]<\/code>\u7684\u72b6\u6001\uff0c\u6240\u4ee5\u5b9a\u4e49<code>dp<\/code>\u6570\u7ec4<code>dp[i][j]<\/code>\u5b9a\u4e49\u4e3a\u5b50\u4e32<code>s[i,\u2026,j]<\/code>\u662f\u5426\u4e3a\u56de\u6587\u5b50\u4e32\uff0c\u8fd9\u91cc\u662f\u4e00\u4e2a<code>boolean<\/code>\u53d8\u91cf\u7684\u4e8c\u7ef4\u6570\u7ec4\uff0c\u8fd9\u91cc\u5b50\u4e32\u5b9a\u4e49\u4e3a\u5de6\u95ed\u53f3\u95ed\u533a\u95f4\uff0c\u5373\u53ef\u4ee5\u53d6\u5230 <code>s[i]<\/code> \u548c <code>s[j]<\/code>\u3002<\/p>\n<h4>2\u3001\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b<\/h4>\n<p>\u5982\u679c<code>s[i] == s[j]<\/code>\uff0c<code>dp[i][j]<\/code>\u5c31\u53d6\u51b3\u4e8e<code>dp[i+1][j-1]<\/code>,\u5982\u679c<code>s[i] != s[j]<\/code>\uff0c<code>dp[i][j]<\/code>\u5c31\u4e3afalse\uff0c\u6240\u4ee5\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u5982\u4e0b\u3002<br \/>\n<img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/02\/2.png\" alt=\"2.png\" \/><\/p>\n<h4>3\u3001\u8fb9\u754c\u6761\u4ef6<\/h4>\n<p>\u6700\u57fa\u7840\u7684\u60c5\u51b5\u662f\u53ea\u6709\u4e00\u4e2a\u5b57\u7b26\uff0c\u90a3\u4e48\u5b83\u80af\u5b9a\u662f\u56de\u6587\u4e32\uff0c\u4e5f\u5c31\u662f\u5728<code>dp<\/code>\u6570\u7ec4\u7684\u5bf9\u89d2\u7ebf\u4e0a\uff0c\u6b64\u65f6<code>i=j<\/code>\u3002<\/p>\n<p>\u5982\u679c<code>s[i,\u2026,j]<\/code>\u53ea\u6709<code>2<\/code>\u4e2a\u5b57\u7b26\uff0c\u5e76\u4e14<code>s[i] == s[j]<\/code>\uff0c\u6bd4\u5982<code>&quot;AA&quot;<\/code>\u90a3\u4e48<code>dp[i][j]<\/code>\u4e3a<code>true<\/code>\u3002<\/p>\n<p>\u5982\u679c<code>s[i,\u2026,j]<\/code>\u53ea\u6709<code>3<\/code>\u4e2a\u5b57\u7b26\uff0c\u5e76\u4e14<code>s[i] == s[j]<\/code>\uff0c\u6bd4\u5982<code>&quot;ABA&quot;<\/code>\u90a3\u4e48<code>dp[i][j]<\/code>\u4e3a<code>true<\/code>\u3002<\/p>\n<p>\u5982\u679ci\u548cj\u4f4d\u7f6e\u7684\u5143\u7d20\u76f8\u540c\uff0c\u90a3\u4e48<code>dp[i][j] <\/code>J\u5c31\u53d6\u51b3\u4e8e <code>dp[i+1][j-1]<\/code>\u4e86\u3002<\/p>\n<p>\u5176\u4f59\u60c5\u51b5\u90fd\u4e3afalse\u5566\u3002<\/p>\n<h4>4\u3001\u6839\u636e\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u904d\u5386<\/h4>\n<p>\u904d\u5386\u4ece\u5de6\u5230\u53f3\u4ece\u4e0a\u5f80\u4e0b\u8fdb\u884c\uff0c\u56e0\u4e3a<code>s[i,\u2026,j]<\/code>\u4e3as\u7684\u4e00\u4e2a\u5b50\u4e32\uff0c\u6240\u4ee5 i \u5c0f\u4e8e j \u3002\u521d\u59cb\u5316\u6211\u4eec\u5c31\u628adp\u5bf9\u89d2\u7ebf\u7684\u5143\u7d20\u90fd\u8bbe\u7f6e\u4e3atrue\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u5b57\u7b26\u7684\u60c5\u51b5\u5728\u904d\u5386\u7684\u65f6\u5019\u5c31\u4e0d\u8003\u8651\u5566\u3002\u65f6\u95f4\u590d\u6742\u5ea6O(n<sup>2<\/sup>)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6O(n<sup>2<\/sup>)\u3002<\/p>\n<pre><code class=\"language-java\">\/\/2.\u52a8\u6001\u89c4\u5212\npublic String longestPalindrome(String s) {\n    char[] charArr = s.toCharArray();\n    \/\/dp[i][j] \u8868\u793a s[i, ... ,j] \u662f\u5426\u662f\u56de\u6587\u4e32\n    boolean dp[][] = new boolean[charArr.length][charArr.length];\n    \/\/dp\u6570\u7ec4\u5bf9\u89d2\u7ebf\u4e0a\u7684\u8868\u793ai=j\uff0c\u5373\u5355\u4e2a\u5b57\u7b26\u4e3a\u56de\u6587\u4e32\n    for(int i = 0; i &lt; charArr.length; i++){\n        dp[i][i] = true;\n    }\n    \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u5f00\u59cb\u4f4d\u7f6e\u548c\u957f\u5ea6\n    int start = 0, maxLen = 1;\n    for(int j = 1; j &lt; charArr.length; j++){\n        for(int i = 0; i &lt; j; i++){\n            if(charArr[i] == charArr[j]){\n                \/\/charArr[i,...,j]\u4e3a\u4e24\u4e2a\u5b57\u7b26\u6216\u8005\u4e09\u4e2a\u5b57\u7b26\uff0c\u5e76\u4e14charArr[i] == charArr[j]\uff0c\u90a3\u4e48\u5c31\u662f\u56de\u6587\u5b50\u4e32\n                if(j - i + 1 == 2 || j - i + 1 == 3){\n                    dp[i][j] = true;\n                }else{\/\/charArr[i,...,j]\u5927\u4e8e\u4e09\u4e2a\u5b57\u7b26\uff0c\u90a3\u4e48\u53d6\u51b3\u4e8echarArr[i+1,...,j-1]\u662f\u5426\u4e3a\u56de\u6587\u5b50\u4e32\n                    dp[i][j] = dp[i+1][j-1];\n                }\n            }else{\n                dp[i][j] = false;\n            }\n            \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u4f4d\u7f6e\n            if(dp[i][j] &amp;&amp; maxLen &lt; j - i + 1){\n                start = i;\n                maxLen = j - i + 1;\n            }\n        }\n    }\n    return s.substring(start,start + maxLen);\n}<\/code><\/pre>\n<h3>\u4e09\u3001\u52a8\u6001\u89c4\u5212\uff0c\u4e8c\u7ef4\u6570\u7ec4: dp[i][j]\u4e3a\u5b50\u4e32s[i,&#8230;,j] \u4ee5i\u5f00\u59cb\u5230j\u7ed3\u5c3e\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u7684\u957f\u5ea6<\/h3>\n<p>\u5982\u679c\u53ea\u7528boolean\u6765\u5b9a\u4e49dp\u4e8c\u7ef4\u6570\u7ec4\u7684\u8bdd\uff0c\u662f\u65e0\u6cd5\u8fdb\u884c\u72b6\u6001\u538b\u7f29\u6210\u4e00\u7ef4\u6570\u7ec4\u7684\uff0c\u5982\u679c\u60f3\u628a\u4e8c\u7ef4\u6570\u7ec4\u538b\u7f29\u6210\u4e00\u7ef4\u6570\u7ec4\uff0c\u90a3\u4e48\u4e00\u7ef4\u6570\u7ec4\u5305\u542b\u7684\u4fe1\u606f\u5fc5\u987b\u505a\u591f\u591a\u3002<\/p>\n<h4>1\u3001\u5b9a\u4e49\u72b6\u6001<\/h4>\n<p><code> dp[i][j]<\/code>\u6570\u7ec4\u7684\u5b9a\u4e49\uff0c\u5fc5\u987b\u80fd\u6839\u636e<code>s[i+1,\u2026,j-1]<\/code>\u7684\u72b6\u6001\u63a8\u7b97\u51fa<code>s[i,\u2026,j]<\/code>\u7684\u72b6\u6001\uff0c\u6211\u4eec\u5b9a\u4e49\u8fd9\u6837\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4\uff0c<code> dp[i][j]<\/code>\u4e3a\u5b50\u4e32<code>s[i,...,j]<\/code> <code>\u4ee5i\u5f00\u59cb\u5230j\u7ed3\u5c3e<\/code>\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u7684<code>\u957f\u5ea6<\/code>\uff0c<strong>\u5fc5\u987b\u4ee5i\u5f00\u5934\u4ee5j\u7ed3\u5c3e<\/strong>\u3002\u8fd9\u91cc\u5b50\u4e32\u5b9a\u4e49\u4e3a\u5de6\u95ed\u53f3\u95ed\u533a\u95f4\uff0c\u5373\u53ef\u4ee5\u53d6\u5230 <code>s[i]<\/code> \u548c <code>s[j]<\/code>\u3002<\/p>\n<h4>2\u3001\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b<\/h4>\n<p>\u5982\u679c<code>s[i] == s[j]<\/code>\uff0c\u5e76\u4e14<code>dp[i+1][j-1]<\/code>\u7b49\u4e8e<code>s[i+1,...,j-1]<\/code>\u7684\u957f\u5ea6\uff0c\u4e5f\u5c31\u662f\u8bf4<code>s[i+1,...,j-1]<\/code>\u5982\u679c\u662f\u56de\u6587\u5b50\u4e32\u7684\u8bdd\uff0c\u5728\u5b83\u524d\u9762\u4e00\u4e2a\u4f4d\u7f6e\u548c\u540e\u9762\u4e00\u4e2a\u4f4d\u7f6e\u5206\u522b\u589e\u52a0\u4e00\u4e2a\u76f8\u540c\u7684\u5143\u7d20\uff0c\u90a3\u4e48<code>s[i,...,j]<\/code>\u4e5f\u662f\u56de\u6587\u5b50\u4e32\uff0c\u53ea\u9700\u8981\u5728\u539f\u6765\u7684\u957f\u5ea6\u52a0\u4e0a2\uff0c\u8fd9\u4e2a\u5c31\u662f\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u7684\u6838\u5fc3\u4e86\u3002\u5982\u679c<code>s[i] != s[j]<\/code>\uff0c<strong>\u5fc5\u987b\u4ee5i\u5f00\u5934\u4ee5j\u7ed3\u5c3e<\/strong>\u7684\u56de\u6587\u5b50\u4e32\u957f\u5ea6\u5c31\u4e3a0\uff0c\u800c\u5982\u679c<code>s[i] == s[j]<\/code>\u4f46\u4ee5<code>i+1<\/code>\u5f00\u5934\u5230<code>j-1<\/code>\u7ed3\u5c3e\u7684\u5b50\u4e32\u4e0d\u662f\u56de\u6587\u5b50\u4e32\uff0c\u90a3\u4e48<code>s[i+1,...,j-1]<\/code>\u4e24\u5934\u589e\u52a0\u4e00\u4e2a\u76f8\u540c\u7684\u5143\u7d20\uff0c\u5b83\u4e5f\u4e0d\u662f\u56de\u6587\u5b50\u4e32\uff0c\u56e0\u4e3a<code>s[i+1,...,j-1]<\/code>\u672c\u8eab\u5c31\u4e0d\u662f\u56de\u6587\u5b50\u4e32\u3002\u6240\u4ee5\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u5982\u4e0b\u3002<br \/>\n<img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/02\/3.png\" alt=\"2.png\" \/><\/p>\n<h4>3\u3001\u8fb9\u754c\u6761\u4ef6<\/h4>\n<p>\u6700\u57fa\u7840\u7684\u60c5\u51b5\u662f\u53ea\u6709\u4e00\u4e2a\u5b57\u7b26\uff0c\u90a3\u4e48\u5b83\u80af\u5b9a\u662f\u56de\u6587\u4e32\uff0c\u5e76\u4e14\u957f\u5ea6\u4e3a1\uff0c\u4e5f\u5c31\u662f\u5728dp\u6570\u7ec4\u7684\u5bf9\u89d2\u7ebf\u4e0a\uff0c\u6b64\u65f6i=j\u3002<\/p>\n<p>\u5206\u4e24\u79cd\u60c5\u51b5\u8fdb\u884c\u8ba8\u8bba\uff0c<code>s[i] == s[j]<\/code>\u548c<code>s[i] != s[j]<\/code>\u3002<\/p>\n<p><code>s[i] == s[j]<\/code>\u65f6\uff1a<\/p>\n<ul>\n<li>\u5982\u679c<code>s[i,\u2026,j]<\/code>\u53ea\u67092\u4e2a\u5b57\u7b26\uff0c\u5e76\u4e14<code>s[i] == s[j]<\/code>\uff0c\u6bd4\u5982<code>&quot;AA&quot;<\/code>\u90a3\u4e48<code>dp[i][j]<\/code>\u7b49\u4e8e2\u3002<\/li>\n<li>\u5982\u679c<code>s[i,\u2026,j]<\/code>\u53ea\u67093\u4e2a\u5b57\u7b26\uff0c\u5e76\u4e14<code>s[i] == s[j]<\/code>\uff0c\u6bd4\u5982<code>&quot;ABA&quot;<\/code>\u90a3\u4e48<code>dp[i][j]<\/code>\u7b49\u4e8e3\u3002<\/li>\n<li><code>s[i+1,...,j-1]<\/code>\u7684\u957f\u5ea6<code>(j - 1) - (i + 1) + 1=dp[i+1][j-1]<\/code>\uff0c\u6839\u636e\u72b6\u6001\u65b9\u7a0b\u6765\u63a8\u7b97\u51fa<code>d[i]p[j]<\/code>\uff0c\u5373<code>dp[i][j] = dp[i+1][j-1] + 2<\/code>\u3002<\/li>\n<li>\u5426\u5219<code>dp[i][j] = 0<\/code>\uff0c\u56e0\u4e3a\u867d\u7136\u6b64\u65f6i\u548cj\u5904\u7684\u5143\u7d20\u76f8\u7b49\uff0c\u4f46<code>s[i+1,\u2026,j-1]<\/code>\u5e76\u4e0d\u662f\u56de\u6587\u5b50\u4e32\uff0c\u8fdb\u800c<code>s[i,\u2026,j]<\/code>\u4e5f\u4e0d\u662f\u56de\u6587\u5b50\u4e32\u3002<\/li>\n<\/ul>\n<p><code>s[i] != s[j]<\/code>\u65f6\uff1a<\/p>\n<ul>\n<li>\u5982\u679c<code>s[i] != s[j]<\/code>\uff0c\u90a3\u4e48<code>dp[i][j]=0<\/code>\u3002<\/li>\n<\/ul>\n<h4>4\u3001\u6839\u636e\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u904d\u5386<\/h4>\n<p>\u904d\u5386\u4ece\u5de6\u5230\u53f3\u4ece\u4e0a\u5f80\u4e0b\u8fdb\u884c\uff0c\u56e0\u4e3a<code>s[i,\u2026,j]<\/code>\u4e3as\u7684\u4e00\u4e2a\u5b50\u4e32\uff0c\u6240\u4ee5 i \u5c0f\u4e8e j \u3002\u56e0\u4e3a\u521d\u59cb\u5316\u6211\u4eec\u5c31\u628adp\u5bf9\u89d2\u7ebf\u7684\u5143\u7d20\u90fd\u8bbe\u7f6e\u4e3a1\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u5b57\u7b26\u7684\u60c5\u51b5\u5728\u904d\u5386\u7684\u65f6\u5019\u5c31\u4e0d\u8003\u8651\u5566\u3002\u65f6\u95f4\u590d\u6742\u5ea6O(n<sup>2<\/sup>)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6O(n<sup>2<\/sup>)\u3002<\/p>\n<pre><code class=\"language-java\">\/\/ 3.\u52a8\u6001\u89c4\u5212,\u4e8c\u7ef4\u6570\u7ec4: dp[i][j]\u4e3a\u5b50\u4e32s[i,...,j] \u4ee5i\u5f00\u59cb\u5230j\u7ed3\u5c3e\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u7684\u957f\u5ea6\npublic String longestPalindrome(String s) {\n    char[] charArr = s.toCharArray();\n    \/\/dp[i][j]\u4e3a\u5b50\u4e32s[i,...,j] \u4ee5i\u5f00\u59cb\u5230j\u7ed3\u5c3e\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u7684\u957f\u5ea6\n    int dp[][] = new int[charArr.length][charArr.length];\n    \/\/dp\u6570\u7ec4\u5bf9\u89d2\u7ebf\u4e0a\u7684\u8868\u793ai=j\uff0c\u5373\u5355\u4e2a\u5b57\u7b26\u4e3a\u56de\u6587\u4e32\uff0c\u521d\u59cb\u5316\u957f\u5ea6\u4e3a1\n    for(int i = 0; i &lt; charArr.length; i++){\n        dp[i][i] = 1;\n    }\n    \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u5f00\u59cb\u4f4d\u7f6e\u548c\u957f\u5ea6\n    int start = 0, maxLen = 1;\n    for(int j = 1; j &lt; charArr.length; j++){\n        for(int i = 0; i &lt; j; i++){\n            if(charArr[i] == charArr[j]){\n                \/\/base case\uff1acharArr[i,...,j]\u4e3a\u4e24\u4e2a\u5b57\u7b26\u6216\u8005\u4e09\u4e2a\u5b57\u7b26\uff0c\u5e76\u4e14charArr[i] == charArr[j]\uff0c\u90a3\u4e48\u5c31\u662f\u56de\u6587\u5b50\u4e32\n                if(j - i + 1 == 2 ){\n                    dp[i][j] = 2;\n                }else if(j - i + 1 == 3){\n                    dp[i][j] = 3;\n                }else if(dp[i+1][j-1] == (j - 1) - (i + 1) + 1){\n                    \/\/charArr[i,...,j]\u5927\u4e8e\u4e09\u4e2a\u5b57\u7b26\uff0c\u90a3\u4e48\u53d6\u51b3\u4e8echarArr[i+1,...,j-1]\u7684\u957f\u5ea6\n                    \/\/\u5982\u679ccharArr[i+1,...,j-1]\u7684\u957f\u5ea6(j - 1) - (i + 1) + 1 = dp[i+1][j-1]\uff0c\u90a3\u4e48charArr[i+1,...,j-1]\u4e3a\u56de\u6587\u4e32\uff0c\u5e76\u4e14charArr[i,...,j]\u4e5f\u662f\u56de\u6587\u4e32\n                    \/\/\u6240\u4ee5dp[i][j] = dp[i+1][j-1] + 2\n                    dp[i][j] = dp[i+1][j-1] + 2;\n                }else{\n                    dp[i][j] = 0;\n                }\n            }else{\n                dp[i][j] = 0;\n            }\n            \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u4f4d\u7f6e\n            if(dp[i][j] &gt; 0 &amp;&amp; maxLen &lt; j - i + 1){\n                start = i;\n                maxLen = j - i + 1;\n            }\n        }\n    }\n    return s.substring(start,start + maxLen);\n}<\/code><\/pre>\n<h3>\u56db\u3001\u52a8\u6001\u89c4\u5212\uff0c\u4e00\u7ef4\u6570\u7ec4: dp[j]\u4e3a\u5b50\u4e32s[i,&#8230;,j] \u4ee5j\u7ed3\u5c3e\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u7684\u957f\u5ea6<\/h3>\n<p>\u65b9\u6cd5\u4e09\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(n<sup>2<\/sup>)\uff0c\u5176\u5b9e\u662f\u53ef\u4ee5\u8fdb\u884c\u72b6\u6001\u538b\u7f29\u7684\uff0c\u53ea\u7528\u4e00\u4e2a\u4e00\u7ef4dp\u6570\u7ec4\u5c31\u53ef\u4ee5\uff0c\u524d\u63d0\u662f\u8fdb\u884c\u538b\u7f29\u7684\u4e8c\u7ef4\u6570\u7ec4\u8981\u6709\u8db3\u591f\u7684\u4fe1\u606f\uff0c\u624d\u80fd\u591f\u538b\u7f29\u6210\u4e00\u7ef4\u6570\u7ec4\uff0c\u5982\u679c\u662f\u65b9\u6cd5\u4e00\u7684Boolean\u7c7b\u578b\u7684\u4e8c\u7ef4\u6570\u7ec4\u5c31\u65e0\u6cd5\u8fdb\u884c\u72b6\u6001\u538b\u7f29\uff0c\u56e0\u4e3a\u5b83\u65e0\u6cd5\u63d0\u4f9b\u8db3\u591f\u591a\u7684\u4fe1\u606f\u3002<\/p>\n<h4>1\u3001\u5b9a\u4e49\u72b6\u6001<\/h4>\n<p><code> dp[j]<\/code>\u5b9a\u4e49\u4e3a\u5b50\u4e32<code>s[i,...,j]<\/code> <code>\u4ecei\u5f00\u59cb\u5bfb\u627e<\/code> <code>\u4ee5j\u7ed3\u5c3e<\/code>\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u7684<code>\u957f\u5ea6<\/code>\uff0c\u6ce8\u610fdp\u91cc\u9762\u5b58\u653e\u7684\u662f\u56de\u6587\u5b50\u4e32\u7684\u957f\u5ea6\u4e86\u3002\u8fd9\u91cc\u5b50\u4e32\u5b9a\u4e49\u4e3a\u5de6\u95ed\u53f3\u95ed\u533a\u95f4\uff0c\u5373\u53ef\u4ee5\u53d6\u5230 <code>s[i]<\/code> \u548c <code>s[j]<\/code>\u3002<\/p>\n<h4>2\u3001\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b<\/h4>\n<p>\u5047\u5982<code>s[i+1,...,j-1]<\/code>\u4e3a\u56de\u6587\u5b50\u4e32\uff0c\u5e76\u4e14\u5b83\u7684\u957f\u5ea6\u4e3a<code>dp[j-1]=(j - 1) - (i + 1) + 