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# Increasing Triplet Subsequence

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.

**Note:** Your algorithm should run in O(n) time complexity and O(1) space complexity.

**Example 1:**

```
Input: [1,2,3,4,5]
Output: true
```

**Example 2:**

```
Input: [5,4,3,2,1]
Output: false
```

```java
class Solution {
    public boolean increasingTriplet(int[] nums) {
        // start with two largest values, as soon as we find a number bigger than both,
        // while both have been updated, return true.
        int small = Integer.MAX_VALUE, big = Integer.MAX_VALUE;
        for (int n : nums) {
            if (n <= small)
                small = n;
            // update small if n is smaller than both
            else if (n <= big)
                big = n;
            // update big only if greater than small but smaller than big
            else
                return true; // return if you find a number bigger than both
        }
        return false;
    }
}
```