Maximize Subsequences Score LeetCode 2542 – Best Approach with Greedy & Heap #leetcode #java #code

The Maximize Subsequences Score problem from LeetCode 2542 is a challenging greedy + heap (priority queue) based problem that requires efficiently selecting a subsequence to maximize the given score. This problem is commonly asked in coding interviews at top tech companies and tests a candidate’s ability to optimize selection and prioritization strategies using sorting, heaps, and greedy algorithms.

In this problem, we are given two integer arrays, nums1 and nums2, along with an integer k. Our goal is to select k elements from nums1, forming a subsequence, while using the corresponding elements from nums2 to compute the final score. The score is determined by multiplying the sum of selected elements from nums1 by the minimum value among their corresponding elements in nums2. This introduces a trade-off: we want a large sum from nums1 but also need to maximize the minimum value from nums2 to obtain the highest score possible.

A naïve brute-force approach would involve generating all possible k-length subsequences, computing their scores, and selecting the maximum, but this leads to exponential time complexity, making it infeasible for large inputs. Instead, we can leverage a Greedy strategy combined with a Min-Heap (Priority Queue) to efficiently select elements while maintaining the highest possible score. The optimal solution involves sorting nums2 in descending order, iterating over the elements, and maintaining a Min-Heap to track the k-largest elements of nums1. By doing this, we can efficiently compute and update the score at each step while ensuring that the smallest value in nums2 among selected elements is maximized.

This problem is an excellent demonstration of Greedy Algorithms, Priority Queues, and Optimization Techniques commonly tested in FAANG coding interviews. Understanding this approach not only helps in solving similar problems efficiently but also improves problem-solving skills for data structures and algorithms.

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