1<\/code>\uff0c\u90a3\u4e48\u5982\u679c<code>s[i] == s[j]<\/code>\uff0c\u4e5f\u5c31\u6709<code>s[i,...,j]<\/code>\u4e5f\u662f\u56de\u6587\u5b50\u4e32\uff0c\u957f\u5ea6\u589e\u52a0\u4e862\uff0c\u8fd9\u4e2a\u5c31\u662f\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u7684\u6838\u5fc3\u4e86\u3002\u5982\u679c<code>s[i] != s[j]<\/code>\uff0c<strong>\u5fc5\u987b\u4ee5j\u7ed3\u5c3e<\/strong>\u7684\u56de\u6587\u5b50\u4e32\u957f\u5ea6\u5c31\u9700\u8981\u91cd\u65b0\u8ba1\u7b97\u4e86\uff0c\u800c\u5982\u679c<code>s[i] == s[j]<\/code>\u4f46\u4ee5<code>i+1<\/code>\u5f00\u5934\u5230<code>j-1<\/code>\u7ed3\u5c3e\u7684\u5b50\u4e32\u4e0d\u662f\u56de\u6587\u5b50\u4e32\uff0c\u90a3\u4e48<strong>\u5fc5\u987b\u4ee5j\u7ed3\u5c3e<\/strong>\u7684\u56de\u6587\u5b50\u4e32\u957f\u5ea6\u4e5f\u9700\u8981\u91cd\u65b0\u8ba1\u7b97\u3002\u6240\u4ee5\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u5982\u4e0b\u3002<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/02\/4.png\" alt=\"2.png\" \/><\/p>\n<h4>3\u3001\u8fb9\u754c\u6761\u4ef6<\/h4>\n<p>\u6700\u57fa\u7840\u7684\u60c5\u51b5\u662f\u7b2c\u4e00\u4e2a\u5b57\u7b26\uff0c\u5b83\u53ea\u6709\u81ea\u5df1\u672c\u8eab\uff0c\u662f\u56de\u6587\u5b50\u4e32\uff0c\u5e76\u4e14\u957f\u5ea6\u4e3a1\uff0c\u6240\u4ee5dp[0]=1\u3002<\/p>\n<p>\u5982\u679c\u6211\u4eec\u77e5\u9053<code>dp[j-1]<\/code>\uff0c\u90a3\u4e48\u4ece<code>s[j]<\/code>\u5f00\u59cb\u5f80\u524d\u63a8\u7b97<code>dp[j-1]<\/code>\u4e2a\u5143\u7d20\u6765\u8fdb\u884c\u6700\u5927\u957f\u5ea6\u56de\u6587\u5b50\u4e32\u7684\u611f\u77e5\u3002<\/p>\n<p>\u6839\u636edp\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u8bb0\u5b50\u4e32P=<code>s[j-dp[j-1],...,j-1]<\/code>\u4e3a\u56de\u6587\u5b50\u4e32\uff0c\u90a3\u4e48P\u524d\u9762\u4e00\u4e2a\u5143\u7d20\u7684\u4e0b\u6807\u4e3a<code>j - dp[j-1] - 1<\/code>\uff0c\u5982\u679c<code>s[j-dp[j-1] - 1] == s[j]<\/code>\uff0c\u90a3\u4e48<code>s[j-dp[j-1]-1,j-dp[j-1],...,j-1,j]<\/code>\u4e5f\u662f\u56de\u6587\u5b50\u4e32\uff0c\u9700\u8981\u6ce8\u610f\u4e0b\u6807<code>j - dp[j-1] - 1<\/code>\u5fc5\u987b\u5927\u4e8e\u96f6\uff0c\u5426\u5219\u5c31\u8d8a\u754c\u4e86\u3002<\/p>\n<p>\u5982\u679c<code>s[j-dp[j-1] - 1] != s[j]<\/code>\uff0c\u6b64\u65f6\u5c31\u6ca1\u6709\u529e\u6cd5\uff0c\u53ea\u80fd\u904d\u5386\u4e86\uff0c\u4f46\u904d\u5386\u7684\u5de6\u8fb9\u6761\u4ef6\u53ef\u4ee5\u7f29\u77ed\u5230<code>j-dp[j - 1]<\/code>\uff0c\u56e0\u4e3a\u6839\u636edp\u6570\u7ec4\u7684\u5b9a\u4e49\uff0c\u4ece\u4e0b\u6807<code>j-dp[j - 1]<\/code>\u518d\u5f80\u524d\u4e0d\u53ef\u80fd\u6784\u6210\u66f4\u957f\u7684\u56de\u6587\u5b50\u4e32\u4e86\uff0c\u53ea\u9700\u8981\u4ece<code>s[j-dp[j-1],j-dp[j-1],...,j-1,j]<\/code>\u627e\u5230\u4e00\u4e2a\u6700\u957f\u7684\u4ee5j\u7ed3\u5c3e\u7684\u56de\u6587\u5b50\u4e32\u5373\u53ef\u3002<\/p>\n<h4>4\u3001\u6839\u636e\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u904d\u5386<\/h4>\n<p>\u904d\u5386\u4ece\u5de6\u5230\u53f3\u8fdb\u884c\uff0c\u56e0\u4e3a<code>s[i,\u2026,j]<\/code>\u4e3as\u7684\u4e00\u4e2a\u5b50\u4e32\uff0c\u6240\u4ee5 i \u5c0f\u4e8e j \u3002\u65f6\u95f4\u590d\u6742\u5ea6O(n<sup>2<\/sup>)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6O(n)\u3002<\/p>\n<pre><code class=\"language-java\">\/\/ 4.\u52a8\u6001\u89c4\u5212,\u4e00\u7ef4\u6570\u7ec4: dp[j]\u4e3a\u5b50\u4e32s[i,...,j] \u4ee5j\u7ed3\u5c3e\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u7684\u957f\u5ea6\npublic String longestPalindrome(String s) {\n    char[] charArr = s.toCharArray();\n    \/\/dp[j]\u4e3a\u5b50\u4e32s[i,...,j] \u4ee5j\u7ed3\u5c3e\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u7684\u957f\u5ea6\n    int dp[] = new int[charArr.length];\n    \/\/\u7b2c\u4e00\u4e2a\u5b57\u7b26\u4e32\u4e3a\u56de\u6587\u4e32\uff0c\u5e76\u4e14\u957f\u5ea6\u4e3a1\n    dp[0] = 1;\n    \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u5f00\u59cb\u4f4d\u7f6e\u548c\u957f\u5ea6\n    int start = 0, maxLen = 1;\n    for(int j = 1; j &lt; charArr.length; j++){\n        if(j - dp[j - 1] - 1 &gt;= 0 &amp;&amp; charArr[j] == charArr[j - dp[j - 1] - 1]){\n            dp[j] = dp[j - 1] + 2;\n        }else{\n            \/\/\u4ecej - dp[j-1]\u5f00\u59cb\u5230j\u8fdb\u884c\u67e5\u627e\uff0c\u4ee5j\u7ed3\u5c3e\u7684\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u957f\u5ea6\n            int j_len = j - (j - dp[j - 1]) + 1;\n            for(int i = j - dp[j - 1],right = j;i &lt; j; i++){\n                if(charArr[i] != charArr[right]){\n                    right = j;\n                    j_len--;\n                    i = j - j_len;\n                }else{\n                    right--;\n                }\n            }\n            dp[j] = j_len;\n        }\n        \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u4f4d\u7f6e\n        if(maxLen &lt; dp[j]){\n            start = j - dp[j] + 1;\n            maxLen = dp[j];\n        }\n    }\n    return s.substring(start,start + maxLen);\n}<\/code><\/pre>\n<h3>\u4e94\u3001\u52a8\u6001\u89c4\u5212\uff0cdp\u4f7f\u7528\u4e00\u7ef4\u6570\u7ec4: \u5b9a\u4e49dp[j]\u8868\u793a\u4ee5\u4f4d\u7f6ej\u7ed3\u675f\u7684\u6700\u957f\u7684\u56de\u6587\u5b50\u4e32\u7684\u8d77\u59cb\u4f4d\u7f6e<\/h3>\n<p>\u65b9\u6cd5\u56db\u662f\u4e00\u79cd\u65b9\u5f0f\u4f7f\u7528\u4e00\u7ef4\u6570\u7ec4\u6765\u6784\u9020\u52a8\u6001\u89c4\u5212\uff0c\u4ece\u800c\u4f7f\u7a7a\u95f4\u590d\u6742\u5ea6\u964d\u4f4e\u4e3aO(n)\u3002\u4e0b\u9762\u6211\u4eec\u4f7f\u7528\u53e6\u5916\u4e00\u79cddp\u4e00\u7ef4\u6570\u7ec4\uff0c\u4e5f\u4f7f\u7a7a\u95f4\u590d\u6742\u5ea6\u964d\u4f4e\u4e3aO(n)\u3002\u6240\u4ee5\u8bf4\uff0c\u5b9a\u4e49\u4e0d\u540c\u7684dp\u6570\u7ec4\u6784\u9020\u4e0d\u540c\u7684\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff0c\u4ece\u800c\u6784\u9020\u4e0d\u540c\u7684\u52a8\u6001\u89c4\u5212\uff0c\u4e0d\u8fc7\u65b9\u6cd5\u90fd\u662f\u5927\u540c\u5c0f\u5f02\u7684\uff0c\u90fd\u5f88\u7c7b\u4f3c\uff0c\u6761\u6761\u5927\u8def\u901a\u7f57\u9a6c\uff0c\u6b8a\u9014\u540c\u5f52\u800c\u5df2\u3002<\/p>\n<h4>1\u3001\u5b9a\u4e49\u72b6\u6001<\/h4>\n<p><code> dp[j]<\/code>\u5b9a\u4e49\u4e3a\u5b50\u4e32<code>s[i,...,j]<\/code> <code>\u4ee5j\u7ed3\u5c3e<\/code>\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u7684<code>\u8d77\u59cb\u4f4d\u7f6e<\/code>\uff0c\u6ce8\u610f\u8fd9\u662f\u6807\u8bb0\u7684\u4e0d\u518d\u662f\u957f\u5ea6\u4e86\u800c\u662f\u56de\u6587\u5b50\u4e32\u8d77\u59cb\u70b9\u7684\u4f4d\u7f6e\u3002<\/p>\n<h4>2\u3001\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b<\/h4>\n<p>\u4e0a\u9762\u7684\u65b9\u5f0f\u662f\u6839\u636e\u957f\u5ea6\u6765\u8ba1\u7b97\uff0c\u8fd9\u6b21\u6839\u636e\u8d77\u59cb\u70b9\u7684\u4f4d\u7f6e\u8ba1\u7b97\uff0c\u4e5f\u4f1a\u66f4\u5bb9\u6613\u4e9b\u3002<\/p>\n<p>\u5982\u679c<code>s[i] == s[j]<\/code>\uff0c\u5e76\u4e14<code>dp[j-1]<\/code>\u7b49\u4e8e<code>s[i+1,...,j-1]<\/code>\u7684\u957f\u5ea6\uff0c\u4e5f\u5c31\u662f\u8bf4<code>s[i+1,...,j-1]<\/code>\u5982\u679c\u662f\u56de\u6587\u5b50\u4e32\u7684\u8bdd\uff0c\u5728\u5b83\u524d\u9762\u4e00\u4e2a\u4f4d\u7f6e\u548c\u540e\u9762\u4e00\u4e2a\u4f4d\u7f6e\u5206\u522b\u589e\u52a0\u4e00\u4e2a\u76f8\u540c\u7684\u5143\u7d20\uff0c\u90a3\u4e48<code>s[i,...,j]<\/code>\u4e5f\u662f\u56de\u6587\u5b50\u4e32\uff0c\u552f\u4e00\u4e0d\u540c\u7684\u662f\uff0c\u6b64\u65f6\u7684\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u8d77\u59cb\u4f4d\u7f6e\u5f80\u524d\u79fb\u52a8\u4e00\u4e2a\u4f4d\u7f6e\uff0c\u4e5f\u5c31\u662f<code>dp[j] = dp[j - 1] - 