{"id":1657,"date":"2022-01-09T18:56:20","date_gmt":"2022-01-09T10:56:20","guid":{"rendered":"http:\/\/139.9.1.231\/?p=1657"},"modified":"2022-01-09T18:56:21","modified_gmt":"2022-01-09T10:56:21","slug":"leetcodeday5","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2022\/01\/09\/leetcodeday5\/","title":{"rendered":"leetcodeday5 –\u6700\u957f\u56de\u6587\u5b50\u4e32"},"content":{"rendered":"\n

\u7ed9\u4f60\u4e00\u4e2a\u5b57\u7b26\u4e32 s<\/code>\uff0c\u627e\u5230 s<\/code> \u4e2d\u6700\u957f\u7684\u56de\u6587\u5b50\u4e32\u3002<\/p>\n\n\n\n

\u793a\u4f8b 1\uff1a<\/p>\n\n\n\n

\u8f93\u5165\uff1as = “babad”
\u8f93\u51fa\uff1a”bab”
\u89e3\u91ca\uff1a”aba” \u540c\u6837\u662f\u7b26\u5408\u9898\u610f\u7684\u7b54\u6848\u3002
\u793a\u4f8b 2\uff1a<\/p>\n\n\n\n

\u8f93\u5165\uff1as = “cbbd”
\u8f93\u51fa\uff1a”bb”
\u793a\u4f8b 3\uff1a<\/p>\n\n\n\n

\u8f93\u5165\uff1as = “a”
\u8f93\u51fa\uff1a”a”
\u793a\u4f8b 4\uff1a<\/p>\n\n\n\n

\u8f93\u5165\uff1as = “ac”
\u8f93\u51fa\uff1a”a”
 <\/p>\n\n\n\n

\u63d0\u793a\uff1a<\/p>\n\n\n\n

1 <= s.length <= 1000
s \u4ec5\u7531\u6570\u5b57\u548c\u82f1\u6587\u5b57\u6bcd\uff08\u5927\u5199\u548c\/\u6216\u5c0f\u5199\uff09\u7ec4\u6210<\/p>\n\n\n\n

<\/p>\n\n\n\n

\u601d\u8def\uff1a\u6839\u636e\u56de\u6587\u4e32\u7684\u7279\u70b9\uff1a \u56de\u6587\u4e32\u4e2d\u5fc3\u5411\u4e24\u8fb9\u7684\u5143\u7d20\u5bf9\u79f0\uff0c\u904d\u5386str\u6bcf\u4e2a\u5143\u7d20\uff0c\u4ee5\u8be5\u5143\u7d20\u4e3a\u4e2d\u5fc3\uff0c\u5224\u65adi-1\u548ci+1\u662f\u5426\u4e00\u81f4\uff0c\u5982\u679c\u4e00\u81f4\uff0c\u7ee7\u7eed\u5224\u65adi-2\u548ci+2\uff0c\u77e5\u9053\u4e0d\u4e00\u81f4\u6216\u8005\u8fbe\u5230\u8fb9\u754c\u505c\u6b62\uff0c\u5e76\u8bb0\u5f55substr\u957f\u5ea6\uff0c\u4f46\u662f\u8fd8\u5fc5\u987b\u8003\u8651\u56de\u6587\u4e32\u4e2d\u5fc3\u662f\u4e24\u4e2a\u76f8\u540c\u7684\u5143\u7d20\u7684\u60c5\u51b5\u3002<\/p>\n\n\n\n

