Longest Palindromic Subsequence

Given a sequence, find the length of the longest palindromic subsequence in it.

Prerequisite: longest common subsequence

• Given string a, lcs of string a and its reverse will be the longest palindromic subsequence👍.

Code

int lcs(int x, int y, string s1, string s2)
{
    int dp[x + 1][y + 1];

    for (int i = 0; i < x + 1; i++)
    {
        for (int j = 0; j < y + 1; j++)
        {
            if (i == 0 || j == 0)
                dp[i][j] = 0;
            else if (s1[i - 1] == s2[j - 1])
                dp[i][j] = 1 + dp[i - 1][j - 1];
            else
                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
        }
    }
    return dp[x][y];
}
int lps(int n, string s)
{
    return lcs(n, n, s, reverse(s.begin(), s.end()));
}

Complexity Analysis

• Time Complexity: O(N^2)
• Space Complexity: O(N^2)

Reference

• GFG: Longest Palindromic Subsequence
• YouTube: AV - Longest Palindromic Subsequence