What is the time complexity of Maximum Number of Balls in a Box?

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

What data structures are used to solve Maximum Number of Balls in a Box?

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

What are the key insights for solving Maximum Number of Balls in a Box?

Insight 1: The sum of digits of a number can be efficiently calculated using modular arithmetic and integer division. Insight 2: A hash table (or array in this case) is ideal for counting the frequency of balls in each box. Using a hash map avoids the need to iterate through all possible box numbers.

Which companies ask LeetCode 1742. Maximum Number of Balls in a Box in interviews?

This problem is frequently asked at AppDynamics, Lucid.

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Maximum Number of Balls in a Box - LeetCode 1742 Solution

Maximum Number of Balls in a Box - Complete Solution Guide

Maximum Number of Balls in a Box is LeetCode problem 1742, 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 working in a ball factory where you have n balls numbered from lowLimit up to highLimit inclusive (i.e., n == highLimit - lowLimit + 1 ), and an infinite number of boxes numbered from 1 to infinity . Your job at this factory is to put each ball in the box with a number equal to the sum of digits of the ball's number. For example, the ball number 321 will be put in the box number 3 + 2 + 1 = 6 and the ball number 10 will be put in the box number 1 + 0 = 1 . Given two integers lowLimit and

Detailed Explanation

The problem asks you to determine the maximum number of balls that end up in the same box. Balls are numbered sequentially from `lowLimit` to `highLimit` (inclusive). Each ball is placed into a box whose number is the sum of the digits of the ball's number. The goal is to find the box with the most balls.

Solution Approach

The solution iterates through each ball number from `lowLimit` to `highLimit`. For each ball, it calculates the sum of its digits and increments the count for the corresponding box in a frequency array. Finally, it finds the maximum value in the frequency array, which represents the maximum number of balls in any single box.

Step-by-Step Algorithm

Step 1: Initialize an integer array `counts` of size 46 (maximum possible sum of digits is 45) to store the number of balls in each box. Initialize all values to 0.
Step 2: Iterate from `lowLimit` to `highLimit` (inclusive). For each number `i`:
Step 3: Calculate the sum of the digits of `i` using modular arithmetic and integer division (repeatedly taking the modulo 10 and dividing by 10).
Step 4: Increment the count in the `counts` array at the index corresponding to the digit sum. For example, `counts[digitSum]`++
Step 5: Keep track of the `maxCount` (the maximum value encountered in `counts` array so far).
Step 6: After iterating through all numbers, return `maxCount`.

Key Insights

Insight 1: The sum of digits of a number can be efficiently calculated using modular arithmetic and integer division.
Insight 2: A hash table (or array in this case) is ideal for counting the frequency of balls in each box. Using a hash map avoids the need to iterate through all possible box numbers.
Insight 3: The maximum sum of digits for a number between 1 and 10^5 is 9 * 5 = 45; hence, a fixed-size array can be used for counting instead of a dynamically resizing hash map.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Hash Table, Math, Counting.

Companies

Asked at: AppDynamics, Lucid.

Maximum Number of Balls in a Box | LeetCode 1742

Easy

Hash Table Math Counting

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

Solution Code

Available in:

class Solution {
    public int countBalls(int lowLimit, int highLimit) {
        int[] counts = new int[46];
        int maxCount = 0;
        for (int i = lowLimit; i <= highLimit; i++) {
            int sum = 0;
            int num = i;
            while (num > 0) {
                sum += num % 10;
                num /= 10;
            }
            counts[sum]++;
            maxCount = Math.max(maxCount, counts[sum]);
        }
        return maxCount;
    }
}

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Problem Info

Description

Problem 1742: Maximum Number of Balls in a Box - Detailed explanation and solution approaches.

Topics

Hash Table Math Counting

Companies

AppDynamicsLucid

Stats

Difficulty:Easy

Languages:4

Companies:2

Problem #:1742

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: Initialize an integer array `counts` of size 46 (maximum possible sum of digits is 45) to store the number of balls in each box. Initialize all values to 0.
2
Step 2: Iterate from `lowLimit` to `highLimit` (inclusive). For each number `i`:
3
Step 3: Calculate the sum of the digits of `i` using modular arithmetic and integer division (repeatedly taking the modulo 10 and dividing by 10).
4
Step 4: Increment the count in the `counts` array at the index corresponding to the digit sum. For example, `counts[digitSum]`++
5
Step 5: Keep track of the `maxCount` (the maximum value encountered in `counts` array so far).
6
Step 6: After iterating through all numbers, return `maxCount`.

💡

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(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The space used is dominated by the `counts` array, which has a fixed size of 46. The size is independent of the input size `n` therefore the space complexity is constant. Other variables use constant space.

📖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

Using a HashMap

Instead of a fixed-size array, use a HashMap to store the counts. This avoids the need to pre-determine the maximum sum of digits but uses more memory.

Time: O(n * k), where n is the number of balls and k is the average number of digits in a ball number. Similar to O(n).Space: O(n) in the worst case (all balls fall in distinct boxes).

Trade-offs: Use a HashMap if the input range is significantly larger or if you're unsure about the maximum possible sum of digits. Use an array for better space efficiency and speed if you know the maximum sum of digits is bounded.

✨

Key Insights

1Insight 1: The sum of digits of a number can be efficiently calculated using modular arithmetic and integer division.
2Insight 2: A hash table (or array in this case) is ideal for counting the frequency of balls in each box. Using a hash map avoids the need to iterate through all possible box numbers.
3Insight 3: The maximum sum of digits for a number between 1 and 10^5 is 9 * 5 = 45; hence, a fixed-size array can be used for counting instead of a dynamically resizing hash map.

📚

Key Terms Explained

For Students

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Edge Cases

Edge case 1: `lowLimit` and `highLimit` are the same. The solution correctly handles this by iterating only once. The `maxCount` will be 1.
Edge case 2: All balls end up in the same box. The solution will correctly report the total number of balls as `maxCount`.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly calculating the sum of digits. Forgetting to handle numbers with only one digit.

✗Common mistake 2: Not considering the case where `lowLimit` equals `highLimit`, leading to incorrect `maxCount` calculations.

✗Common mistake 3: Using a hashmap unnecessarily and failing to optimize for space complexity.

✅

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: Analyzing sales data where each item has a unique ID, and the IDs are grouped based on the sum of their digits for reporting purposes.

🏦Real-world scenario 2: Distributing tasks or resources based on some characteristic of the task or resource ID, where the sum of digits acts as a grouping or routing key.

💡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

Hash tables trade space for time. Before using one, consider if the problem constraints allow the extra memory. In interviews, always mention this trade-off.

🎯 Interview Tip

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

⚠️ Watch Out

Don't forget to handle key collisions and null/undefined keys. Consider what happens with duplicate 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: October 1, 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

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

@InterviewProJul 14

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

@CodeNinjaJul 7

❓

Frequently Asked Questions

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

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 "Maximum Number of Balls in a Box"?

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

🤖 Need help with this problem?