From fbf0ef369f17dacb7db7620ebe02593f36317bca Mon Sep 17 00:00:00 2001
From: Bilwasiva <tintinmyself@gmail.com>
Date: Mon, 11 Oct 2021 18:56:16 +0530
Subject: [PATCH] Created longest_palindromic_subsequence.cpp

Dynamic Programming based C++ program for LPS problem
---
 .../longest_palindromic_subsequence.cpp       | 42 +++++++++++++++++++
 1 file changed, 42 insertions(+)
 create mode 100644 dynamic_programming/longest_palindromic_subsequence.cpp

diff --git a/dynamic_programming/longest_palindromic_subsequence.cpp b/dynamic_programming/longest_palindromic_subsequence.cpp
new file mode 100644
index 00000000..0a3c7ea8
--- /dev/null
+++ b/dynamic_programming/longest_palindromic_subsequence.cpp
@@ -0,0 +1,42 @@
+// A Dynamic Programming based C++ program for LPS problem
+// Returns the length of the longest palindromic subsequence in seq
+#include<stdio.h>
+#include<string.h>
+
+int max (int x, int y) { return (x > y)? x : y; }
+
+int lps(char *str)
+{
+int n = strlen(str);
+int i, j, cl;
+int L[n][n]; 
+
+for (i = 0; i < n; i++)
+	L[i][i] = 1;
+
+	for (cl=2; cl<=n; cl++)
+	{
+		for (i=0; i<n-cl+1; i++)
+		{
+			j = i+cl-1;
+			if (str[i] == str[j] && cl == 2)
+			L[i][j] = 2;
+			else if (str[i] == str[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 */
+int main()
+{
+	char seq[] = "GEEKS FOR GEEKS";
+	int n = strlen(seq);
+	printf ("The length of the LPS is %d", lps(seq));
+	getchar();
+	return 0;
+}