Increasing Triplet Subsequence
Category
Array / String
Checkbox
Checkbox
Difficulty
Medium
Index
8
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
334
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).Tags
Array
Greedy