1<\/code>\uff0c\u8fd9\u4e2a\u5c31\u662f\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u7684\u6838\u5fc3\u4e86\u3002\u5982\u679c<code>s[i] != s[j]<\/code>\uff0c<strong>\u5fc5\u987b\u4ee5j\u7ed3\u5c3e<\/strong>\u7684\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u8d77\u59cb\u4f4d\u7f6e\u5c31\u9700\u8981\u8ba1\u7b97\u4e86\uff0c\u53ea\u4e0d\u8fc7\u4e0d\u9700\u8981\u4ece\u5934\u5f00\u59cb\u7b97\uff0c\u56e0\u4e3a<code>dp[j-1]<\/code>\u8bb0\u5f55\u4e86j\u4f4d\u7f6e\u524d\u9762\u5143\u7d20\u6240\u80fd\u611f\u77e5\u7684\u8303\u56f4\u7684\u5f00\u59cb\u4f4d\u7f6e\uff0c\u56e0\u6b64\u4ece\u8fd9\u4e2a\u8d77\u59cb\u4f4d\u7f6e\u5f00\u59cb\u5bfb\u627e\u4ee5j\u7ed3\u5c3e\u7684\u6700\u5927\u56de\u6587\u5b50\u4e32\u5c31\u53ef\u4ee5\u3002\u6240\u4ee5\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u5982\u4e0b\u3002<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/02\/5.png\" alt=\"2.png\" \/><\/p>\n<h4>3\u3001\u8fb9\u754c\u6761\u4ef6<\/h4>\n<p>\u6700\u57fa\u7840\u7684\u60c5\u51b5\u662f\u7b2c\u4e00\u4e2a\u5b57\u7b26\uff0c\u5b83\u53ea\u6709\u81ea\u5df1\u672c\u8eab\uff0c\u662f\u56de\u6587\u5b50\u4e32\uff0c\u5e76\u4e14\u8d77\u59cb\u4f4d\u7f6e\u4e3a0\uff0c\u6240\u4ee5dp[0]=0\u3002<\/p>\n<p>\u5982\u679c\u6211\u4eec\u77e5\u9053<code>dp[j-1]<\/code>\uff0c\u6839\u636edp\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u8bb0\u5b50\u4e32P=<code>s[dp[j-1],...,j-1]<\/code>\u4e3a\u4ee5j-1\u7ed3\u5c3e\u7684\u6700\u957f\u56de\u6587\u5b50\u4e32\uff0c\u90a3\u4e48P\u524d\u9762\u4e00\u4e2a\u5143\u7d20\u7684\u4e0b\u6807\u4e3a<code>dp[j-1] - 1<\/code>\uff0c\u5982\u679c<code>s[dp[j-1] - 1] == s[j]<\/code>\uff0c\u90a3\u4e48<code>s[dp[j-1]-1,dp[j-1],...,j-1,j]<\/code>\u4e5f\u662f\u56de\u6587\u5b50\u4e32\u3002<\/p>\n<p>\u5982\u679c<code>s[dp[j-1] - 1] != s[j]<\/code>\uff0c\u6b64\u65f6\u5c31\u6ca1\u6709\u529e\u6cd5\uff0c\u53ea\u80fd\u904d\u5386\u4e86\uff0c\u4f46\u904d\u5386\u7684\u5de6\u8fb9\u6761\u4ef6\u53ef\u4ee5\u7f29\u77ed\u5230<code>dp[j - 1]<\/code>\uff0c\u56e0\u4e3a\u6839\u636edp\u6570\u7ec4\u7684\u5b9a\u4e49\uff0c\u4ece\u4e0b\u6807<code>dp[j - 1]<\/code>\u518d\u5f80\u524d\u4e0d\u53ef\u80fd\u6784\u6210\u66f4\u957f\u7684\u56de\u6587\u5b50\u4e32\u4e86\uff0c\u53ea\u9700\u8981\u4ece<code>s[dp[j-1],dp[j-1]+1,...,j-1,j]<\/code>\u627e\u5230\u4e00\u4e2a\u6700\u957f\u7684\u4ee5j\u7ed3\u5c3e\u7684\u6700\u957f\u56de\u6587\u5b50\u4e32\u5373\u53ef\u3002<\/p>\n<h4>4\u3001\u6839\u636e\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u904d\u5386<\/h4>\n<p>\u904d\u5386\u4ece\u5de6\u5230\u53f3\u8fdb\u884c\uff0c\u56e0\u4e3a<code>s[i,\u2026,j]<\/code>\u4e3as\u7684\u4e00\u4e2a\u5b50\u4e32\uff0c\u6240\u4ee5 i \u5c0f\u4e8e j \u3002\u65f6\u95f4\u590d\u6742\u5ea6O(n<sup>2<\/sup>)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6O(n)\u3002<\/p>\n<pre><code class=\"language-java\">\/\/ 5.\u52a8\u6001\u89c4\u5212\uff0cdp\u4f7f\u7528\u4e00\u7ef4\u6570\u7ec4: \u5b9a\u4e49dp[j]\u8868\u793a\u5df2\u4f4d\u7f6ej\u7ed3\u675f\u7684\u6700\u957f\u7684\u56de\u6587\u5b50\u4e32\u7684\u8d77\u59cb\u4f4d\u7f6e\npublic String longestPalindrome5(String s) {\n    char[] charArr = s.toCharArray();\n    \/\/\u5b9a\u4e49dp[j]\u8868\u793a\u5df2\u4f4d\u7f6ej\u7ed3\u675f\u7684\u6700\u957f\u7684\u56de\u6587\u5b50\u4e32\u7684\u8d77\u59cb\u4f4d\u7f6e\n    int dp[] = new int[charArr.length];\n    \/\/\u9ed8\u8ba4\u7b2c\u4e00\u4e2a\u5143\u7d20\u4ece0\u53f7\u5143\u7d20\u5f00\u59cb\uff0c\u6240\u4ee5\u521d\u59cb\u5316\u4e3adp[0]\u521d\u59cb\u5316\u4e3a0\n    dp[0] = 0;\n    \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u5f00\u59cb\u4f4d\u7f6e\u548c\u957f\u5ea6\n    int start = 0, maxLen = 1;\n    for(int j = 1; j &lt; charArr.length; j++){\n        \/\/\u5f53\u524d\u4f4d\u7f6es[j]\u7b49\u4e8e\u4e0a\u4e00\u6b21\u56de\u6587\u5b50\u4e32\u5de6\u8fb9\u5b57\u7b26\uff0c\u4e5f\u5c31\u662fs[dp[j-1],...,j-1]\u4e32\u5de6\u53f3\u4e24\u8fb9\u7684\u5b57\u7b26\u76f8\u7b49\n        if(dp[j - 1] &gt; 0 &amp;&amp; charArr[j] == charArr[dp[j - 1] - 1]){\n            dp[j] = dp[j - 1] - 1;\n        }else{\n            \/\/\u4ecedp[j-1]\u5f00\u59cb\u5230j\u8fdb\u884c\u67e5\u627e\uff0c\u4ee5j\u7ed3\u5c3e\u7684\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u8d77\u59cb\u4f4d\u7f6e\n            int j_start = dp[j - 1];\n            for(int i = dp[j - 1],right = j;i &lt; right;i++){\n                if(charArr[i] != charArr[right]){\n                    right = j;\n                    j_start = i + 1;\n                }else{\n                    right--;\n                }\n            }\n            dp[j] = j_start;\n        }\n\n        \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u4f4d\u7f6e\n        if(maxLen &lt; j - dp[j] + 1){\n            start = dp[j];\n            maxLen = j - dp[j] + 1;\n        }\n\n    }\n    return s.substring(start,start + maxLen);\n}<\/code><\/pre>\n<h3>\u516d\u3001\u4e2d\u5fc3\u6269\u6563\u6cd5<\/h3>\n<p>\u4e2d\u5fc3\u6269\u6563\u7684\u4e3b\u8981\u601d\u60f3\u4e3a\uff0c\u4ee5\u5f53\u524d\u5143\u7d20\u4e3a\u4e2d\u5fc3\uff0c\u5411\u4e24\u8fb9\u8fdb\u884c\u6269\u5c55\uff0c\u76f4\u5230\u627e\u5230\u4e00\u4e2a\u6700\u957f\u7684\u56de\u6587\u5b50\u4e32\u4e3a\u6b62\u3002\u4ece\u4e2d\u5fc3\u6269\u5c55\u7684\u65f6\u5019\uff0c\u8003\u8651\u4ece\u4e2d\u5fc3\u4e00\u4e2a\u5143\u7d20\u6269\u5c55\u6216\u8005\u4ece\u4e2d\u5fc3\u4e24\u4e2a\u5143\u7d20\u8fdb\u884c\u6269\u5c55\uff0c\u56e0\u4e3a\u56de\u6587\u5b50\u4e32\u53ef\u80fd\u662f\u5947\u6570\u4e5f\u53ef\u80fd\u662f\u5076\u6570\u3002\u65f6\u95f4\u590d\u6742\u5ea6O(n<sup>2<\/sup>)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6O(1)\u3002<\/p>\n<pre><code class=\"language-java\">\/\/3.\u4e2d\u5fc3\u6269\u6563\u6cd5\npublic String longestPalindrome3(String s) {\n    \/\/\u8bb0\u5f55\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u5f00\u59cb\u4f4d\u7f6e\u548c\u957f\u5ea6\n    String palindrome = &quot;&quot;;\n    for(int k = 0; k &lt; s.length(); k++){\n        String temp = getPalindrome(s,k);\n        if(palindrome.length() &lt; temp.length()){\n            palindrome = temp;\n        }\n    }\n    return  palindrome;\n}\n\npublic String getPalindrome(String s, int i){\n    \/\/\u5bfb\u627e\u4ee5i\u4e3a\u4e2d\u5fc3\u7684\u56de\u6587\u5b50\u4e32\n    int from = i, to = i;\n    while(from &gt;= 0 &amp;&amp; to &lt; s.length() &amp;&amp; s.charAt(from) == s.charAt(to)){\n        from--;\n        to++;\n    }\n    String palindrome = s.substring(from + 1,to);\n\n    \/\/\u5bfb\u627e\u4ee5 i\u3001i+1 \u4e3a\u4e2d\u5fc3\u7684\u56de\u6587\u5b50\u4e32\n    from = i;\n    to = i + 1;\n    while(from &gt;= 0 &amp;&amp; to &lt; s.length() &amp;&amp; s.charAt(from) == s.charAt(to)){\n        from--;\n        to++;\n    }\n    String palindrome2 = s.substring(from + 1, to);\n    \/\/\u8fd4\u56de\u4e24\u4e2a\u4e2d\u6700\u957f\u7684\u90a3\u4e2a\n    return palindrome.length() &gt; palindrome2.length()?palindrome:palindrome2;\n}<\/code><\/pre>\n<h3>\u4e03\u3001Manacher\u7b97\u6cd5<\/h3>\n<h4>1\u3001\u80cc\u666f\u4ecb\u7ecd<\/h4>\n<p>\u9a6c\u62c9\u8f66\u7b97\u6cd5\u539f\u540d\u53ebManacher\u7b97\u6cd5\uff0c\u662f\u4e00\u4f4d\u53ebManacher\u7684\u4eba\u53d1\u660e\u7684\u3002\u56e0\u4e3a\u8c10\u97f3\u7684\u7f18\u6545\uff0c\u88ab\u56fd\u5185\u7a0b\u5e8f\u5458\u620f\u79f0\u4e3a\u9a6c\u62c9\u8f66\u7b97\u6cd5\u3002\u9a6c\u62c9\u8f66\u7b97\u6cd5\u4e3b\u8981\u7528\u6765\u89e3\u51b3\u6700\u957f\u56de\u6587\u5b50\u4e32\u7684\u95ee\u9898\uff0c\u4e00\u822c\u7684\u89e3\u6cd5\u65e0\u8bba\u662f\u4e2d\u5fc3\u63a2\u6d4b\u8fd8\u662f\u52a8\u6001\u89c4\u5212\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u90fd\u662fO(n<sup>2<\/sup>)\uff0c\u800c\u9a6c\u62c9\u8f66\u7b97\u6cd5\u53ef\u4ee5\u5c06\u65f6\u95f4\u4f18\u5316\u5230O(n)\u3002<\/p>\n<p>\u9a6c\u62c9\u8f66\u7b97\u6cd5\u9700\u8981\u9884\u5148\u5bf9\u5b57\u7b26\u4e32\u505a\u4e00\u4e9b\u5904\u7406\uff0c\u5728\u5b57\u7b26\u4e32\u4e2d\u63d2\u5165\u4e00\u4e9b\u7279\u6b8a\u5206\u9694\u7b26\u3002\u672c\u8d28\u4e0a\u6b64\u4e5f\u662f\u57fa\u4e8e\u4e2d\u5fc3\u63a2\u6d4b\u6cd5\uff0c\u4f46\u4e2d\u5fc3\u63a2\u6d4b\u6ca1\u6709\u8003\u8651\u5230\u56de\u6587\u7684\u5bf9\u79f0\u6027\uff0c\u505a\u4e86\u5f88\u591a\u65e0\u7528\u529f\u3002\u800c\u9a6c\u62c9\u8f66 \u7b97\u6cd5\u5728\u7a7a\u95f4\u4e0a\u505a\u4e86\u5f88\u591a\u6587\u7ae0\uff0c\u5c06\u4e4b\u524d\u5df2\u7ecf\u8ba1\u7b97\u8fc7\u7684\u5185\u5bb9\uff0c\u7f13\u5b58\u8d77\u6765\uff0c\u907f\u514d\u91cd\u590d\u7684\u8ba1\u7b97\uff0c\u8fd9\u6837\u5c31\u80fd\u5927\u5e45\u5ea6\u63d0\u9ad8\u6027\u80fd\u3002<\/p>\n<p>\u9996\u5148\u6765\u56de\u5fc6\u4e0b\u56de\u6587\u4e32\u662f\u4ec0\u4e48\uff0c\u56de\u6587\u4e32\u5c31\u662f\uff1a<\/p>\n<ul>\n<li>bab <\/li>\n<li>aba<\/li>\n<li>\u4e0a\u6d77\u81ea\u6765\u6c34\u6765\u81ea\u6d77\u4e0a<\/li>\n<\/ul>\n<p>\u5373\u6b63\u7740\u8bfb\u3001\u53cd\u7740\u8bfb\u90fd\u662f\u4e00\u6837\u7684\u5b57\u7b26\u4e32\u3002\u73b0\u5728\u7ed9\u4f60\u4e00\u4e2a\u5b57\u7b26\u4e32\uff0c\u6bd4\u5982babad\uff0c\u5982\u4f55\u6c42\u51fa\u8fd9\u4e2a\u5b57\u7b26\u4e32\u4e2d\u6700\u957f\u7684\u56de\u6587\u5b50\u4e32\u5462\uff1f\u8fd9\u56de\u5c31\u8981\u9760\u9a6c\u62c9\u8f66\u7b97\u6cd5\u4e86\u3002<\/p>\n<h4>2\u3001\u6539\u8fdb\u4e2d\u5fc3\u63a2\u6d4b\u6cd5<\/h4>\n<p>\u5148\u8bf4\u4e0b\u4e2d\u5fc3\u63a2\u6d4b\u6cd5\uff0c\u8fd9\u79cd\u65b9\u6cd5\u5f88\u597d\u7406\u89e3\uff0c\u4ee5<code>babad<\/code>\u8fd9\u4e2a\u5b57\u7b26\u4e32\u4e3a\u4f8b\uff0c\u4e2d\u5fc3\u63a2\u6d4b\u6cd5\u5de5\u4f5c\u539f\u7406\u5982\u4e0b\uff1a<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/1.png\" alt=\"2.png\" \/><\/p>\n<p>\u904d\u5386\u5b57\u7b26\u4e32\uff0c\u6bcf\u904d\u5386\u5230\u4e00\u4e2a\u5b57\u7b26\uff0c\u5c31\u4ee5\u8fd9\u4e2a\u5b57\u7b26\u4e3a\u4e2d\u5fc3\uff0c\u540c\u65f6\u5f80\u4e24\u8fb9\u6269\u5c55\uff0c\u76f4\u5230\u4e24\u8fb9\u4e0d\u7b49\u6216\u8d8a\u754c\u3002<br \/>\n\u6839\u636e\u4e0a\u8ff0\u505a\u6cd5\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u6c42\u51fa\u6700\u957f\u56de\u6587\u4e32\u4e3a<code>bab<\/code>\uff0c\u5f53\u65f6<code>aba<\/code>\u4e5f\u662f\u3002<\/p>\n<p>\u4e0d\u8fc7\u4e0a\u8ff0\u505a\u6cd5\u4f1a\u6709\u4e2a\u95ee\u9898\uff0c\u4ee5<code>abb<\/code>\u4e3a\u4f8b\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/2.png\" alt=\"2.png\" \/><\/p>\n<p>\u5982\u679c\u4ee5\u4e2d\u5fc3\u63a2\u6d4b\u6765\u8ba1\u7b97\uff0c\u6700\u7ec8\u4f1a\u5f97\u5230\u6700\u957f\u56de\u6587\u4e32\u4e3a<code>a<\/code>\uff0c\u4f46\u5b9e\u9645\u5e94\u8be5\u662f<code>bb<\/code><\/p>\n<p>\u4e0a\u8ff0\u505a\u6cd5\u9519\u8bef\u7684\u539f\u56e0\u662f\uff0c\u6ca1\u6709\u8003\u8651\u5230\u56de\u6587\u4e32\u7684\u5947\u5076\u957f\u5ea6\u95ee\u9898\u3002<code>abbcbba<\/code>\u8fd9\u4e2a\u5b57\u7b26\u4e32\u957f\u5ea6\u4e3a7\uff0c\u662f\u4ee5<code>c<\/code>\u4e3a\u4e2d\u5fc3\uff0c\u4e24\u8fb9\u5bf9\u79f0\u7684\u3002\u800c<code>abddbc<\/code>\u8fd9\u4e2a\u5b57\u7b26\u4e32\u957f\u5ea6\u4e3a6\uff0c\u662f\u4ee5\u4e24\u4e2a<code>d<\/code>\u4e2d\u95f4\u7684\u7a7a\u9699\u4e3a\u4e2d\u5fc3\uff0c\u4e24\u8fb9\u5bf9\u79f0\u7684\u3002\u56de\u6587\u4e32\u7684\u5947\u5076\u6027\u8d28\u4f1a\u5bfc\u81f4\u4e0d\u540c\u7684\u8ba1\u7b97\u65b9\u5f0f\u3002\u8ba1\u7b97\u7b2c\u4e8c\u4e2a\u5b57\u7b26\u4e32\u65f6\uff0c\u5e94\u5f53\u5c06\u7b2c\u4e00\u4e2a\u6307\u9488\u6307\u5411\u5de6\u8fb9\u7684<code>d<\/code>\uff0c\u518d\u5c06\u7b2c\u4e8c\u4e2a\u6307\u9488\u6307\u5411\u53f3\u8fb9\u7684<code>d<\/code>\uff0c\u7b2c\u4e00\u4e2a\u6307\u9488\u5f80\u5de6\u8fb9\u63a2\u6d4b\uff0c\u7b2c\u4e8c\u4e2a\u6307\u9488\u5f80\u53f3\u8fb9\u63a2\u6d4b\uff0c\u76f4\u5230\u4e24\u4e2a\u6307\u9488\u6307\u5411\u7684\u5b57\u7b26\u4e0d\u7b49\u3001\u6216\u8005\u8d8a\u754c\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/3.png\" alt=\"2.png\" \/><\/p>\n<p>\u7531\u4e8e\u6211\u4eec\u5e76\u4e0d\u77e5\u9053<strong>\u6700\u957f\u56de\u6587\u5b50\u4e32<\/strong>\u5230\u5e95\u662f\u5947\u6570\u957f\u5ea6\u3001\u8fd8\u662f\u5076\u6570\u957f\u5ea6\u3002<br \/>\n\u6240\u4ee5\u5728\u8ba1\u7b97\u7684\u65f6\u5019\uff0c\u9700\u8981\u5c06\u5947\u6570\u548c\u5076\u6570\u7684\u60c5\u51b5\u90fd\u8ba1\u7b97\u4e00\u6b21\uff0c\u518d\u6c42\u4e00\u4e2a\u6700\u5927\u503c\u3002<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/4.png\" alt=\"2.png\" \/><\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5bf9\u539f\u59cb\u5b57\u7b26\u4e32\u505a\u4e00\u4e9b\u5904\u7406\uff0c\u6765\u89e3\u51b3\u5b50\u4e32\u5947\u5076\u957f\u5ea6\u95ee\u9898\uff0c\u5982\u4e0b\u56fe\uff1a<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/5.png\" alt=\"2.png\" \/><\/p>\n<p>\u4e4b\u540e\u6211\u4eec\u5c31\u53ef\u4ee5\u5ffd\u7565\u5947\u5076\u957f\u5ea6\u95ee\u9898\uff0c\u7edf\u4e00\u7684\u7528\u4e2d\u5fc3\u63a2\u6d4b\u6cd5\u6765\u6c42\u6700\u957f\u56de\u6587\u5b50\u4e32\uff0c\u5047\u8bbe\u539f\u59cb\u5b57\u7b26\u4e32\u4e3a<code>xabbcbbay<\/code>\uff0c\u7ecf\u8fc7\u5904\u7406\u540e\u5982\u4e0b\u56fe\uff1a<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/6.png\" alt=\"2.png\" \/><\/p>\n<p>\u4e0a\u56fe\u4e2d\uff0c\u6700\u91cd\u8981\u7684\u662f\u7b2c\u4e09\u884c\uff0c\u5373<strong>\u56de\u6587\u534a\u5f84<\/strong>\uff0c<\/p>\n<ul>\n<li>\u6700\u5de6\u8fb9\u7684\u7bad\u5934\u4e0a\u6307\u5411\u7684<code>a<\/code>\u8fd9\u4e2a\u5b57\u7b26\uff0c\u5b83\u53ef\u4ee5\u5411\u5de6\/\u5411\u53f3\u6269\u5c551\u4f4d\uff0c\u4e5f\u5c31\u662f\u53d8\u6210<code>#a#<\/code>\u8fd9\u6837\u7684\u56de\u6587\u4e32\uff0c\u8fd9\u4e2a\u5b57\u7b26\u4e32\u603b\u957f\u5ea6\u662f<code>3<\/code>\uff0c\u4ee5<code>a<\/code>\u4e3a\u4e2d\u5fc3\u53ef\u4ee5\u5411\u4e24\u8fb9\u6269\u5c55<code>1<\/code>\u4f4d(\u4e0d\u5305\u62eca\u5b57\u7b26\u672c\u8eab)\uff0c\u6240\u4ee5\u8fd9\u4e2a\u5b57\u7b26\u7684\u56de\u6587\u534a\u5f84\u662f<code>1<\/code>\u3002<\/li>\n<li>\u4e2d\u95f4\u7bad\u5934\u6307\u5411\u7684<code>c<\/code>\u8fd9\u4e2a\u5b57\u7b26\uff0c\u5b83\u53ef\u4ee5\u5411\u5de6\/\u5411\u53f3\u6269\u5c557\u4f4d\uff0c\u5373\u5f80\u5de6\u662f:<code>#a#b#b#<\/code>\uff0c\u5f80\u53f3\u662f<code>#b#b#a#<\/code>\uff0c\u4ee5<code>c<\/code>\u4e3a\u4e2d\u5fc3\u53ef\u4ee5\u5411\u4e24\u8fb9\u6269\u5c557\u4f4d(\u4e0d\u5305\u62ecc\u5b57\u7b26\u672c\u8eab)\uff0c\u6240\u4ee5\u8fd9\u4e2a\u5b57\u7b26\u7684\u56de\u6587\u534a\u5f84\u662f<code>7<\/code>\u3002<\/li>\n<li>\u6700\u53f3\u8fb9\u7bad\u5934\u6307\u5411\u7684<code>#<\/code>\u8fd9\u4e2a\u5b57\u7b26\uff0c\u5b83\u53ef\u4ee5\u5411\u5de6\/\u5411\u53f3\u6269\u5c552\u4f4d\uff0c\u4e5f\u5c31\u662f\u53d8\u6210<code>#b#b#<\/code>\u8fd9\u6837\u7684\u56de\u6587\u4e32\uff0c\u8fd9\u4e2a\u5b57\u7b26\u4e32\u603b\u957f\u5ea6\u662f<code>5<\/code>\uff0c\u4ee5#\u4e3a\u4e2d\u5fc3\u53ef\u4ee5\u5411\u4e24\u8fb9\u6269\u5c55<code>2<\/code>\u4f4d\uff0c\u6240\u4ee5\u8fd9\u4e2a\u5b57\u7b26\u7684\u56de\u6587\u534a\u5f84\u662f<code>2<\/code>\u3002<\/li>\n<\/ul>\n<p>\u597d\uff0c\u91cd\u70b9\u6765\u4e86\u3002<\/p>\n<p>\u539f\u59cb\u5b57\u7b26\u662f<code>xabbcbbay<\/code>\uff0c\u5b83\u7684\u957f\u5ea6\u4e3a<code>9<\/code>\u3002\u800c\u7ecf\u8fc7\u5904\u7406\u540e\u7684\u5b57\u7b26\u4e32<code>#x#a#b#b#c#b#b#a#y#<\/code>\uff0c\u5b83\u7684\u957f\u5ea6\u4e3a<code>19<\/code>\uff0c\u4e5f\u5c31\u662f\u8bf4 *<em>\u539f\u5b57\u7b26\u4e32\u957f\u5ea6 <\/em> 2 + 1<strong> \u5c31\u7b49\u4e8e \u5904\u7406\u540e\u7684\u5b57\u7b26\u4e32\u957f\u5ea6\u3002\u73b0\u5728\u8ba1\u7b97<\/strong>\u56de\u6587\u534a\u5f84**\u65f6\uff0c\u8fd9\u4e2a\u957f\u5ea6\u4e0d\u5305\u62ec\u7bad\u5934\u6307\u5411\u7684\u5b57\u7b26\u672c\u8eab\u3002<\/p>\n<p>\u90a3\u4e48\u8ba1\u7b97\u51fa\u6765\u7684<strong>\u56de\u6587\u534a\u5f84\u6700\u5927\u503c<\/strong>\uff0c\u5c31\u7b49\u4e8e\u539f\u59cb\u5b57\u7b26\u4e32\u4e2d<strong>\u6700\u957f\u56de\u6587\u4e32\u7684\u957f\u5ea6<\/strong>\uff0c\u5373\u4e0a\u56fe\u4e2d\u95f4\u90a3\u4e2a\u7bad\u5934\u6307\u5411\u7684\u5b57\u7b26<code>c<\/code>\u5176\u56de\u6587\u534a\u5f84\u957f\u5ea6\u4e3a<code>7<\/code>(\u5bf9\u5e94\u7684\u6570\u7ec4\u4e0b\u6807\u662f<code>9<\/code>)\uff0c\u800c\u539f\u59cb\u5b57\u7b26\u4e32\u4e2d\u6700\u957f\u56de\u6587\u4e32\u4e3a<code>abbcbba<\/code>\uff0c\u5176\u957f\u5ea6\u4e5f\u662f<code>7<\/code>\u3002\u4e8e\u662f\u6211\u4eec\u904d\u5386\u5904\u7406\u540e\u7684\u5b57\u7b26\u4e32\uff0c\u5f53\u904d\u5386\u5230\u4e0b\u6807<code>9<\/code>\u65f6\uff0c\u5c31\u4f1a\u5f97\u5230\u8ba1\u7b97\u51fa\u6700\u957f\u56de\u6587\u534a\u5f84<code>7<\/code>\uff0c\u6211\u4eec\u901a\u8fc7\u4e0b\u6807\u548c\u56de\u6587\u534a\u5f84\u5c31\u53ef\u4ee5\u66f4\u65b0<strong>start<\/strong>(\u539f\u59cb\u5b57\u7b26\u6700\u957f\u56de\u6587\u4e32\u7684\u8d77\u59cb\u4f4d\u7f6e)\uff1a<\/p>\n<pre><code class=\"language-java\">i:\u5f53\u524d\u904d\u5386\u5230\u7684\u6570\u7ec4\u4e0b\u6807\narmLen:\u4ee5i\u4e3a\u4e2d\u5fc3\uff0c\u8ba1\u7b97\u51fa\u7684\u56de\u6587\u534a\u5f84\nstart = (i - armLen) \/ 2\nmaxLen = armLen\n<\/code><\/pre>\n<p>\u7b49\u5b57\u7b26\u4e32\u5168\u90e8\u904d\u5386\u5b8c\uff0c\u6211\u4eec\u6839\u636e<code>start<\/code>\u548c<code>maxLen<\/code>\u8fd9\u4e24\u4e2a\u53d8\u91cf\uff0c\u5c31\u53ef\u4ee5\u4ece\u539f\u59cb\u5b57\u7b26\u4e32<code>s<\/code>\u4e2d\u622a\u53d6\u51fa\u6700\u957f\u56de\u6587\u5b50\u4e32\uff1a<\/p>\n<p><code>s[start : start + maxLen]<\/code><\/p>\n<p>\u6211\u4eec\u7528<code>#<\/code>\u4f5c\u4e3a\u5206\u9694\u7b26\uff0c\u5982\u679c\u539f\u59cb\u5b57\u7b26\u4e32\u4e2d\u5305\u542b\u4e86\u8fd9\u4e2a\u5b57\u7b26\u600e\u4e48\u529e\u5462\uff1f\u6ca1\u5173\u7cfb\uff0c\u5206\u9694\u7b26\u53ef\u4ee5\u7528\u4efb\u610f\u5b57\u7b26\uff0c\u751a\u81f3\u8ddf\u539f\u59cb\u5b57\u7b26\u4e32\u4e2d\u7684\u67d0\u4e2a\u5b57\u7b26\u91cd\u590d\u4e5f\u53ef\u4ee5\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u53ea\u662f\u8981\u8ba1\u7b97\u51fa\u67d0\u4e2a\u5b57\u7b26\u7684\u56de\u6587\u534a\u5f84\uff0c\u5e76\u4e0d\u9700\u8981\u5206\u9694\u7b26\u672c\u8eab\u3002\u7531\u4e8e\u6bcf\u904d\u5230\u4e00\u4e2a\u5b57\u7b26\uff0c\u90fd\u9700\u8981\u5f80\u5de6\/\u53f3\u8fdb\u884c\u63a2\u6d4b\uff0c\u6545\u8fd9\u79cd\u65b9\u5f0f\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(n<sup>2<\/sup>)\u7a7a\u95f4\u590d\u6742\u5ea6\u662fO(1)\u3002\u6548\u7387\u4ecd\u7136\u662f\u4e0d\u9ad8\uff0c\u4f46\u662f\u5df2\u6709\u6709\u9a6c\u62c9\u8f66\u7b97\u6cd5\u7684\u57fa\u672c\u96cf\u5f62\u4e86\uff0c\u540e\u9762\u5c31\u662f\u5728\u6b64\u57fa\u7840\u4e0a\u505a\u4f18\u5316\uff0c\u589e\u52a0\u8f85\u52a9\u7a7a\u95f4\u6765\u4f18\u5316\u65f6\u95f4\u3002<\/p>\n<p>\u4ee3\u7801\u5b9e\u73b0\uff1a<\/p>\n<pre><code class=\"language-java\">class Solution {\n    public String longestPalindrome(String s) {\n        if(s==null || s.length() == 0) {\n            return &quot;&quot;;\n        }\n        \/\/\u5bf9\u539f\u59cb\u5b57\u7b26\u4e32\u505a\u5904\u7406\uff0c\u5c06abc\u53d8\u6210#a#b#c#\n        StringBuilder tmp = new StringBuilder();\n        tmp.append(&quot;#&quot;);\n        for(int i = 0; i &lt; s.length(); ++i) {\n            tmp.append(&quot;#&quot;);\n            tmp.append(s.charAt(i));\n        }\n        tmp.append(&quot;#&quot;);\n        int start = 0;\n        int maxLen = 0;\n        int n = tmp.length();\n        \/\/\u4ece\u5de6\u5230\u53f3\u904d\u5386\u5904\u7406\u8fc7\u7684\u5b57\u7b26\u4e32\uff0c\u6c42\u6bcf\u4e2a\u5b57\u7b26\u7684\u56de\u6587\u534a\u5f84\n        for(int i = 0; i &lt; n; ++i) {\n            \/\/\u8ba1\u7b97\u5f53\u524d\u4ee5i \u4e3a\u4e2d\u5fc3\u7684\u56de\u6587\u534a\u5f84\n            int cur = expand(tmp, i, i);\n            \/\/\u5982\u679c\u5f53\u524d\u8ba1\u7b97\u7684\u534a\u5f84\u5927\u4e8emaxLen\uff0c\u5c31\u66f4\u65b0start(\u539f\u59cb\u5b57\u7b26\u7684\u8d77\u59cb\u4f4d\u7f6e)\n            if(cur &gt; maxLen) {\n                start = (i - cur) \/ 2;\n                maxLen = cur;\n            }\n        }\n        \/\/\u6839\u636estart\u548cmaxLen\uff0c\u4ece\u539f\u59cb\u5b57\u7b26\u4e32\u4e2d\u622a\u53d6\u4e00\u6bb5\u8fd4\u56de\n        return s.substring(start, start + maxLen);\n    }\n\n    \/\/\u4ee5left\u548cright\u4e3a\u8d77\u70b9\uff0c\u8ba1\u7b97\u56de\u6587\u534a\u5f84\uff0c\u7531\u4e8ewhile\u5faa\u73af\u9000\u51fa\u540eleft\u548cright\u5404\u591a\u8d70\u4e86\u4e00\u6b65\n    \/\/\u6240\u4ee5\u5728\u8fd4\u56de\u7684\u603b\u957f\u5ea6\u65f6\u8981\u51cf\u53bb2\n    private int expand(StringBuilder s, int left, int right) {\n        while(left &gt;= 0 &amp;&amp; right &lt; s.length() &amp;&amp; s.charAt(left) == s.charAt(right)) {\n            --left;\n            ++right;\n        }\n        return (right - left - 2) \/ 2;\n    }\n}\n<\/code><\/pre>\n<h4>3\u3001\u9a6c\u62c9\u8f66\u7b97\u6cd5<\/h4>\n<p>\u4e0a\u9762\u7684\u4ee3\u7801\u5728\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\uff0c\u6ca1\u6709\u7528\u5230\u8f85\u52a9\u7a7a\u95f4\uff0c\u8ba1\u7b97<code>#x#a#b#b#c#b#b#a#y#<\/code>\u4e2d\u6bcf\u4e2a\u5b57\u7b26\u7684\u56de\u6587\u534a\u5f84\u65f6\uff0c\u90fd\u9700\u8981\u5f80\u4e24\u8fb9\u6269\u5c55\u4e00\u70b9\u70b9\u8ba1\u7b97\u3002\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e4b\u524d\u8ba1\u7b97\u8fc7\u7684\u56de\u6587\u534a\u5f84<strong>\u4fdd\u5b58<\/strong>\u5230\u4e00\u4e2a\u6570\u7ec4\u4e2d\uff0c\u540e\u9762\u518d\u8ba1\u7b97\u67d0\u4e2a\u5b57\u7b26\u7684\u56de\u6587\u534a\u5f84\u65f6\uff0c\u5c31\u53ef\u4ee5\u5229\u7528\u5230\u4e4b\u524d\u5df2\u7ecf\u8ba1\u7b97\u8fc7\u7684\u503c\u3002<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/7.png\" alt=\"2.png\" \/>\u5982\u4e0a\u56fe\uff0c\u6211\u4eec\u9700\u8981\u4e24\u4e2a\u8f85\u52a9\u53d8\u91cf\uff1a<\/p>\n<ul>\n<li>right\uff0c\u8868\u793a\u5df2\u7ecf\u63a2\u6d4b\u5230\u7684\u5b57\u7b26\u4e32\u6700\u53f3\u8fb9\u7684\u53ef\u8fbe\u8303\u56f4<\/li>\n<li>center\uff0c\u6839\u636e\u6700\u53f3\u8fb9\u7684\u53ef\u8fbe\u8303\u56f4\u7684\u4e2d\u5fc3\u5bf9\u79f0\u4f4d\u7f6e<\/li>\n<\/ul>\n<p>\u56e0\u4e3a\u6211\u4eec\u662f\u4ece\u5de6\u5f80\u53f3\u904d\u5386\u5b57\u7b26\u4e32\u7684\uff0c\u6bd4\u5982\u5f53\u6211\u4eec\u8ba1\u7b97<code>c<\/code>\u8fd9\u4e2a\u5b57\u7b26\u65f6\uff0c\u53ef\u4ee5\u5f97\u77e5\u5b83\u7684\u56de\u6587\u534a\u5f84\u662f<code>7<\/code>\uff0c\u90a3\u4e48\u5c31\u4ee5<code>c<\/code>\u4e3a\u4e2d\u5fc3\u70b9\uff0c\u5411\u53f3\u6269\u5c55<code>7<\/code>\u4f4d\uff0c\u8fd9\u4e2a\u4f4d\u7f6e\u5c31\u662f<code>right<\/code>\u6307\u5411\u7684\u4f4d\u7f6e(\u5bf9\u5e94\u4e0a\u56fe\u4e2d\u6700\u53f3\u8fb9\u7684\u7bad\u5934)\u3002<br \/>\n<code>right<\/code>\u8fd9\u4e2a\u4f4d\u7f6e\uff0c\u5c31\u662f\u6211\u4eec\u76ee\u524d\u5df2\u7ecf\u8ba1\u7b97\u51fa\u7684\u6700\u53f3\u7aef\u53ef\u8fbe\u8303\u56f4\uff0c\u4ee5<code>right<\/code>\u548c\u4e2d\u5fc3\u5bf9\u79f0\u4f4d\u7f6e<code>center<\/code>\u5f97\u5230\u7684\u56de\u6587\u4e32\u4e0d\u4e00\u5b9a\u662f\u6700\u957f\u7684\uff0c\u4f46\u662f<code>right<\/code>\u662f\u76ee\u524d\u6211\u4eec\u80fd\u63a2\u6d4b\u5230\u7684\u6700\u8fdc\u7684\u53f3\u7aef\u4f4d\u7f6e\u3002\u6211\u4eec\u5728\u904d\u5386\u5b57\u7b26\u4e32\u7684\u540c\u65f6\uff0c\u4e5f\u5728\u4e0d\u65ad\u6269\u5927<code>right<\/code>\u7684\u8303\u56f4\uff0c<code>right<\/code>\u548c\u5b83\u7684\u5de6\u8fb9\u90fd\u662f\u5df2\u7ecf\u63a2\u6d4b\u8fc7\u7684\uff0c<code>right<\/code>\u7684\u53f3\u8fb9\u662f\u672a\u63a2\u6d4b\u7684\u3002<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/8.png\" alt=\"2.png\" \/><\/p>\n<p>\u4e0a\u56fe\u4e2d\uff0c\u7ea2\u8272\u7bad\u5934\u6307\u5411\u4e86<code>#<\/code>\u5b57\u7b26\uff0c\u5982\u679c\u7528\u4e2d\u5fc3\u63a2\u6d4b\u6cd5\u8ba1\u7b97\u8fd9\u4e2a\u5b57\u7b26\u7684\u56de\u6587\u534a\u5f84\uff0c\u6211\u4eec\u5c31\u5f97\u4e0d\u65ad\u5f80\u5de6\/\u53f3\u8fb9\u8fdb\u884c\u6269\u5c55\uff0c\u76f4\u5230\u5de6\u53f3\u5b57\u7b26\u4e0d\u7b49\u6216\u8005\u8d8a\u754c\u3002\u7531\u4e8e\u662f\u4ece\u5de6\u5f80\u53f3\u904d\u5386\u7684\uff0c<code>center<\/code>\u548c<code>right<\/code>\u7684\u4f4d\u7f6e\u4e5f\u662f\u6839\u636ei\u6765\u63a8\u52a8\u7684\uff0c\u6240\u4ee5i\u80af\u5b9a\u662f\u5927\u4e8e\u7b49\u4e8e<code>center<\/code>\u7684\u3002\u800c\u56de\u6587\u7684\u7279\u70b9\u662f\u5de6\u53f3\u5bf9\u79f0\uff0c\u6839\u636e\u4e2d\u5fc3\u4f4d\u7f6e<code>center<\/code>\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u627e\u5230i\u7684\u955c\u50cf\u4f4d\u7f6e\uff0c\u4e5f\u5c31\u662f\u4e0a\u56fe\u4e2d\u6700\u5de6\u8fb9\u7bad\u5934\u6307\u5411\u7684i\u955c\u50cf\u5bf9\u79f0(<code>i_mirror<\/code>)\u3002\u5b9e\u9645\u4e0a<strong>i\u955c\u50cf<\/strong>\u7684\u503c\u662f\u5df2\u7ecf\u8ba1\u7b97\u8fc7\u7684\uff0c\u5b83\u7684\u56de\u6587\u534a\u5f84\u662f<code>2<\/code>\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5df2\u77e5\u7684<strong>i\u955c\u50cf<\/strong>\u7684\u503c\u6765\u8ba1\u7b97\u51fa<code>i<\/code>\u7684\u503c\u3002\u56e0\u4e3a<code>i<\/code>\u548c<code>i_mirror<\/code>\u662f\u6839\u636e<code>center<\/code>\u5bf9\u79f0\u7684\uff0c\u6545<code>i + i_mirror = 2 * center<\/code>\uff0c\u4e8e\u662f\u53ef\u4ee5\u5f97\u5230i\u955c\u50cf\u7684\u4e0b\u6807\u4e3a\uff1a<\/p>\n<p><code>i_mirror = 2 * center - i<\/code><\/p>\n<p>\u5047\u5b9a\u6570\u7ec4<strong>p<\/strong>\u4e2d\u4fdd\u5b58\u4e86\u5df2\u8ba1\u7b97\u8fc7\u7684\u56de\u6587\u534a\u5f84\u503c\uff0c\u90a3\u4e48<code>p[i_mirror]<\/code>\u5c31\u662f<code>i<\/code>\u4ee5<code>center<\/code>\u4e3a\u4e2d\u5fc3\u955c\u50cf\u5bf9\u79f0\u4f4d\u7f6e\u7684\u56de\u6587\u534a\u5f84\u957f\u5ea6\u3002\u6839\u636e\u6570\u7ec4<code>p[i_mirror]<\/code>\u6765\u8ba1\u7b97<code>p[i]<\/code>\u53c8\u5206\u4e24\u79cd\u60c5\u51b5\uff1a<\/p>\n<ol>\n<li>right &lt; i<\/li>\n<li>right &gt;= i<\/li>\n<\/ol>\n<p>\u7b2c\u4e00\u79cd\u60c5\u51b5<strong>right &lt; i<\/strong>\uff0c\u8bf4\u660e\u8981\u8ba1\u7b97\u7684<code>i<\/code>\u8d85\u8fc7\u4e86<code>right<\/code>\u7684\u8303\u56f4\uff0c\u5982\u4e0b\u5982\u6240\u793a\uff1a<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/9.png\" alt=\"2.png\" \/><\/p>\n<p>\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7531\u4e8e<code>i<\/code>\u6240\u6307\u5411\u7684\u5b57\u7b26\u843d\u5728<code>right<\/code>\u8303\u56f4\u4e4b\u5916\uff0c\u8bf4\u660e\u8fd9\u4e2a\u5b57\u7b26\u6ca1\u6709\u88ab\u63a2\u6d4b\u8fc7\uff0c\u8fd9\u6837\u7684\u8bdd\uff0c\u5c31\u4e0d\u80fd\u518d\u5229\u7528\u5df2\u6709\u7684\u4fe1\u606f\u4e86\uff0c\u53ea\u80fd\u7528\u4e2d\u5fc3\u63a2\u6d4b\u6cd5\uff0c\u4e00\u70b9\u4e00\u70b9\u7684\u5411\u5916\u6269\u5c55\u8ba1\u7b97\u3002<\/p>\n<p>\u7b2c\u4e8c\u79cd\u60c5\u51b5<strong>right &gt;= i<\/strong>\uff0c\u53c8\u5206\u7ec6\u5206\u6210\u4e09\u79cd\u5c0f\u60c5\u51b5\u3002<\/p>\n<p>(1)\u3001\u5982\u679c<strong>right &#8211; i &gt; p[i_mirror]<\/strong><\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/10.png\" alt=\"2.png\" \/><\/p>\n<p>\u5982\u4e0a\u56fe\uff0c<code>p[i_mirror]<\/code>\u4e3a<code>2<\/code>\uff0c\u5b83\u8868\u793a\u4ee5<code>i_mirror<\/code>\u4e3a\u4e2d\u5fc3\u53ef\u4ee5\u5411\u5de6\/\u53f3\u6269\u5c55<code>2<\/code>\u4f4d\u3002<strong>right &#8211; i<\/strong>\u4e3a<code>4<\/code>\uff0c\u5b83\u8868\u793a\u4ece<code>i<\/code>\u7684\u4f4d\u7f6e\u5230\u5df2\u63a2\u6d4b\u7684\u6700\u53f3\u7aef<code>right<\/code>\u8ddd\u79bb\u4e3a<code>4<\/code>\u3002\u5728\u8ba1\u7b97<code>i<\/code>\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u9009\u62e9\u6269\u5c55<code>2<\/code>\u4f4d\uff0c\u56e0\u4e3a<code>i_mirror<\/code>\u548c<code>i<\/code>\u662f\u955c\u50cf\u5bf9\u79f0\u7684\uff0c<code>p[i_mirror]<\/code>\u53ef\u4ee5\u6269\u5c55\u4e24\u4f4d\uff0c\u90a3\u4e48<code>i<\/code>\u4e5f\u6709\u53ef\u80fd\u6269\u5c55<code>2<\/code>\u4f4d\u3002\u4e5f\u53ef\u4ee5\u9009\u62e9\u6269\u5c55<code>4<\/code>\u4f4d\uff0c<code>i<\/code>\u5230<code>right<\/code>\u7684\u8ddd\u79bb\u662f<code>4<\/code>\uff0c\u7531<code>right<\/code>\u662f\u5df2\u63a2\u6d4b\u7684\u6700\u53f3\u7aef\u4f4d\u7f6e\uff0c\u90a3\u4e48<strong>i-right<\/strong>\u8fd9\u6bb5\uff0c\u7406\u8bba\u4e0a\u6765\u8bf4\u4e5f\u6709\u53ef\u80fd\u662f\u56de\u6587\uff0c\u6240\u4ee5\u4e5f\u6709\u53ef\u80fd\u6269\u5c55<code>4<\/code>\u4f4d\u3002\u4f46\u6211\u4eec\u9700\u8981\u9009\u62e9\u4e00\u4e2a\u4fdd\u5b88\u7684\uff0c\u4ece\u4e0a\u56fe\u4e2d\u4e5f\u53ef\u4ee5\u53d1\u73b0\uff0c\u5982\u679c\u9009\u62e9<code>4<\/code>\u5c31\u4e0d\u5bf9\u4e86\uff0c\u6240\u4ee5\u5f53<strong>right &#8211; i<\/strong>\u548c<code>p[i_mirror]<\/code>\u4e0d\u540c\u65f6\uff0c\u6211\u4eec\u9009\u62e9\u8f83\u5c0f\u7684\u90a3\u4e2a\u503c\u3002<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/11.png\" alt=\"2.png\" \/><\/p>\n<p>\u5982\u4e0a\u56fe\uff0c\u8fd9\u6b21\u6211\u4eec\u5728\u8ba1\u7b97<code>i<\/code>\u7684\u65f6\u5019\uff0c\u5c31\u4e0d\u7528\u50cf\u4e2d\u5fc3\u63a2\u6d4b\u6cd5\u90a3\u6837\uff0c\u4ee5<code>i<\/code>\u4e3a\u4e2d\u5fc3\u5411\u4e24\u8fb9\u63a2\u6d4b\u4e86\uff0c\u800c\u662f\u8ba1\u7b97\u51fa\u4e24\u4e2a\u65b0\u8d77\u70b9<code>i_left<\/code>\u548c<code>i_right<\/code>\u3002<code>i_left<\/code>\u5c31\u7b49\u4e8e<code>i - 2<\/code>\uff0c<code>i_right<\/code>\u7b49\u4e8e<code>i + 2<\/code>\uff0c\u8fd9\u91cc\u7684<code>2<\/code>\u5c31\u662f<code>p[i_mirror]<\/code>\u7684\u503c\u3002\u6211\u4eec\u8ba9<code>i_left<\/code>\u548c<code>i_right<\/code>\u4e00\u4e2a\u5f80\u5de6\u3001\u4e00\u4e2a\u5f80\u53f3\u5f00\u59cb\u63a2\u6d4b\uff0c\u8fd9\u7b49\u4e8e\u662f\u8df3\u8fc7\u4e86\u4e00\u4e9b\u68c0\u67e5\u7684\u4f4d\u7f6e\uff0c\u8fd9\u5c31\u662f\u9a6c\u62c9\u8f66\u7b97\u6cd5\u7684\u5173\u952e\u6240\u5728\uff0c\u5229\u7528\u5df2\u77e5\u7684<code>i_mirror<\/code>\u4fe1\u606f\u6765\u6269\u5c55<code>i<\/code>\uff0c\u8df3\u8fc7\u4e00\u4e9b\u5df2\u7ecf\u786e\u5b9a\u7684\u4f4d\u7f6e\uff0c\u7701\u53bb\u4e86\u591a\u4f59\u7684\u5224\u65ad\u3002<\/p>\n<p>(2)\u3001\u5982\u679c<strong>right &#8211; i == p[i_mirror]<\/strong><\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/12.png\" alt=\"2.png\" \/><\/p>\n<p>\u5982\u4e0a\u56fe\uff0c<code>p[i_mirror]<\/code>\u4e3a<code>1<\/code>\uff0c<strong>right &#8211; i<\/strong>\u4e5f\u662f\u4e3a<code>1<\/code>\u3002\u8fd9\u5c31\u8bf4\u660e\u4ee5<code>i<\/code>\u4e3a\u4e2d\u5fc3\u81f3\u5c11\u53ef\u4ee5\u518d\u5411\u5de6\/\u53f3\u6269\u5c55<code>1<\/code>\u4f4d\u3002\u6211\u4eec\u8ba9<code>i_left = i + 1<\/code>\uff0c\u8ba9<code>i_right = i + 1<\/code>\uff0c\u7136\u540e\u4ee5<code>i_left<\/code>\u548c<code>i_right<\/code>\u4e3a\u65b0\u8d77\u70b9\uff0c\u7ee7\u7eed\u5f80\u5de6\/\u53f3\u6269\u5c55\u3002<\/p>\n<p>(3)\u5982\u679c<strong>right &#8211; i &lt; p[i_mirror]<\/strong><\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/2022\/03\/01\/13.png\" alt=\"2.png\" \/><\/p>\n<p>\u5982\u4e0a\u56fe\uff0c\u6211\u4eec\u8981\u8ba1\u7b97<code>i<\/code>\uff0c\u6b64\u65f6<code>p[i_mirror]<\/code>\u4e3a<code>7<\/code>\uff0c\u4e5f\u5c31\u662f<code>i\u7684\u955c\u50cf\u4f4d\u7f6e<\/code>\u662f\u53ef\u4ee5\u5411\u5de6\/\u53f3\u6269\u5c55<code>7<\/code>\u7684\uff0c\u4f46\u662f<code>i<\/code>\u53ef\u80fd\u4e0d\u884c\uff0c\u56e0\u4e3a<strong>right &#8211; i<\/strong>\u4e3a<code>5<\/code>\uff0c<strong>right<\/strong>\u662f\u6211\u4eec\u5df2\u7ecf\u8003\u5bdf\u8fc7\u7684\u6700\u53f3\u7aef\u7684\u4f4d\u7f6e\uff0c<code>i<\/code>\u662f\u5426\u53ef\u4ee5\u6269\u5c55\u5230<code>right<\/code>\u53f3\u8fb9\u6211\u4eec\u5e76\u4e0d\u6e05\u695a\uff0c\u4f46\u662f\u53ef\u4ee5\u80af\u5b9a\u662f\u662f\uff0c\u81f3\u5c11\u6211\u4eec\u53ef\u4ee5\u5411\u5de6\/\u53f3\u6269\u5c55<code>5<\/code>\u4f4d\uff0c\u4e5f\u5c31\u662f\u9009\u62e9<strong>right &#8211; i<\/strong>\u548c<code>p[i_mirror]<\/code>\u4e2d\u8f83\u5c0f\u7684<code>5<\/code>\u6765\u6269\u5c55\u3002<\/p>\n<p>\u7efc\u4e0a(1)\u3001(2)\u3001(3)\u6211\u4eec\u8ba1\u7b97<code>i<\/code>\u7684\u56de\u6587\u534a\u5f84\u65b9\u5f0f\u5982\u4e0b\uff1a<\/p>\n<pre><code class=\"language-java\">i_mirror = 2 * center - i\n\u6700\u5c0f\u6269\u5c55\u5355\u4f4d = min(right - i, p[i_mirror])\n\u4ee5i\u4e3a\u4e2d\u5fc3\u7684\u56de\u6587\u534a\u5f84 = expand(i - \u6700\u5c0f\u6269\u5c55\u5355\u4f4d, i + \u6700\u5c0f\u6269\u5c55\u5355\u4f4d)\n<\/code><\/pre>\n<p>\u9a6c\u62c9\u8f66\u7b97\u6cd5\u4ecd\u7136\u662f\u5916\u9762\u4e00\u4e2a<code>for<\/code>\u5faa\u73af\uff0c\u91cc\u9762\u518d\u5957\u4e86\u4e00\u4e2a<code>while<\/code>\u5faa\u73af\u3002\u4f46\u5bf9\u4e8e\u6bcf\u4e2a\u4f4d\u7f6e<code>i<\/code>\uff0c\u6269\u5c55\u8981\u4e48\u4ece\u5f53\u524d\u7684\u6700\u53f3\u7aef\u7684<code>right<\/code>\u5f00\u59cb\uff0c\u8981\u4e48\u53ea\u4f1a\u8fdb\u884c\u4e00\u6b65\uff0c\u800c<code>right<\/code>\u6700\u591a\u5411\u524d\u8d70N\uff0c\u6545\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n)\uff0c\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(n)\u3002<\/p>\n<p>\u4ee3\u7801\u5b9e\u73b0\uff1a<\/p>\n<pre><code class=\"language-java\">\/\/4.Manacher\u7b97\u6cd5\npublic String longestPalindrome4(String s) {\n    if(null == s || s.length() == 0){\n        return &quot;&quot;;\n    }\n    \/\/\u5bf9\u539f\u59cb\u5b57\u7b26\u4e32\u505a\u5904\u7406\uff0c\u5c06abc\u53d8\u6210#a#b#c#\n    StringBuilder tmp = new StringBuilder();\n    for(int i = 0; i &lt; s.length(); ++i) {\n        tmp.append(&quot;#&quot;);\n        tmp.append(s.charAt(i));\n    }\n    tmp.append(&quot;#&quot;);\n    int n = tmp.length();\n    \/\/right\u8868\u793a\u76ee\u524d\u8ba1\u7b97\u51fa\u7684\u6700\u53f3\u7aef\u8303\u56f4\uff0cright\u548c\u5de6\u8fb9\u90fd\u662f\u5df2\u63a2\u6d4b\u8fc7\u7684\n    int right = 0;\n    \/\/center\u6700\u53f3\u7aef\u4f4d\u7f6e\u7684\u4e2d\u5fc3\u5bf9\u79f0\u70b9\n    int center = 0;\n    int start = 0;\n    int maxLen = 0;\n    \/\/p\u6570\u7ec4\u8bb0\u5f55\u6240\u6709\u5df2\u63a2\u6d4b\u8fc7\u7684\u56de\u6587\u534a\u5f84\uff0c\u540e\u9762\u6211\u4eec\u518d\u8ba1\u7b97i\u65f6\uff0c\u6839\u636ep[i_mirror]\u8ba1\u7b97i\n    int[] p = new int[n];\n    \/\/\u4ece\u5de6\u5230\u53f3\u904d\u5386\u5904\u7406\u8fc7\u7684\u5b57\u7b26\u4e32\uff0c\u6c42\u6bcf\u4e2a\u5b57\u7b26\u7684\u56de\u6587\u534a\u5f84\n    for(int i = 0; i &lt; n; ++i) {\n        \/\/\u6839\u636ei\u548cright\u7684\u4f4d\u7f6e\u5206\u4e3a\u4e24\u79cd\u60c5\u51b5\uff1a\n        \/\/1\u3001i&lt;=right\u5229\u7528\u5df2\u77e5\u7684\u4fe1\u606f\u6765\u8ba1\u7b97i\n        \/\/2\u3001i&gt;right\uff0c\u8bf4\u660ei\u7684\u4f4d\u7f6e\u65f6\u672a\u63a2\u6d4b\u8fc7\u7684\uff0c\u53ea\u80fd\u7528\u4e2d\u5fc3\u63a2\u6d4b\u6cd5\n        if(right &gt;= i) {\n            \/\/\u8fd9\u53e5\u662f\u5173\u952e\uff0c\u4e0d\u7528\u518d\u50cf\u4e2d\u5fc3\u63a2\u6d4b\u90a3\u6837\uff0c\u4e00\u70b9\u70b9\u7684\u5f80\u5de6\/\u53f3\u6269\u6563\uff0c\u6839\u636e\u5df2\u77e5\u4fe1\u606f\n            \/\/\u51cf\u5c11\u4e0d\u5fc5\u8981\u7684\u63a2\u6d4b\uff0c\u5fc5\u987b\u9009\u62e9\u4e24\u8005\u4e2d\u7684\u8f83\u5c0f\u8005\u4f5c\u4e3a\u5de6\u53f3\u63a2\u6d4b\u8d77\u70b9\n            int minArmLen = Math.min(right - i, p[2 * center - i]);\n            p[i] = expand(tmp, i - minArmLen, i + minArmLen);\n        }\n        else {\n            \/\/i\u843d\u5728right\u53f3\u8fb9\uff0c\u662f\u6ca1\u88ab\u63a2\u6d4b\u8fc7\u7684\uff0c\u53ea\u80fd\u7528\u4e2d\u5fc3\u63a2\u6d4b\u6cd5\n            p[i] = expand(tmp, i, i);\n        }\n        \/\/\u5927\u4e8eright\uff0c\u8bf4\u660e\u53ef\u4ee5\u66f4\u65b0\u6700\u53f3\u7aef\u8303\u56f4\u4e86\uff0c\u540c\u65f6\u66f4\u65b0center\n        if(i + p[i] &gt; right) {\n            center = i;\n            right = i + p[i];\n        }\n        \/\/\u627e\u5230\u4e86\u4e00\u4e2a\u66f4\u957f\u7684\u56de\u6587\u534a\u5f84\uff0c\u66f4\u65b0\u539f\u59cb\u5b57\u7b26\u4e32\u7684start\u4f4d\u7f6e\n        if(p[i] &gt; maxLen) {\n            start = (i - p[i]) \/ 2;\n            maxLen = p[i];\n        }\n    }\n    \/\/\u6839\u636estart\u548cmaxLen\uff0c\u4ece\u539f\u59cb\u5b57\u7b26\u4e32\u4e2d\u622a\u53d6\u4e00\u6bb5\u8fd4\u56de\n    return s.substring(start, start + maxLen);\n}\n\n\/\/\u4ee5left\u548cright\u4e3a\u8d77\u70b9\uff0c\u8ba1\u7b97\u56de\u6587\u534a\u5f84\uff0c\u7531\u4e8ewhile\u5faa\u73af\u9000\u51fa\u540eleft\u548cright\u5404\u591a\u8d70\u4e86\u4e00\u6b65\n\/\/\u6240\u4ee5\u5728\u8fd4\u56de\u7684\u603b\u957f\u5ea6\u65f6\u8981\u51cf\u53bb2\nprivate int expand(StringBuilder s, int left, int right) {\n    while(left &gt;= 0 &amp;&amp; right &lt; s.length() &amp;&amp; s.charAt(left) == s.charAt(right)) {\n        --left;\n        ++right;\n    }\n    return (right - left - 2) \/ 2;\n}\n<\/code><\/pre>\n<p><a href=\"https:\/\/leetcode-cn.com\/problems\/longest-palindromic-substring\/solution\/tu-jie-ma-la-che-suan-fa-by-wang_ni_ma-if33\/\">\u7b97\u6cd5\u53c2\u8003<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4ee3\u7801\u4ed3\u5e93 \u7ed9\u4f60\u4e00\u4e2a\u5b57\u7b26\u4e32 s\uff0c\u627e\u5230 s \u4e2d\u6700\u957f\u7684\u56de\u6587\u5b50\u4e32\u3002 \u793a\u4f8b 1\uff1a \u8f93\u5165\uff1as = &quot;babad&#038; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-204","post","type-post","status-publish","format-standard","hentry","category-leecode"],"_links":{"self":[{"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=\/wp\/v2\/posts\/204","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=204"}],"version-history":[{"count":2,"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=\/wp\/v2\/posts\/204\/revisions"}],"predecessor-version":[{"id":510,"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=\/wp\/v2\/posts\/204\/revisions\/510"}],"wp:attachment":[{"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=204"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=204"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.huerpu.cc:7000\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}