[LeetCode] Problem 516 - Longest Palindromic Subsequence

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Given a string s, find the longest palindromic subsequence’s length in s. You may assume that the maximum length of s is 1000.

Example

No.1

Input:
“bbbab”

Output:
4

One possible longest palindromic subsequence is “bbbb”.

No. 2

Input:
“cbbd”

Output:
2

One possible longest palindromic subsequence is “bb”.

Code

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public int longestPalindromeSubseq(String s) {
    int n = s.length();
    int[][] dp = new int[n][n];

    // dp[i][j] = dp[i+1][j-1] + 2            (Si == Sj)
    // dp[i][j] = Max(dp[i+1][j], dp[i][j-1]) (Si != Sj)
    for (int i = n - 1; i >= 0; i--) {
        dp[i][i] = 1;

        for (int j = i + 1; j < n; j++) {
            if (s.charAt(i) == s.charAt(j))
                dp[i][j] = dp[i+1][j-1] + 2;
            else
                dp[i][j] = Math.max(dp[i+1][j], dp[i][j-1]);
        }
    }

    return dp[0][n-1];
}