Print Longest Palindromic Subsequence

Given a sequence, print a longest palindromic subsequence of it.
Examples :

Output : BABCBAB
The above output is the longest
palindromic subsequence of given
sequence. "BBBBB" and "BBCBB" are 
also palindromic subsequences of
the given sequence, but not the 
longest ones.

Output : Output can be either EEKEE
         or EESEE or EEGEE, ..

We have discussed a solution in below post to find length of longest palindromic subsequence.
Dynamic Programming | Set 12 (Longest Palindromic Subsequence)

In this post a solution to print the longest palindromic subsequence is discussed.

This problem is close to the Longest Common Subsequence (LCS) problem. In fact, we can use LCS as a subroutine to solve this problem. Following is the two step solution that uses LCS.
1) Reverse the given sequence and store the reverse in another array say rev[0..n-1]
2) LCS of the given sequence and rev[] will be the longest palindromic sequence.
3) Once we have found LCS, we can print the LCS.

/* CPP program to print longest palindromic
   subsequence */
using namespace std;

/* Returns LCS X and Y */
string lcs(string &X, string &Y)
    int m = X.length();
    int n = Y.length();

    int L[m+1][n+1];

    /* Following steps build L[m+1][n+1] in bottom
       up fashion. Note that L[i][j] contains
       length of LCS of X[0..i-1] and Y[0..j-1] */
    for (int i=0; i<=m; i++)
        for (int j=0; j<=n; j++)
            if (i == 0 || j == 0)
                L[i][j] = 0;
            else if (X[i-1] == Y[j-1])
                L[i][j] = L[i-1][j-1] + 1;
                L[i][j] = max(L[i-1][j], L[i][j-1]);

    // Following code is used to print LCS
    int index = L[m][n];

    // Create a string length index+1 and
    // fill it with \0
    string lcs(index+1, '\0');

    // Start from the right-most-bottom-most
    // corner and one by one store characters
    // in lcs[]
    int i = m, j = n;
    while (i > 0 && j > 0)
        // If current character in X[] and Y
        // are same, then current character
        // is part of LCS
        if (X[i-1] == Y[j-1])
            // Put current character in result
            lcs[index-1] = X[i-1];

            // reduce values of i, j and index

        // If not same, then find the larger of
        // two and go in the direction of larger
        // value
        else if (L[i-1][j] > L[i][j-1])

    return lcs;

// Returns longest palindromic subsequence
// of str
string longestPalSubseq(string &str)
    // Find reverse of str
    string rev = str;
    reverse(rev.begin(), rev.end());

    // Return LCS of str and its reverse
    return lcs(str, rev);

/* Driver program to test above function */
int main()
    string str = "GEEKSFORGEEKS";
    cout << longestPalSubseq(str);
    return 0;



This article is contributed by Kartik. If you like GeeksforGeeks and would like to contribute, you can also write an article using or mail your article to See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Recommended Posts:

3.5 Average Difficulty : 3.5/5.0
Based on 6 vote(s)