Final Array State After K Multiplication Operations II - Solution & Explanation

Utilize a Min-Heap (Priority Queue) to efficiently track the minimum value in the array. After each operation, extract the minimum value, update it, and re-insert it into the heap with the modified value.

The solution uses a min-heap to maintain the minimum element in the array. Initially, each element's value and index are pushed to the heap. The minimum element is removed and updated, then reinserted into the heap, ensuring the heap property is maintained. This process continues, reducing k until it reaches zero. Finally, the solution applies a modulo operation to each element in the array as required.

In this approach, iteratively find and replace the minimum value directly in the array without any auxiliary data structures, scanning the array each time an operation is performed.

This algorithm directly manipulates the input array, avoiding priority queues or auxiliary data structures. In each of the k iterations, it locates the minimum value in the array by a linear search and updates it by multiplying it with multiplier.