C# Program for Longest Palindromic Subsequence | DP-12

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

longest-palindromic-subsequence

As another example, if the given sequence is “BBABCBCAB”, then the output should be 7 as “BABCBAB” is the longest palindromic subseuqnce in it. “BBBBB” and “BBCBB” are also palindromic subsequences of the given sequence, but not the longest ones.
1) Optimal Substructure:
Let X[0..n-1] be the input sequence of length n and L(0, n-1) be the length of the longest palindromic subsequence of X[0..n-1].

If last and first characters of X are same, then L(0, n-1) = L(1, n-2) + 2.
Else L(0, n-1) = MAX (L(1, n-1), L(0, n-2)).
Following is a general recursive solution with all cases handled.

C#

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// C# program of above approach
using System;
  
public class GFG {
  
    // A utility function to get max of two integers
    static int max(int x, int y)
    {
        return (x > y) ? x : y;
    }
    // Returns the length of the longest palindromic subsequence in seq
  
    static int lps(char[] seq, int i, int j)
    {
        // Base Case 1: If there is only 1 character
        if (i == j) {
            return 1;
        }
  
        // Base Case 2: If there are only 2 characters and both are same
        if (seq[i] == seq[j] && i + 1 == j) {
            return 2;
        }
  
        // If the first and last characters match
        if (seq[i] == seq[j]) {
            return lps(seq, i + 1, j - 1) + 2;
        }
  
        // If the first and last characters do not match
        return max(lps(seq, i, j - 1), lps(seq, i + 1, j));
    }
  
    /* Driver program to test above function */
    public static void Main()
    {
        String seq = "GEEKSFORGEEKS";
        int n = seq.Length;
        Console.Write("The length of the LPS is " + lps(seq.ToCharArray(), 0, n - 1));
    }
}
  
// This code is contributed by Rajput-Ji

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Output:



The length of the LPS is 5

Dynamic Programming Solution

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// A Dynamic Programming based C# Program
// for the Egg Dropping Puzzle
using System;
  
class GFG {
  
    // A utility function to get max of
    // two integers
    static int max(int x, int y)
    {
        return (x > y) ? x : y;
    }
  
    // Returns the length of the longest
    // palindromic subsequence in seq
    static int lps(string seq)
    {
        int n = seq.Length;
        int i, j, cl;
  
        // Create a table to store results
        // of subproblems
        int[, ] L = new int[n, n];
  
        // Strings of length 1 are
        // palindrome of lentgh 1
        for (i = 0; i < n; i++)
            L[i, i] = 1;
  
        // Build the table. Note that the
        // lower diagonal values of table
        // are useless and not filled in
        // the process. The values are
        // filled in a manner similar to
        // Matrix Chain Multiplication DP
        // solution (See
        // https:// www.geeksforgeeks.org/matrix-chain-multiplication-dp-8/
        // cl is length of substring
        for (cl = 2; cl <= n; cl++) {
            for (i = 0; i < n - cl + 1; i++) {
                j = i + cl - 1;
  
                if (seq[i] == seq[j] && cl == 2)
                    L[i, j] = 2;
                else if (seq[i] == seq[j])
                    L[i, j] = L[i + 1, j - 1] + 2;
                else
                    L[i, j] = max(L[i, j - 1], L[i + 1, j]);
            }
        }
  
        return L[0, n - 1];
    }
  
    /* Driver program to test above 
    functions */
    public static void Main()
    {
        string seq = "GEEKS FOR GEEKS";
        int n = seq.Length;
        Console.Write("The lnegth of the "
                      + "lps is " + lps(seq));
    }
}
  
// This code is contributed by nitin mittal.

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Output:

The lnegth of the lps is 7

Please refer complete article on Longest Palindromic Subsequence | DP-12 for more details!




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