Take Gifts From the Richest Pile

Take Gifts From the Richest Pile

What is this problem about?

The Take Gifts From the Richest Pile coding problem is a simulation-based challenge that involves managing a set of values over several iterations. You are given an array gifts, where each element represents the number of gifts in a pile. In each of k seconds, you must choose the pile with the most gifts and replace it with its floor-square-root value (i.e., floor(sqrt(pile_value))). Your goal is to return the total number of gifts remaining in all piles after k seconds.

Why is this asked in interviews?

Companies like Amazon, Google, and DE Shaw ask this "Easy" level question to test a candidate's familiarity with priority queues. While the problem can be solved by repeatedly sorting the array, that approach is inefficient for large k and large arrays. Using a Max-Heap is the optimal way to handle "find the largest" operations repeatedly. It evaluates your ability to select the right data structure to optimize a repetitive simulation.

Algorithmic pattern used

The primary algorithmic pattern is the Heap (Priority Queue) interview pattern. Specifically, you use a Max-Heap to store all the gift piles.

1. Push all values from the gifts array into the Max-Heap.
2. For k iterations:
   • Pop the largest value from the heap.
   • Calculate its square root and floor the result.
   • Push the new value back into the heap.
3. Finally, sum all the values remaining in the heap to get the answer.

Example explanation

Piles: [25, 64, 9], k = 2.

• Initial Heap: [64, 25, 9]
• Iteration 1: Pop 64. sqrt(64) = 8. Push 8. Heap: [25, 9, 8]
• Iteration 2: Pop 25. sqrt(25) = 5. Push 5. Heap: [9, 8, 5]
• Total remaining: 9 + 8 + 5 = 22. By using a heap, we always find the richest pile in logarithmic time.

Common mistakes candidates make

A common mistake is using a simple array and sorting it in every iteration, which leads to a time complexity of O(k * n log n). Another error is forgetting to use the "floor" of the square root or handling potential integer overflow if summing very large pile values at the end (though 64-bit integers usually suffice). Some candidates also fail to consider the case where k is larger than the number of piles.

Interview preparation tip

When preparing for the Take Gifts From the Richest Pile interview question, make sure you know how to implement a Max-Heap in your preferred language (e.g., heapq with negative values in Python, or PriorityQueue with a comparator in Java). Understanding when to use a heap vs. a sorted list is a fundamental skill for efficiency-focused coding problems.