Added Longest common subsequence

C/Algorithms/Dynamic-Programming/LonestCommonSubsequence.c

@@ -0,0 +1,25 @@
+#include<stdio.h>
+#include<stdlib.h>
+int max(int a,int b){
+    return (a>b)? a: b;
+}
+int LCS(char * a,char * b,int n1,int n2){
+    if(n1==0 || n2==0) return 0;
+
+    // if two character are common than check for subproblems 
+    if(a[n1-1]==b[n2-1])
+      return 1+LCS(a,b,n1-1,n2-1);
+    // If two character is not common than two cases are arises
+    // case 1:  to leave the character of first string and check for subproblem with second string
+    // case 2: to leave the character of second string and check for subproblem with first string
+    return max(LCS(a,b,n1-1,n2),LCS(a,b,n1,n2-1));
+}
+int main(){
+    int n1,n2; scanf("%d %d",&n1,&n2);
+
+    char a[n1],b[n2];
+    scanf("%s",a);
+    scanf("%s",b);
+    printf("longest common subsequence is %d\n",LCS(a,b,n1,n2));
+    return 0;
+}