Lis (#396)

* Added Longest Common Subsequence

* Renamed the File

* Optimized the code

* Optimized the code

* Changed some styles as per the rule

* Again some style fixed

* Added Longest Increasing Subsequence program to the list

* Style changed

Dynamic-Programming/LongestCommonSubsequence.js

@@ -0,0 +1,33 @@
+/*
+    * 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]) {
+        dp[x][y] = 1 + longestCommonSubsequence(x - 1, y - 1, str1, str2, dp)
+        return dp[x][y]
+      } else {
+        dp[x][y] = Math.max(longestCommonSubsequence(x - 1, y, str1, str2, dp), longestCommonSubsequence(x, y - 1, str1, str2, dp))
+        return dp[x][y]
+      }
+    }
+  }
+}
+
+function main () {
+  const str1 = 'ABCDGH'
+  const str2 = 'AEDFHR'
+  const 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()