# [5] \u6700\u957f\u56de\u6587\u5b50\u4e32\n#\n\n# @lc code=start\nclass Solution:\n    def longestPalindrome(self, s: str) -> str:\n        length=len(s)\n        mx=\"\"\n        if length ==1:\n           return s\n        if length ==2 and s[0]==s[1]:\n            return s\n        elif length ==2 and s[0]!=s[1]:\n            return s[0]\n#\u5bf9\u4e8e\u56de\u6587\u4e32\u4e2d\u5fc3\u662f\u5355\u4e2a\u5143\u7d20\n        for i in range(length):\n            start =end = i\n            if i ==0: mx=s[0]\n            else: \n                for j in range(i):\n                    start -=1\n                    end +=1\n                    #if start>=0 and end<length: \n                    #   print(i-j-1,i+j+1)\n                    if start>=0 and end<length and s[i-j-1]==s[i+j+1]:\n\n                        mx=s[i-j-1:i+j+1+1] if 2*j+3>len(mx) else mx\n                    else:break\n    \n#\u5bf9\u4e8e\u56de\u6587\u4e32\u4e2d\u5fc3\u662f\u76f8\u90bb\u4e24\u4e2a\u5143\u7d20\u7684\u60c5\u51b5\uff1a \n        for i in range(length):\n            end = i\n            start =i-1\n            if i ==0: continue\n            if i ==1 and s[0]==s[1]: \n                \n                mx=s[0:2] if 2>len(mx) else mx\n                print(mx)\n                continue\n            elif s[i]==s[i-1]: \n                mx=s[i-1:i+1] if 2>=len(mx) else mx\n                print(mx)\n                for j in range(i):\n                    start -=1\n                    end +=1\n                    \n                    if start>=0 and end<length and s[i-1-j-1]==s[i+j+1]:\n\n                        mx=s[i-1-j-1:i+j+1+1] if 2*j+4>len(mx) else mx\n                    else:break\n            else:continue\n        return mx                  \n               \n# @lc code=end\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure><\/div>\n\n\n\n
\u518d\u6765\u770b\u770b\u5b98\u65b9\u89e3\u6cd5\uff1a<\/p>\n\n\n\n
\u65b9\u6cd5\u4e00\uff1a\u52a8\u6001\u89c4\u5212
\u601d\u8def\u4e0e\u7b97\u6cd5<\/p>\n\n\n\n
\u5bf9\u4e8e\u4e00\u4e2a\u5b50\u4e32\u800c\u8a00\uff0c\u5982\u679c\u5b83\u662f\u56de\u6587\u4e32\uff0c\u5e76\u4e14\u957f\u5ea6\u5927\u4e8e 22\uff0c\u90a3\u4e48\u5c06\u5b83\u9996\u5c3e\u7684\u4e24\u4e2a\u5b57\u6bcd\u53bb\u9664\u4e4b\u540e\uff0c\u5b83\u4ecd\u7136\u662f\u4e2a\u56de\u6587\u4e32\u3002\u4f8b\u5982\u5bf9\u4e8e\u5b57\u7b26\u4e32 \u201cababa\u201d\uff0c\u5982\u679c\u6211\u4eec\u5df2\u7ecf\u77e5\u9053 <\/code>\u201cbab\u201d \u662f\u56de\u6587\u4e32\uff0c\u90a3\u4e48\u201cababa\u201d \u4e00\u5b9a\u662f\u56de\u6587\u4e32\uff0c\u8fd9\u662f\u56e0\u4e3a\u5b83\u7684\u9996\u5c3e\u4e24\u4e2a\u5b57\u6bcd\u90fd\u662f<\/code>\u201ca\u201d\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/p>\n\n\n\n
