What is the time complexity of Distribute Candies Among Children I?

The optimal solution has a time complexity of O(limit^2).

What data structures are used to solve Distribute Candies Among Children I?

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

What are the key insights for solving Distribute Candies Among Children I?

Insight 1: The problem can be solved using a three-nested loop approach (although this is not the most efficient approach for larger numbers). Each loop represents the number of candies given to one child. Insight 2: The constraints (no child gets more than 'limit' candies) are crucial and need to be checked in each iteration.

Which companies ask LeetCode 2928. Distribute Candies Among Children I in interviews?

This problem is frequently asked at Rubrik.

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Distribute Candies Among Children I - LeetCode 2928 Solution

Distribute Candies Among Children I - Complete Solution Guide

Distribute Candies Among Children I is LeetCode problem 2928, 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 two positive integers n and limit . Return the total number of ways to distribute n candies among 3 children such that no child gets more than limit candies. Example 1: Input: n = 5, limit = 2 Output: 3 Explanation: There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1). Example 2: Input: n = 3, limit = 3 Output: 10 Explanation: There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0

Detailed Explanation

The problem asks you to find the total number of ways to distribute 'n' candies among 3 children, with the constraint that no child receives more than 'limit' candies. The input consists of two positive integers: 'n' (the total number of candies) and 'limit' (the maximum number of candies a child can receive). The output is a single integer representing the total number of valid distributions.

Solution Approach

The provided solution uses a brute-force approach with three nested loops. The outer two loops iterate through all possible combinations of candies for the first two children (up to the 'limit'). The inner loop calculates the remaining candies for the third child and verifies if it also satisfies the limit constraint. If all constraints are met, the count of valid distributions is incremented.

Step-by-Step Algorithm

Step 1: Initialize a counter 'count' to 0. This will store the total number of valid distributions.
Step 2: Iterate through all possible numbers of candies for the first child ('i') from 0 to 'limit'.
Step 3: For each value of 'i', iterate through all possible numbers of candies for the second child ('j') from 0 to 'limit'.
Step 4: Calculate the number of candies remaining for the third child ('k') as n - i - j.
Step 5: Check if 'k' is within the valid range (0 <= k <= limit).
Step 6: If 'k' is within the valid range, increment the 'count'.
Step 7: After all iterations, return the final 'count'.

Key Insights

Insight 1: The problem can be solved using a three-nested loop approach (although this is not the most efficient approach for larger numbers). Each loop represents the number of candies given to one child.
Insight 2: The constraints (no child gets more than 'limit' candies) are crucial and need to be checked in each iteration.
Insight 3: A brute-force approach is sufficient given the small constraints (1 <= n <= 50, 1 <= limit <= 50). More efficient algorithms are possible but unnecessary for this problem.

Complexity Analysis

Time Complexity: O(limit^2)

Space Complexity: O(1)

Topics

This problem involves: Math, Combinatorics, Enumeration.

Companies

Asked at: Rubrik.

Distribute Candies Among Children I | LeetCode 2928

Easy

Math Combinatorics Enumeration

Time: O(limit^2)Space: O(1)

Solution Code

Available in:

class Solution {
    public int distributeCandies(int n, int limit) {
        int count = 0;
        for (int i = 0; i <= limit; i++) {
            for (int j = 0; j <= limit; j++) {
                int k = n - i - j;
                if (k >= 0 && k <= limit) {
                    count++;
                }
            }
        }
        return count;
    }
}

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Problem Info

Description

Problem 2928: Distribute Candies Among Children I - Detailed explanation and solution approaches.

Topics

Math Combinatorics Enumeration

Companies

Rubrik

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2928

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

7 steps

1
Step 1: Initialize a counter 'count' to 0. This will store the total number of valid distributions.
2
Step 2: Iterate through all possible numbers of candies for the first child ('i') from 0 to 'limit'.
3
Step 3: For each value of 'i', iterate through all possible numbers of candies for the second child ('j') from 0 to 'limit'.
4
Step 4: Calculate the number of candies remaining for the third child ('k') as n - i - j.
5
Step 5: Check if 'k' is within the valid range (0 <= k <= limit).
6
Step 6: If 'k' is within the valid range, increment the 'count'.
7
Step 7: After all iterations, return the final 'count'.

💡

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(limit^2)

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(limit^2) because the outer two loops iterate from 0 to 'limit' resulting in approximately limit*limit iterations. The space complexity is O(1) because only a constant amount of extra space is used to store variables like 'count', 'i', 'j', and 'k'.

📖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

Dynamic Programming

A dynamic programming solution could potentially be more efficient for larger values of n and limit, although it adds complexity.

Time: O(n*limit)Space: O(n*limit)

Trade-offs: Dynamic programming provides better performance for larger inputs, but adds code complexity and requires more space.

✨

Key Insights

1Insight 1: The problem can be solved using a three-nested loop approach (although this is not the most efficient approach for larger numbers). Each loop represents the number of candies given to one child.
2Insight 2: The constraints (no child gets more than 'limit' candies) are crucial and need to be checked in each iteration.
3Insight 3: A brute-force approach is sufficient given the small constraints (1 <= n <= 50, 1 <= limit <= 50). More efficient algorithms are possible but unnecessary for this problem.

📚

Key Terms Explained

For Students

Edge Cases

Edge case 1: When n is 0. The solution correctly handles this; it will only count (0,0,0) as the only valid distribution.
Edge case 2: When limit is less than n/3. The solution correctly accounts for this by only considering valid combinations where the sum of candies is less than or equal to n.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to check the constraint that the third child's candies also doesn't exceed 'limit'.

✗Common mistake 2: Off-by-one errors in loop boundaries. Incorrectly using < instead of <= (or vice-versa) when looping from 0 to limit.

✅

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 (like budget, time, or personnel) among different projects or teams, with constraints on the maximum resource allocation for each.

🏦Real-world scenario 2: Combinatorial problems in logistics. Determining the number of ways to distribute packages to different delivery locations, given vehicle capacity constraints.

💡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

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ 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: July 19, 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

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 "Distribute Candies Among Children I"?

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 combinatorics techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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