Given an integer array nums, determine whether there exist indices i, j, and k such that i < j < k and nums[i] < nums[j] < nums[k].

Return true if such a triplet exists; otherwise, return false.

Note: Could you implement a solution that runs in O(n) time complexity and O(1) space complexity?

Constraints:

• $1 \leq$ nums.length $\leq 5 * 10^5$

• $-2^{31} \leq$ nums[i] $\leq 2^{31} - 1$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.