class Solution:\ndef longestPalindrome(self, s: str) -> str:\n    n = len(s)\n    if n < 2:\n       return s    \n    max_len = 1\n    begin = 0\n    # dp[i][j] \u8868\u793a s[i..j] \u662f\u5426\u662f\u56de\u6587\u4e32\n    dp = [[False] * n for _ in range(n)]\n    for i in range(n):\n        dp[i][i] = True\n\n    # \u9012\u63a8\u5f00\u59cb\n    # \u5148\u679a\u4e3e\u5b50\u4e32\u957f\u5ea6\n    for L in range(2, n + 1):\n        # \u679a\u4e3e\u5de6\u8fb9\u754c\uff0c\u5de6\u8fb9\u754c\u7684\u4e0a\u9650\u8bbe\u7f6e\u53ef\u4ee5\u5bbd\u677e\u4e00\u4e9b\n        for i in range(n):\n            # \u7531 L \u548c i \u53ef\u4ee5\u786e\u5b9a\u53f3\u8fb9\u754c\uff0c\u5373 j - i + 1 = L \u5f97\n            j = L + i - 1\n            # \u5982\u679c\u53f3\u8fb9\u754c\u8d8a\u754c\uff0c\u5c31\u53ef\u4ee5\u9000\u51fa\u5f53\u524d\u5faa\u73af\n            if j >= n:\n                break\n\n            if s[i] != s[j]:\n                dp[i][j] = False \n            else:\n                if j - i < 3:\n                    dp[i][j] = True\n                else:\n                    dp[i][j] = dp[i + 1][j - 1]\n\n            # \u53ea\u8981 dp[i][L] == true \u6210\u7acb\uff0c\u5c31\u8868\u793a\u5b50\u4e32 s[i..L] \u662f\u56de\u6587\uff0c\u6b64\u65f6\u8bb0\u5f55\u56de\u6587\u957f\u5ea6\u548c\u8d77\u59cb\u4f4d\u7f6e\n            if dp[i][j] and j - i + 1 > max_len:\n                max_len = j - i + 1\n                begin = i\n    return s[begin:begin + max_len]<\/code><\/pre>\n\n\n\n
\u65b9\u6cd5\u4e8c\uff1a\u4e2d\u5fc3\u6269\u5c55\u7b97\u6cd5<\/h4>\n\n\n\n
\u601d\u8def\u4e0e\u7b97\u6cd5<\/strong><\/p>\n\n\n\n
\u6211\u4eec\u4ed4\u7ec6\u89c2\u5bdf\u4e00\u4e0b\u65b9\u6cd5\u4e00\u4e2d\u7684\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff1a<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u53ef\u4ee5\u53d1\u73b0\uff0c\u6240\u6709\u7684\u72b6\u6001\u5728\u8f6c\u79fb\u7684\u65f6\u5019\u7684\u53ef\u80fd\u6027\u90fd\u662f\u552f\u4e00\u7684\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u6bcf\u4e00\u79cd\u8fb9\u754c\u60c5\u51b5\u5f00\u59cb\u300c\u6269\u5c55\u300d\uff0c\u4e5f\u53ef\u4ee5\u5f97\u51fa\u6240\u6709\u7684\u72b6\u6001\u5bf9\u5e94\u7684\u7b54\u6848\u3002<\/p>\n\n\n\n
\u8fb9\u754c\u60c5\u51b5\u5373\u4e3a\u5b50\u4e32\u957f\u5ea6\u4e3a 11 \u6216 22 \u7684\u60c5\u51b5\u3002\u6211\u4eec\u679a\u4e3e\u6bcf\u4e00\u79cd\u8fb9\u754c\u60c5\u51b5\uff0c\u5e76\u4ece\u5bf9\u5e94\u7684\u5b50\u4e32\u5f00\u59cb\u4e0d\u65ad\u5730\u5411\u4e24\u8fb9\u6269\u5c55\u3002\u5982\u679c\u4e24\u8fb9\u7684\u5b57\u6bcd\u76f8\u540c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u7ee7\u7eed\u6269\u5c55\uff0c\u4f8b\u5982\u4ece P(i+1,j-1)P(i+1,j\u22121) \u6269\u5c55\u5230 P(i,j)P(i,j)\uff1b\u5982\u679c\u4e24\u8fb9\u7684\u5b57\u6bcd\u4e0d\u540c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u505c\u6b62\u6269\u5c55\uff0c\u56e0\u4e3a\u5728\u8fd9\u4e4b\u540e\u7684\u5b50\u4e32\u90fd\u4e0d\u80fd\u662f\u56de\u6587\u4e32\u4e86\u3002<\/p>\n\n\n\n
