# C# Program for Longest Palindromic Subsequence | DP-12

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

 `// 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 `

Output:

```The length of the LPS is 5
```

Dynamic Programming Solution

## C#

 `// 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. `

Output:

```The lnegth of the lps is 7
```

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