What is the time complexity of Distribute Money to Maximum Children?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Distribute Money to Maximum Children?

This problem uses Math, Greedy. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Distribute Money to Maximum Children?

Insight 1: The problem can be solved greedily by first giving each child 1 dollar, then trying to give as many children as possible 8 dollars. Insight 2: After distributing 1 dollar to each child, the remaining money can be efficiently used to determine the maximum number of children receiving 8 dollars.

Which companies ask LeetCode 2591. Distribute Money to Maximum Children in interviews?

This problem is frequently asked at Zendesk.

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Distribute Money to Maximum Children - LeetCode 2591 Solution

Distribute Money to Maximum Children - Complete Solution Guide

Distribute Money to Maximum Children is LeetCode problem 2591, 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 money denoting the amount of money (in dollars) that you have and another integer children denoting the number of children that you must distribute the money to. You have to distribute the money according to the following rules: All money must be distributed. Everyone must receive at least 1 dollar. Nobody receives 4 dollars. Return the maximum number of children who may receive exactly 8 dollars if you distribute the money according to the aforementioned rules . If ther

Detailed Explanation

The problem asks to find the maximum number of children who can receive exactly 8 dollars when distributing a given amount of `money` among `children`. Each child must receive at least 1 dollar, all money must be distributed, and no child can receive exactly 4 dollars. The input consists of two integers: `money` (the total amount of money) and `children` (the number of children). The output is an integer representing the maximum number of children who can receive 8 dollars, or -1 if it's impossible to distribute the money according to the rules.

Solution Approach

The solution uses a greedy approach. It first ensures there's enough money to give each child at least 1 dollar. Then, it subtracts the initial 1 dollar from the total money for each child. The remaining money is then used to give as many children as possible 8 dollars. Finally, it handles edge cases where there might be remaining money that can't be distributed without violating the rules (e.g., a child receiving 4 dollars).

Step-by-Step Algorithm

Step 1: Check if there's enough money to give each child at least 1 dollar. If not, return -1.
Step 2: Subtract 1 dollar from the total money for each child. This represents the minimum distribution.
Step 3: Calculate the maximum number of children who can receive 8 dollars using integer division (`money // 8`).
Step 4: Update the remaining money after giving 8 dollars to the calculated number of children.
Step 5: Handle edge cases: If there are no children left or the remaining money is such that a child would receive 4 dollars, adjust the count of children receiving 8 dollars.
Step 6: Return the final count of children receiving 8 dollars.

Key Insights

Insight 1: The problem can be solved greedily by first giving each child 1 dollar, then trying to give as many children as possible 8 dollars.
Insight 2: After distributing 1 dollar to each child, the remaining money can be efficiently used to determine the maximum number of children receiving 8 dollars.
Insight 3: Edge cases need to be handled carefully, such as when there's not enough money to distribute or when the remaining money after giving out eights results in a child receiving 4 dollars.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(1)

Topics

This problem involves: Math, Greedy.

Companies

Asked at: Zendesk.

Distribute Money to Maximum Children | LeetCode 2591

Easy

Math Greedy

Time: O(1)Space: O(1)

Solution Code

Available in:

class Solution {
    public int distMoney(int money, int children) {
        if (money < children) return -1;
        money -= children;
        int count8 = Math.min(money / 8, children);
        money -= count8 * 8;
        if (money == 0) return count8;
        if (money < children - count8) return -1;
        if (count8 == children) return count8 -1;
        
        return count8;

    }
}

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Problem Info

Description

Problem 2591: Distribute Money to Maximum Children - Detailed explanation and solution approaches.

Topics

Math Greedy

Companies

Zendesk

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2591

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: Check if there's enough money to give each child at least 1 dollar. If not, return -1.
2
Step 2: Subtract 1 dollar from the total money for each child. This represents the minimum distribution.
3
Step 3: Calculate the maximum number of children who can receive 8 dollars using integer division (`money // 8`).
4
Step 4: Update the remaining money after giving 8 dollars to the calculated number of children.
5
Step 5: Handle edge cases: If there are no children left or the remaining money is such that a child would receive 4 dollars, adjust the count of children receiving 8 dollars.
6
Step 6: Return the final count of children receiving 8 dollars.

💡

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(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The algorithm involves a fixed number of arithmetic operations. The number of operations does not depend on the input size. Therefore, both time and space complexity are constant.

📖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

Iterative Approach

Iterate through possible numbers of children receiving 8 dollars, checking for feasibility at each step. This is less efficient but more explicit.

Time: O(children)Space: O(1)

Trade-offs: Less efficient than the greedy approach, but might be easier to understand for beginners. The greedy approach is preferred for its efficiency.

✨

Key Insights

1Insight 1: The problem can be solved greedily by first giving each child 1 dollar, then trying to give as many children as possible 8 dollars.
2Insight 2: After distributing 1 dollar to each child, the remaining money can be efficiently used to determine the maximum number of children receiving 8 dollars.
3Insight 3: Edge cases need to be handled carefully, such as when there's not enough money to distribute or when the remaining money after giving out eights results in a child receiving 4 dollars.

📚

Key Terms Explained

For Students

Greedy Algorithm

Making the best choice at each step without looking ahead.

Edge Cases

Edge case 1: `money < children`: There is not enough money to give each child at least 1 dollar. The solution correctly returns -1.
Edge case 2: `children == 1 and money == 3`: In this edge case, after giving 1 dollar to the child, 2 dollars are left which isn't enough to satisfy 8 dollars requirement, nor can it be distributed to follow the rules. This edge case should be checked as it can negatively impact the final result.
Edge case 3: After giving out as many 8s as possible, there might be some remainder which, when distributed, can create a situation where a child receives 4 dollars. The solution needs to account for this.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Failing to handle the edge case where there isn't enough money to give each child at least 1 dollar.

✗Common mistake 2: Not considering the constraint that no child can receive exactly 4 dollars. Incorrectly distributing the remaining money can lead to wrong answers.

✗Common mistake 3: Not considering cases where after giving as many 8's as possible, remaining amount can be only used to give some of the children more than 1 dollar while leaving some children with 1 dollar.

✅

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 – distributing limited resources (e.g., budget, time) among multiple projects or individuals, with constraints on minimum and maximum allocations.

🏦Real-world scenario 2: Fair division problems – dividing assets or tasks fairly among participants, with certain restrictions on individual shares.

💡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

Always test your solution with edge cases: empty input, single element, and boundary values.

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: August 11, 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

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 13

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 6

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

@CodeNinjaJun 29

❓

Frequently Asked Questions

What are common greedy problem patterns?

Activity selection (sort by end time), interval scheduling (sort by start/end), Huffman coding (always combine smallest), fractional knapsack (sort by value/weight ratio), and minimum spanning tree. Look for problems where local decisions don't affect future options.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Distribute Money to Maximum Children"?

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

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