\u806a\u660e\u7684\u8bfb\u8005\u6b64\u65f6\u5e94\u8be5\u53ef\u4ee5\u53d1\u73b0\uff0c\u300c\u8fb9\u754c\u60c5\u51b5\u300d\u5bf9\u5e94\u7684\u5b50\u4e32\u5b9e\u9645\u4e0a\u5c31\u662f\u6211\u4eec\u300c\u6269\u5c55\u300d\u51fa\u7684\u56de\u6587\u4e32\u7684\u300c\u56de\u6587\u4e2d\u5fc3\u300d\u3002\u65b9\u6cd5\u4e8c\u7684\u672c\u8d28\u5373\u4e3a\uff1a\u6211\u4eec\u679a\u4e3e\u6240\u6709\u7684\u300c\u56de\u6587\u4e2d\u5fc3\u300d\u5e76\u5c1d\u8bd5\u300c\u6269\u5c55\u300d\uff0c\u76f4\u5230\u65e0\u6cd5\u6269\u5c55\u4e3a\u6b62\uff0c\u6b64\u65f6\u7684\u56de\u6587\u4e32\u957f\u5ea6\u5373\u4e3a\u6b64\u300c\u56de\u6587\u4e2d\u5fc3\u300d\u4e0b\u7684\u6700\u957f\u56de\u6587\u4e32\u957f\u5ea6\u3002\u6211\u4eec\u5bf9\u6240\u6709\u7684\u957f\u5ea6\u6c42\u51fa\u6700\u5927\u503c\uff0c\u5373\u53ef\u5f97\u5230\u6700\u7ec8\u7684\u7b54\u6848<\/p>\n\n\n\n
<\/p>\n\n\n\n
class Solution:\n   def expandAroundCenter(self, s, left, right):\n       while left >= 0 and right < len(s) and s[left] == s[right]:\n             left -= 1\n             right += 1\n       return left + 1, right - 1\ndef longestPalindrome(self, s: str) -> str:\n    start, end = 0, 0\n    for i in range(len(s)):\n        left1, right1 = self.expandAroundCenter(s, i, i)\n        left2, right2 = self.expandAroundCenter(s, i, i + 1)\n        if right1 - left1 > end - start:\n            start, end = left1, right1\n        if right2 - left2 > end - start:\n            start, end = left2, right2\n    return s[start: end + 1]<\/code><\/pre>\n\n\n\n
\u65b9\u6cd5\u4e09\uff1aManacher \u7b97\u6cd5
\u8fd8\u6709\u4e00\u4e2a\u590d\u6742\u5ea6\u4e3a O(n) \u7684 Manacher \u7b97\u6cd5\u3002\u7136\u800c\u672c\u7b97\u6cd5\u5341\u5206\u590d\u6742\uff0c\u4e00\u822c\u4e0d\u4f5c\u4e3a\u9762\u8bd5\u5185\u5bb9\u3002\u8fd9\u91cc\u7ed9\u51fa\uff0c\u4ec5\u4f9b\u6709\u5174\u8da3\u7684\u540c\u5b66\u6311\u6218\u81ea\u5df1\u3002<\/p>\n\n\n\n
\u4e3a\u4e86\u8868\u8ff0\u65b9\u4fbf\uff0c\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u65b0\u6982\u5ff5\u81c2\u957f\uff0c\u8868\u793a\u4e2d\u5fc3\u6269\u5c55\u7b97\u6cd5\u5411\u5916\u6269\u5c55\u7684\u957f\u5ea6\u3002\u5982\u679c\u4e00\u4e2a\u4f4d\u7f6e\u7684\u6700\u5927\u56de\u6587\u5b57\u7b26\u4e32\u957f\u5ea6\u4e3a 2 * length + 1 \uff0c\u5176\u81c2\u957f\u4e3a length\u3002<\/p>\n\n\n\n
\u4e0b\u9762\u7684\u8ba8\u8bba\u53ea\u6d89\u53ca\u957f\u5ea6\u4e3a\u5947\u6570\u7684\u56de\u6587\u5b57\u7b26\u4e32\u3002\u957f\u5ea6\u4e3a\u5076\u6570\u7684\u56de\u6587\u5b57\u7b26\u4e32\u6211\u4eec\u5c06\u4f1a\u5728\u6700\u540e\u4e0e\u957f\u5ea6\u4e3a\u5947\u6570\u7684\u60c5\u51b5\u7edf\u4e00\u8d77\u6765\u3002<\/p>\n\n\n\n
\u601d\u8def\u4e0e\u7b97\u6cd5<\/p>\n\n\n\n
