Longest Palindromic Subsequence II — LeetCode 1682 Python Solution

The problem

A subsequence of a string s is considered a good palindromic subsequence if: It is a subsequence of s. It is a palindrome (has the same value if reversed).

Example

Input

s = "bbabab"

Output

4

Explanation

The longest good palindromic subsequence of s is "baab".

Python solution

class Solution:
    def longestPalindromeSubseq(self, s: str) -> int:
        @cache
        def dfs(i, j, x):
            if i >= j:
                return 0
            if s[i] == s[j] and s[i] != x:
                return dfs(i + 1, j - 1, s[i]) + 2
            return max(dfs(i + 1, j, x), dfs(i, j - 1, x))

        ans = dfs(0, len(s) - 1, '')
        dfs.cache_clear()
        return ans

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1682. Longest Palindromic Subsequence II is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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