516. Longest Palindromic Subsequence

问题

求最长的回文子序列

Input: "bbbab"
Output: 4
Explanation: One possible longest palindromic subsequence is "bbbb"

思路

dp[i][j]表示从i到j的最大回文子序列的长度。
对于dp[i][j]时，如果s[i] == s[j]，显然dp[i][j]会等于dp[i+1][j-1] + 2，相当于在两头扩展相等字符。
如果不相等的话，dp[i][j] = max(dp[i+1][j], dp[i][j-1])，相当于在原来的两个dp上选一个最大的。

时间复杂度O(n^{2)，空间复杂度O(n}2)

代码

class Solution(object):
    def longestPalindromeSubseq(self, s):
        """
        :type s: str
        :rtype: int
        """
        if(s==None or s ==''):
            return 0
        if(len(s)==1):
            return 1
        dp = [[0 for _ in range(len(s))] for _ in range(len(s))]

        for i in range(len(s))[::-1]:
            dp[i][i] = 1
            for j in range(i+1,len(s)):
                if(s[i]==s[j]):
                    dp[i][j] = dp[i+1][j-1] + 2
                else:
                    dp[i][j] = max(dp[i+1][j], dp[i][j-1])
        return dp[0][len(s)-1]