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

The optimal solution has a time complexity of O(k*log(n)).

What data structures are used to solve Take Gifts From the Richest Pile?

This problem uses Array, Heap (Priority Queue), Simulation. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Take Gifts From the Richest Pile?

Insight 1: Using a priority queue (heap) is crucial for efficiently finding and updating the pile with the maximum number of gifts in each iteration. A simple linear scan would lead to O(n) time complexity per iteration, resulting in a total time complexity of O(nk), which is less efficient. Insight 2: The problem inherently involves iterative reduction and selection of the maximum element, which is a classic use case for a priority queue. The `heapq` module (Python) or `PriorityQueue` (Java, C++) provides the necessary functionality for this task.

Which companies ask LeetCode 2558. Take Gifts From the Richest Pile in interviews?

This problem is frequently asked at DE Shaw.

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Take Gifts From the Richest Pile - LeetCode 2558 Solution

Take Gifts From the Richest Pile - Complete Solution Guide

Take Gifts From the Richest Pile is LeetCode problem 2558, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

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. Example 1: Input: gifts = [25,64,9,4,100], k = 4 Output: 29 Explanation: The gifts

Detailed Explanation

The problem asks you to simulate a process of taking gifts from piles. You have several piles of gifts, each represented by a number in the `gifts` array. Every second, you select the pile with the maximum number of gifts and reduce the number of gifts in that pile to the floor of its square root. This process is repeated `k` times. Finally, the problem requires you to return the total number of gifts remaining after `k` seconds.

Solution Approach

The provided solutions use a priority queue (max-heap) to efficiently manage the piles of gifts. Initially, all the gift counts are added to the heap. In each iteration, the maximum element (pile) is extracted, its square root is calculated, and the result (new gift count) is pushed back into the heap. This continues for `k` iterations. Finally, the sum of all remaining elements in the heap is returned as the total number of gifts.

Step-by-Step Algorithm

Step 1: Create a max-heap (priority queue) and add all the gift counts from the `gifts` array.
Step 2: Iterate `k` times. In each iteration:
Step 2.1: Extract the maximum element (pile) from the heap.
Step 2.2: Calculate the floor of the square root of the extracted element.
Step 2.3: Insert the result (new gift count) back into the heap.
Step 3: After `k` iterations, sum up all the elements (remaining gift counts) in the heap and return the sum.

Key Insights

Insight 1: Using a priority queue (heap) is crucial for efficiently finding and updating the pile with the maximum number of gifts in each iteration. A simple linear scan would lead to O(n) time complexity per iteration, resulting in a total time complexity of O(nk), which is less efficient.
Insight 2: The problem inherently involves iterative reduction and selection of the maximum element, which is a classic use case for a priority queue. The `heapq` module (Python) or `PriorityQueue` (Java, C++) provides the necessary functionality for this task.
Insight 3: Handling the case where all piles have the same value (or very similar values near the end) is important. The solution needs to correctly handle this without causing any infinite loops or incorrect calculations.

Complexity Analysis

Time Complexity: O(k*log(n))

Space Complexity: O(n)

Topics

This problem involves: Array, Heap (Priority Queue), Simulation.

Companies

Asked at: DE Shaw.

Take Gifts From the Richest Pile | LeetCode 2558

Easy

Array Heap (Priority Queue)Simulation

Time: O(k*log(n))Space: O(n)

Solution Code

Available in:

class Solution {
    public long pickGifts(int[] gifts, int k) {
        PriorityQueue<Long> pq = new PriorityQueue<>(Collections.reverseOrder());
        for (int gift : gifts) {
            pq.offer((long) gift);
        }
        for (int i = 0; i < k; i++) {
            long curr = pq.poll();
            long next = (long) Math.floor(Math.sqrt(curr));
            pq.offer(next);
        }
        long sum = 0;
        while (!pq.isEmpty()) {
            sum += pq.poll();
        }
        return sum;
    }
}

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Problem Info

Description

Problem 2558: Take Gifts From the Richest Pile - Detailed explanation and solution approaches.

Topics

Array Heap (Priority Queue)Simulation

Companies

DE Shaw

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2558

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

6 steps

1
Step 1: Create a max-heap (priority queue) and add all the gift counts from the `gifts` array.
2
Step 2: Iterate `k` times. In each iteration:
3
Step 2.1: Extract the maximum element (pile) from the heap.
4
Step 2.2: Calculate the floor of the square root of the extracted element.
5
Step 2.3: Insert the result (new gift count) back into the heap.
6
Step 3: After `k` iterations, sum up all the elements (remaining gift counts) in the heap and return the sum.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(k*log(n))

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The heap operations (insertion and extraction) take O(log n) time, where n is the number of piles. We perform these operations `k` times. Therefore, the overall time complexity is O(k log n). The space complexity is O(n) because we store all the gift counts in the heap.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Sorting-based approach

Sort the `gifts` array in descending order. Iterate `k` times, taking the square root of the largest element and re-sorting. This is less efficient than the heap-based approach.

Time: O(k * n log n)Space: O(n)

Trade-offs: This approach is less efficient due to the repeated sorting. The heap-based approach is preferred for its better time complexity, especially when `k` is large.

✨

Key Insights

1Insight 1: Using a priority queue (heap) is crucial for efficiently finding and updating the pile with the maximum number of gifts in each iteration. A simple linear scan would lead to O(n) time complexity per iteration, resulting in a total time complexity of O(nk), which is less efficient.
2Insight 2: The problem inherently involves iterative reduction and selection of the maximum element, which is a classic use case for a priority queue. The `heapq` module (Python) or `PriorityQueue` (Java, C++) provides the necessary functionality for this task.
3Insight 3: Handling the case where all piles have the same value (or very similar values near the end) is important. The solution needs to correctly handle this without causing any infinite loops or incorrect calculations.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Edge case 1: If k is larger than the number of iterations needed to reduce all elements to 1, the algorithm still functions correctly because repeatedly taking the square root of 1 will continue to produce 1. The heap will still be processed k times.
Edge case 2: If `gifts` array is empty, the code should either handle this gracefully (returning 0) or be modified to explicitly check for this case before proceeding. The provided solutions implicitly handle this correctly by starting the heap with no elements.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not using a priority queue (heap) and instead using a simple linear scan to find the maximum element in each iteration. This leads to O(nk) time complexity, which is significantly slower.

✗Common mistake 2: Forgetting to handle the case where the square root calculation results in a floating-point number. The problem explicitly states to use the floor of the square root, so proper casting or flooring is necessary.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Resource allocation. Imagine you have multiple tasks with varying resource requirements. You want to allocate resources iteratively, prioritizing the tasks with the highest resource needs. Each iteration might involve reducing the requirement based on some function (like square root here).

🏦Real-world scenario 2: Game development. You might simulate a scenario where players collect resources from multiple sources, and the rate of resource collection decreases based on the current amount (maybe the square root). This algorithm helps to simulate the decreasing returns of resource collection.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: July 9, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 13

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Take Gifts From the Richest Pile"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether heap (priority queue) techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?