How do you solve Maximum Number of Balls in a Box on LeetCode?

Maximum Number of Balls in a Box (LeetCode #1742) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The sum of digits for numbers in a specific range can be calculated efficiently using a simple loop.

What is the brute force solution for Maximum Number of Balls in a Box?

The brute force approach for Maximum Number of Balls in a Box is Brute Force, with O(n²) time complexity and O(1) space complexity. We can iterate through each ball number from lowLimit to highLimit, calculate the sum of its digits, and keep track of how many balls go into each box. This is straightforward but not efficient for larger ranges. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Number of Balls in a Box?

Maximum Number of Balls in a Box uses the following concepts: Hash Table, Math, Counting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Maximum Number of Balls in a Box?

Always start with a brute-force solution to understand the problem better. Look for patterns in the problem that can help optimize your solution. Discuss your thought process clearly with the interviewer to show your problem-solving skills.

What are common mistakes when solving Maximum Number of Balls in a Box?

Not considering the maximum possible digit sum when choosing data structures. Overcomplicating the solution by using unnecessary data structures.

#1742

Maximum Number of Balls in a Box

Easy

Hash TableMathCountingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

Instead of using a dictionary, we can use a fixed-size array since the maximum possible digit sum for numbers up to 100,000 is 45 (when all digits are 9). This reduces overhead and improves performance.

⚙️

Algorithm

4 steps

1Step 1: Initialize an array of size 46 (0 to 45) to count balls in boxes.
2Step 2: For each number from lowLimit to highLimit, calculate the sum of its digits.
3Step 3: Increment the count for the corresponding index in the array.
4Step 4: Return the maximum value from the array.

solution.py8 lines

1# Full working Python code
2def countBalls(lowLimit, highLimit):
3    box_count = [0] * 46
4    for num in range(lowLimit, highLimit + 1):
5        digit_sum = sum(int(digit) for digit in str(num))
6        box_count[digit_sum] += 1
7    return max(box_count)
8

ℹ

Complexity note: The time complexity is O(n) because we iterate through each number once and compute the sum of digits in constant time, while the space complexity is O(1) since the array size is fixed at 46.

1The sum of digits for numbers in a specific range can be calculated efficiently using a simple loop.
2Using an array instead of a dictionary for counting can significantly reduce overhead and improve performance.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.