\u5728\u4e2d\u5fc3\u6269\u5c55\u7b97\u6cd5\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u80fd\u591f\u5f97\u51fa\u6bcf\u4e2a\u4f4d\u7f6e\u7684\u81c2\u957f\u3002\u90a3\u4e48\u5f53\u6211\u4eec\u8981\u5f97\u51fa\u4ee5\u4e0b\u4e00\u4e2a\u4f4d\u7f6e i \u7684\u81c2\u957f\u65f6\uff0c\u80fd\u4e0d\u80fd\u5229\u7528\u4e4b\u524d\u5f97\u5230\u7684\u4fe1\u606f\u5462\uff1f<\/p>\n\n\n\n
\u7b54\u6848\u662f\u80af\u5b9a\u7684\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5982\u679c\u4f4d\u7f6e j \u7684\u81c2\u957f\u4e3a length\uff0c\u5e76\u4e14\u6709 j + length > i\uff0c\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u5f53\u5728\u4f4d\u7f6e i \u5f00\u59cb\u8fdb\u884c\u4e2d\u5fc3\u62d3\u5c55\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u5148\u627e\u5230 i \u5173\u4e8e j \u7684\u5bf9\u79f0\u70b9 2 * j – i\u3002\u90a3\u4e48\u5982\u679c\u70b9 2 * j – i \u7684\u81c2\u957f\u7b49\u4e8e n\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u77e5\u9053\uff0c\u70b9 i \u7684\u81c2\u957f\u81f3\u5c11\u4e3a min(j + length – i, n)\u3002\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u76f4\u63a5\u8df3\u8fc7 i \u5230 i + min(j + length – i, n) \u8fd9\u90e8\u5206\uff0c\u4ece i + min(j + length – i, n) + 1 \u5f00\u59cb\u62d3\u5c55\u3002<\/p>\n\n\n\n
\u6211\u4eec\u53ea\u9700\u8981\u5728\u4e2d\u5fc3\u6269\u5c55\u6cd5\u7684\u8fc7\u7a0b\u4e2d\u8bb0\u5f55\u53f3\u81c2\u5728\u6700\u53f3\u8fb9\u7684\u56de\u6587\u5b57\u7b26\u4e32\uff0c\u5c06\u5176\u4e2d\u5fc3\u4f5c\u4e3a j\uff0c\u5728\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u5c31\u80fd\u6700\u5927\u9650\u5ea6\u5730\u907f\u514d\u91cd\u590d\u8ba1\u7b97\u3002<\/p>\n\n\n\n
\u90a3\u4e48\u73b0\u5728\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898\uff1a\u5982\u4f55\u5904\u7406\u957f\u5ea6\u4e3a\u5076\u6570\u7684\u56de\u6587\u5b57\u7b26\u4e32\u5462\uff1f<\/p>\n\n\n\n
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class Solution:\n    def expand(self, s, left, right):\n        while left >= 0 and right < len(s) and s[left] == s[right]:\n            left -= 1\n            right += 1\n        return (right - left - 2) \/\/ 2\n\n    def longestPalindrome(self, s: str) -> str:\n        end, start = -1, 0\n        s = '#' + '#'.join(list(s)) + '#'\n        arm_len = []\n        right = -1\n        j = -1\n        for i in range(len(s)):\n            if right >= i:\n                i_sym = 2 * j - i\n                min_arm_len = min(arm_len[i_sym], right - i)\n                cur_arm_len = self.expand(s, i - min_arm_len, i + min_arm_len)\n            else:\n                cur_arm_len = self.expand(s, i, i)\n            arm_len.append(cur_arm_len)\n            if i + cur_arm_len > right:\n                j = i\n                right = i + cur_arm_len\n            if 2 * cur_arm_len + 1 > end - start:\n                start = i - cur_arm_len\n                end = i + cur_arm_len\n        return s[start+1:end+1:2]<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
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