How do you solve Take Gifts From the Richest Pile on LeetCode?

Take Gifts From the Richest Pile (LeetCode #2558) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n + k log n) time complexity and O(n) space complexity. Key insight: Using a max-heap allows for efficient retrieval and updating of the maximum gifts pile.

What is the time complexity of Take Gifts From the Richest Pile?

The optimal solution for Take Gifts From the Richest Pile runs in O(n log n + k log n) time and uses O(n) space. The initial heap creation takes O(n log n), and each of the k operations takes O(log n). Thus, the overall complexity is dominated by O(n log n).

What is the brute force solution for Take Gifts From the Richest Pile?

The brute force approach for Take Gifts From the Richest Pile is Brute Force, with O(n²) time complexity and O(1) space complexity. In this approach, we repeatedly find the maximum pile of gifts and reduce it until we've done this k times. This is straightforward but inefficient as we may need to scan the entire array multiple times. The optimal Optimal Solution approach improves this to O(n log n + k log n).

What algorithm or data structure is used to solve Take Gifts From the Richest Pile?

Take Gifts From the Richest Pile uses the following concepts: Array, Heap (Priority Queue), Simulation. The recommended patterns to study are: Heap, Array.

What are the interview tips for Take Gifts From the Richest Pile?

Discuss your thought process clearly; explain why you choose a particular data structure. Consider edge cases, such as when all piles are equal or minimal. Practice explaining your code as you write it, as this mimics the interview environment.

What are common mistakes when solving Take Gifts From the Richest Pile?

Not using a heap when the problem involves repeatedly finding maximums or minimums. Forgetting to floor the square root when updating the gift counts.

#2558

Take Gifts From the Richest Pile

Easy

ArrayHeap (Priority Queue)SimulationHeapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n + k log n)
Space	O(1)	O(n)

💡

Intuition

Time O(n log n + k log n)Space O(n)

Using a max-heap (priority queue) allows us to efficiently retrieve and update the pile with the maximum gifts in logarithmic time. This significantly reduces the number of operations needed.

⚙️

Algorithm

3 steps

1Step 1: Create a max-heap from the gifts array.
2Step 2: For k seconds, extract the maximum pile, compute its square root, and push it back into the heap.
3Step 3: After k seconds, sum all remaining gifts in the heap.

solution.py9 lines

1import heapq
2
3def remainingGifts(gifts, k):
4    max_heap = [-gift for gift in gifts]
5    heapq.heapify(max_heap)
6    for _ in range(k):
7        max_gift = -heapq.heappop(max_heap)
8        heapq.heappush(max_heap, -int(max_gift ** 0.5))
9    return -sum(max_heap)

ℹ

Complexity note: The initial heap creation takes O(n log n), and each of the k operations takes O(log n). Thus, the overall complexity is dominated by O(n log n).

1Using a max-heap allows for efficient retrieval and updating of the maximum gifts pile.
2Understanding how to manipulate heaps is crucial for optimizing problems involving maximum or minimum values.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.