Maximize Sum Of Array After K Negations - Solution & Explanation

Approach 1: Sorting and Greedy Negation

This approach involves sorting the array first, which helps address the negativity in a prioritized fashion. By sorting, negative numbers are brought to the forefront. The plan is to turn all negative numbers positive for immediate gains. After flipping the necessary negatives or using up the flips, if flips remain, we aim them repeatedly at the smallest number in terms of absolute value to ensure no more productive use of a negation exists.

The C solution uses the standard qsort to sort the array. The core logic emphasizes negating the smallest negative numbers first, iterating through the array until either all negative numbers are converted or k negations are exhausted. Should negations remain post initial conversion, an odd count of k means a further single alteration is advantageous, specifically targeting the smallest number.

Approach 2: Using Priority Queue (Min-Heap)

A priority queue (or min-heap) will provide an elegant method to always operate on the smallest element. The process involves inserting all numbers into a heap, then multiple negations individualizing the smallest available value until k operations are exhausted. This method efficiently manages both negation and retrieval of minimal elements.

The C++ implementation uses a min-heap, inserting all numbers initially. We invoke k negations, ensuring to log the negated value back into the heap, thus retaining a valid minimum tracking mechanism. The strategy processes/instruments flipping k times and sums up the remainder through a cumulative heap pop.