Given an unsorted array return whether an increasing subsequence of length 3 exists or not in the array.

Formally the function should:
Return true if there exists i, j, k 
such that arr[i] < arr[j] < arr[k] given 0 ≤ i < j < k ≤ n-1 else return false.
Your algorithm should run in O(n) time complexity and O(1) space complexity.

Examples:
Given [1, 2, 3, 4, 5],
return true.

Given [5, 4, 3, 2, 1],
return false.

 1 public class Solution {
 2     public boolean increasingTriplet(int[] nums) {
 3         int[] dp = new int[nums.length];
 4         for (int i=0; i<nums.length; i++) {
 5             dp[i] = 1;
 6             for (int j=0; j<i; j++) {
 7                 if (nums[j] < nums[i]) {
 8                     dp[i] = Math.max(dp[i], dp[j]+1);
 9                 }
10                 if (dp[i] == 3) return true;
11             }
12         }
13         return false;
14     }
15 }