Added Longest Common Subsequence

Dynamic-Programming/longestCommonSubsequence.js

@@ -0,0 +1,31 @@
+/*
+    * Given two sequences, find the length of longest subsequence present in both of them. 
+    * A subsequence is a sequence that appears in the same relative order, but not necessarily contiguous. 
+    * For example, “abc”, “abg”, “bdf”, “aeg”, ‘”acefg”, .. etc are subsequences of “abcdefg”
+*/
+
+function longestCommonSubsequence(x, y, str1, str2, dp) {
+  if (x == -1 || y == -1) return 0;
+  else {
+    if (dp[x][y] != 0) return dp[x][y];
+    else {
+      if (str1[x] == str2[y]) {
+        return dp[x][y] = 1 + longestCommonSubsequence(x - 1, y - 1, str1, str2, dp);
+      }
+      else {
+        return dp[x][y] = Math.max(longestCommonSubsequence(x - 1, y, str1, str2, dp), longestCommonSubsequence(x, y - 1, str1, str2, dp))
+      }
+    }
+  }
+
+}
+
+function main() {
+  const str1 = "ABCDGH"
+  const str2 = "AEDFHR"
+  let dp = new Array(str1.length + 1).fill(0).map(x => new Array(str2.length + 1).fill(0))
+  const res = longestCommonSubsequence(str1.length - 1, str2.length - 1, str1, str2, dp)
+  console.log(res);
+}
+
+main()