What is the time complexity of Count Largest Group?

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

What data structures are used to solve Count Largest Group?

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

What are the key insights for solving Count Largest Group?

Insight 1: The sum of digits of a number can range from 1 (for numbers 1-9) to 36 (for 9999). This limits the number of possible groups. Insight 2: A hash table (or array) can efficiently store and count the number of elements in each group, based on their digit sum.

Which companies ask LeetCode 1399. Count Largest Group in interviews?

This problem is frequently asked at Mercari.

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Count Largest Group - LeetCode 1399 Solution

Count Largest Group - Complete Solution Guide

Count Largest Group is LeetCode problem 1399, 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 n . We need to group the numbers from 1 to n according to the sum of its digits. For example, the numbers 14 and 5 belong to the same group, whereas 13 and 3 belong to different groups. Return the number of groups that have the largest size, i.e. the maximum number of elements. Example 1: Input: n = 13 Output: 4 Explanation: There are 9 groups in total, they are grouped according sum of its digits of numbers from 1 to 13: [1,10], [2,11], [3,12], [4,13], [5], [6], [7], [8

Detailed Explanation

The problem asks to count the number of groups with the largest size, where each group contains numbers from 1 to n that share the same sum of their digits. For example, 14 and 5 belong to the same group because 1+4 = 5. The input is an integer `n`, and the output is the count of groups with the maximum number of elements.

Solution Approach

The solution uses a hash table (dictionary in Python, array in Java/C++) to count the occurrences of each digit sum. It iterates through numbers from 1 to n, calculates the sum of digits for each number, and increments the count for the corresponding digit sum in the hash table. Finally, it iterates through the hash table to find the maximum count and the number of groups having that maximum count.

Step-by-Step Algorithm

Step 1: Initialize a hash table (or array of size 37, since the maximum sum of digits for numbers up to 9999 is 36).
Step 2: Iterate from 1 to n. For each number:
Step 3: Calculate the sum of its digits.
Step 4: Increment the count in the hash table at the index corresponding to the digit sum.
Step 5: After iterating through all numbers, find the maximum count among all entries in the hash table.
Step 6: Iterate through the hash table again and count the number of entries with the maximum count.

Key Insights

Insight 1: The sum of digits of a number can range from 1 (for numbers 1-9) to 36 (for 9999). This limits the number of possible groups.
Insight 2: A hash table (or array) can efficiently store and count the number of elements in each group, based on their digit sum.
Insight 3: After counting group sizes, a single pass is needed to find the maximum group size and the number of groups with that size.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(n)

Topics

This problem involves: Hash Table, Math.

Companies

Asked at: Mercari.

Count Largest Group | LeetCode 1399

Easy

Hash Table Math

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

Solution Code

Available in:

class Solution {
    public int countLargestGroup(int n) {
        int[] count = new int[37];
        int maxCount = 0;
        for (int i = 1; i <= n; i++) {
            int sum = 0;
            int num = i;
            while (num > 0) {
                sum += num % 10;
                num /= 10;
            }
            count[sum]++;
            maxCount = Math.max(maxCount, count[sum]);
        }
        int result = 0;
        for (int i = 1; i < 37; i++) {
            if (count[i] == maxCount) {
                result++;
            }
        }
        return result;
    }
}

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Problem Info

Description

Problem 1399: Count Largest Group - Detailed explanation and solution approaches.

Topics

Hash Table Math

Companies

Mercari

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:1399

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 a hash table (or array of size 37, since the maximum sum of digits for numbers up to 9999 is 36).
2
Step 2: Iterate from 1 to n. For each number:
3
Step 3: Calculate the sum of its digits.
4
Step 4: Increment the count in the hash table at the index corresponding to the digit sum.
5
Step 5: After iterating through all numbers, find the maximum count among all entries in the hash table.
6
Step 6: Iterate through the hash table again and count the number of entries with the maximum 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(n log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is dominated by the loop iterating from 1 to n. Calculating the sum of digits for each number takes O(log n) time in the worst case (for numbers close to n, the number of digits is proportional to log n). The space complexity is O(1) because the hash table size is fixed at 37 regardless of n. The space used by the hash table is 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

Using a sorted array

Calculate digit sums, then sort the sums and count consecutive occurrences of the maximum value.

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

Trade-offs: This approach has a higher space complexity because it stores all digit sums, while the hash table approach uses constant space. However, the sorting step is efficient.

✨

Key Insights

1Insight 1: The sum of digits of a number can range from 1 (for numbers 1-9) to 36 (for 9999). This limits the number of possible groups.
2Insight 2: A hash table (or array) can efficiently store and count the number of elements in each group, based on their digit sum.
3Insight 3: After counting group sizes, a single pass is needed to find the maximum group size and the number of groups with that size.

📚

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: n = 1. The solution correctly handles this by creating a group with size 1 and returning 1.
Edge case 2: n = 9999 (or any large number). The solution efficiently handles this due to the fixed size of the hash table. The time complexity remains O(n log n).

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling the case where multiple groups have the same maximum size. The solution needs to count all groups with the maximum size.

✗Common mistake 2: Incorrect calculation of the sum of digits. Off-by-one errors or using integer division incorrectly might lead to wrong results.

✅

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: Data analysis and categorization. This problem is analogous to grouping data points based on a calculated attribute (digit sum here), then finding the most frequent group.

🏦Real-world scenario 2: Network traffic analysis. Grouping network packets based on some characteristic (e.g., source port sum) and identifying the most frequent group can be useful in anomaly detection.

💡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

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ 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 18, 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

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

@TechLeadJul 13

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 6

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

@AlgoMasterJun 29

❓

Frequently Asked Questions

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

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 "Count Largest Group"?

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.

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