Mastering the "Sorted Subsequence of Size 3" Problem: Two Efficient Java Approaches

Finding a sorted subsequence of a specific size is a classic algorithmic challenge that tests your ability to optimize array traversals. The problem asks us to find three elements in an array such that arr[i] < arr[j] < arr[k] and their indices satisfy i < j < k . If you are preparing for coding interviews or just sharpening your problem-solving skills, this problem is a fantastic way to transition from brute-force thinking to highly optimized logic. In this post, we will explore two distinct approaches to solving this problem in Java: an intuitive Precomputation Approach and a highly optimized Single-Pass Greedy Approach . Approach 1: The Prefix and Suffix Arrays (Precomputation) The Intuition To find our three numbers, let's focus on the middle element, arr[j] . For any element to act as a valid middle number in our sequence, two conditions must be met: There must be a strictly smaller number somewhere to its left. There must be a strictly larger number somewhere to its right. Instea