Take Gifts From the Richest Pile

Problem Description

You are given an integer array gifts denoting the number of gifts in various piles. Every second, you do the following:

• Choose the pile with the maximum number of gifts.
• If there is more than one pile with the maximum number of gifts, choose any.
• Reduce the number of gifts in the pile to the floor of the square root of the original number of gifts in the pile.

Return the number of gifts remaining after k seconds.

Key Insights

• The problem requires simulating the process of selecting the pile with the maximum gifts multiple times.
• A max-heap (or priority queue) can efficiently help in retrieving the largest pile.
• The floor square root operation needs to be performed on the selected pile's gift count.
• The process needs to be repeated k times.

Space and Time Complexity

Time Complexity: O(k log n) where n is the number of piles, as we need to adjust the max-heap k times. Space Complexity: O(n) for storing the max-heap of gifts.

Solution

To solve the problem, we utilize a max-heap data structure to keep track of the piles of gifts. The algorithm proceeds as follows:

1. Insert all elements from the gifts array into a max-heap.
2. For each of the k seconds, extract the maximum element from the heap.
3. Calculate the new number of gifts as the floor of the square root of the maximum.
4. Insert the new value back into the heap.
5. After k seconds, sum up all the remaining gifts in the heap.

This approach ensures we always operate on the pile with the maximum gifts efficiently.

Code Solutions