diff --git a/Dynamic Programming/LongestPalindromicSubsequence.cpp b/Dynamic Programming/LongestPalindromicSubsequence.cpp
new file mode 100644
index 0000000..d032f44
--- /dev/null
+++ b/Dynamic Programming/LongestPalindromicSubsequence.cpp	
@@ -0,0 +1,33 @@
+
+#include<bits/stdc++.h> 
+using namespace std; 
+
+ 
+int max (int x, int y) { return (x > y)? x : y; } 
+
+
+int lps(char *seq, int i, int j) 
+{ 
+if (i == j) 
+	return 1; 
+
+
+if (seq[i] == seq[j] && i + 1 == j) 
+	return 2; 
+
+
+if (seq[i] == seq[j]) 
+	return lps (seq, i+1, j-1) + 2; 
+
+return max( lps(seq, i, j-1), lps(seq, i+1, j) ); 
+} 
+
+
+int main() 
+{ 
+	char seq[] = "HACKTOBERFEST"; 
+	int n = strlen(seq); 
+	cout << "The length of the LPS is "
+		<< lps(seq, 0, n-1); 
+	return 0; 
+}