Added Longest Increasing Subsequence using Recursion

Author: preritasaini1

src/main/java/com/thealgorithms/recursion/LongestIncreasingSubsequence.java

@@ -0,0 +1,31 @@
+package com.thealgorithms.recursion;
+
+public class LongestIncreasingSubsequence {
+
+    public static int solve(int[] nums, int prev, int idx) {
+        // base case
+        if (idx == nums.length) return 0;
+
+        // process
+        // 1. include 
+        // 2. exclude
+        int include = 0;
+        if (prev == -1 || nums[idx] > nums[prev]) {
+            include = 1 + solve(nums, idx, idx + 1);
+        }
+
+        int exclude = solve(nums, prev, idx + 1);
+        return Math.max(include, exclude);
+    }
+
+    public int lengthOfLIS(int[] nums) {
+        int prev = -1;
+        return solve(nums, prev, 0);
+    }
+
+    public static void main(String[] args) {
+        int[] nums = {10, 22, 9, 33, 21, 50, 41, 60};
+        LongestIncreasingSubsequence lis = new LongestIncreasingSubsequence();
+        System.out.println("Length of LIS: " + lis.lengthOfLIS(nums));
+    }
+}