added Longest common subsequence problem to Dynamic Programming

Author: vasugoel062

Dynamic Programming/LongestCommonSubSequence.java

@@ -0,0 +1,29 @@
+import java.util.*;
+
+public class LongestCommonSubSequence {
+    static int countlcs(String s1, String s2) {
+        int[][] count = new int[s1.length() + 1][s2.length() + 1];
+        for (int i = s1.length(); i >= 0; i--) {
+            for (int j = s2.length(); j >= 0; j--) {
+                if (i == s1.length()) {
+                    count[i][j] = 0;
+                } else if (j == s2.length()) {
+                    count[i][j] = 0;
+                } else if (i == s1.length() && j == s2.length()) {
+                    count[i][j] = 0;
+                } else {
+                    count[i][j] = s1.charAt(i) == s2.charAt(j) ? count[i + 1][j + 1] + 1
+                            : Math.max(count[i + 1][j], count[i][j + 1]);
+                }
+            }
+        }
+        return count[0][0];
+    }
+
+    public static void main(String[] args) {
+        String s1 = "abcdabr";
+        String s2 = "aebdabr";
+        System.out.println(countlcs(s1, s2));
+
+    }
+}