Leetcode #1742: Maximum Number of Balls in a Box
In this guide, we solve Leetcode #1742 Maximum Number of Balls in a Box in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Hash Table, Math, Counting
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: lowLimit = 1, highLimit = 10
Output: 2
Explanation:
Box Number: 1 2 3 4 5 6 7 8 9 10 11 ...
Ball Count: 2 1 1 1 1 1 1 1 1 0 0 ...
Box 1 has the most number of balls with 2 balls.
Python Solution
class Solution:
def countBalls(self, lowLimit: int, highLimit: int) -> int:
cnt = [0] * 50
for x in range(lowLimit, highLimit + 1):
y = 0
while x:
y += x % 10
x //= 10
cnt[y] += 1
return max(cnt)
Complexity
The time complexity is . The space complexity is O(n).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.