Increasing Triplet Subsequence

Array / String
Key Ideas
The key idea to solve this problem is to keep track of the smallest two elements encountered so far and check if there is a third element greater than both of them.
Problem Number
Problem Summary
Given an unsorted array of integers, the "Increasing Triplet Subsequence" problem asks to determine if there exists a subsequence of length 3 in the array where the elements are in increasing order. A key pitfall is to mistakenly assume that finding three distinct numbers in increasing order is sufficient, when in fact the subsequence must be contiguous. Another pitfall is to use a brute force approach that involves checking all possible triplets, which has a time complexity of O(n^3) and is not efficient.
Solution Summary
The best solution to solve the Increasing Triplet Subsequence problem is to use a greedy approach. We initialize two variables, first and second, with maximum possible values. We iterate through the array, and if we find a number smaller than first, we update first to that number. If we find a number greater than first but smaller than second, we update second to that number. If we find a number greater than second, we have found the increasing triplet subsequence and return True. If we reach the end of the array without finding an increasing triplet subsequence, we return False. This solution has a time complexity of O(n) and a space complexity of O(1).