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55 lines
1.8 KiB
Python
55 lines
1.8 KiB
Python
#!/usr/bin/env python
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# coding=utf-8
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#######################################################################################
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# Leetcode 5 最长回文子串
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#
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# 给定一个字符串 s，找到 s 中最长的回文子串。你可以假设 s 的最大长度为 1000。
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#
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# 示例 1：
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# 输入: "babad"
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# 输出: "bab"
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# 注意: "aba" 也是一个有效答案。
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#
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# 示例 2：
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# 输入: "cbbd"
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# 输出: "bb"
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#######################################################################################
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class Solution:
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def longestPalindrome(self, s):
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"""
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:type s: str
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:rtype str
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(knowledge)
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思路：
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1. 使用动态规划
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2. dp[i][j] => s[i:j] 子串是否是一个回文字符串
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3. 状态转移方程
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f(i, j) = True i == j
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s[i] == s[j] i + 1 == j
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f(i + 1, j - 1) && s[i] == s[j] i + 1 < j
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"""
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dp, resultStart, resultEnd = [[True if i == j else False for j in range(len(s))] for i in range(len(s))], 0, 1
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for j in range(0, len(s) - 1):
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dp[j][j + 1] = s[j] == s[j + 1]
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if dp[j][j + 1]:
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resultStart, resultEnd = j, j + 2
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for i in range(2, len(s)):
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for j in range(0, len(s) - i):
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if dp[j + 1][j + i - 1] and s[j] == s[j + i]:
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resultStart, resultEnd, dp[j][j + i] = j, j + i + 1, True
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return s[resultStart: resultEnd]
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if __name__ == '__main__':
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solution = Solution()
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print(solution.longestPalindrome("abcba"), "= abcba")
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print(solution.longestPalindrome("babad"), "= aba")
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print(solution.longestPalindrome("cbbd"), "= bb")
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print(solution.longestPalindrome("ccc"), "= ccc")
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