Added lcs

dynamic_programing/longest_common_subsequence/c++/longest_common_subsequence.cpp

@@ -0,0 +1,40 @@
+#include<iostream>
+#include<bits/stdc++.h>
+using namespace std;
+
+int lpsH(string s, int start, int end, int **output){
+	if(start > end){
+		return 0;
+	}
+
+	if(s.length() == 1 || start == end){
+		return 1;
+	}
+
+	if(output[start][end] > -1){
+		return output[start][end];
+	}
+	if(s[start] == s[end]){
+		output[start][end] = 2 + lpsH(s, start+1, end-1, output);
+		return output[start][end];
+	}
+	output[start][end] = max(lpsH(s, start+1, end, output), lpsH(s, start, end-1, output));
+	return output[start][end];
+}
+int lcs(string s1, string s2){
+  int n1 = s1.length();
+  int **output = new int*[n1+1];
+
+  for(int i = 0; i <= s1.length(); i++){
+    output[i] = new int[s2.length()+1];
+    for(int j = 0; j <= s2.length(); j++){
+      output[i][j] = -1;
+    }
+  }
+  return lpsH(s1, 0, s1.length()-1, output);
+}
+int main{
+	string s1, s2;
+	cin >> s1 >> s2;
+	cout << lcs(s1, s2);
+}