Leetcode 516. Longest Palindromic Subsequence

Problem

Given a string s, find the longest palindromic subsequence's length in s.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Algorithm

Dynamic Programming (DP). Define state f(left, right) is the Longest Palindromic Subsequence in s[left...right], so we have
f ( l e f t , r i g h t ) = { f ( l e f t + 1 , r i g h t − 1 ) + 2 if s [ l e f t ] = = s [ r i g h t ] max ⁡ [ f ( l e f t + 1 , r i g h t ) , f ( l e f t , r i g h t − 1 ) ] otherwise f(left, right) = \begin{cases} f(left+1, right-1) + 2 & \text{if } s[left] == s[right ]\\ \max[f(left+1, right), f(left, right-1)] & \text{otherwise} \end{cases} f(left,right)={f(left+1,right−1)+2max[f(left+1,right),f(left,right−1)]if s[left]==s[right]otherwise

Code

class Solution:
    def longestPalindromeSubseq(self, s: str) -> int:
        slen = len(s)
        if slen == 0:
            return 0
        
        dp = [[0] * slen for i in range(slen)]
        for i in range(slen):
            dp[i][i] = 1
        for L in range(2, slen+1):
            for i in range(slen - L + 1):
                j = i + L - 1
                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][slen-1]