Added Longest Increasing Subsequence program to the list

Dynamic-Programming/LongestIncreasingSubsequence.js

@@ -0,0 +1,26 @@
+/**
+ * A Dynamic Programming based solution for calculating Longest Increasing Subsequence
+ * https://en.wikipedia.org/wiki/Longest_increasing_subsequence
+ */
+
+function main () {
+  const x = [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]
+  const length = x.length
+  const dp = Array(length).fill(1)
+
+  let res = 1
+
+  for (let i = 0; i < length; i++) {
+    for (let j = 0; j < i; j++) {
+      if (x[i] > x[j]) {
+        dp[i] = Math.max(dp[i], 1 + dp[j])
+        if (dp[i] > res)
+          res = dp[i]
+      }
+    }
+  }
+  
+  console.log('Length of Longest Increasing Subsequence is:', res)
+}
+
+main()