You are given a collection of numbered balls and instructed to sort them into boxes for a nearly balanced distribution. There are two rules you must follow:
Return the fewest number of boxes to sort these balls following these rules.
Example 1:
Input: balls = [3,2,3,2,3]
Output: 2
Explanation:
We can sort balls into boxes as follows:
[3,3,3][2,2]The size difference between the two boxes doesn't exceed one.
Example 2:
Input: balls = [10,10,10,3,1,1]
Output: 4
Explanation:
We can sort balls into boxes as follows:
[10][10,10][3][1,1]You can't use fewer than four boxes while still following the rules. For example, putting all three balls numbered 10 in one box would break the rule about the maximum size difference between boxes.
Constraints:
1 <= nums.length <= 1051 <= nums[i] <= 109This approach focuses on counting the frequency of each unique ball type and distributing them into boxes, prioritizing minimizing deviation in box sizes.
In this solution, we calculate the frequency of each ball using a Counter. The number of boxes is determined by the highest frequency of any single ball number. This ensures that while distributing, the max box count rule is maintained, as any imbalance would require fewer max frequency boxes than needed.
Java
Time Complexity: O(n), where n is the number of balls.
Space Complexity: O(n), storing the frequency count.
This approach works by first computing the frequency of each ball type, then attempts to distribute the balls such that the resulting box configuration is balanced as specified.
The C++ solution uses an unordered_map to track ball frequency and computes the number of required boxes by determining the maximum frequency. This ensures a nearly uniform distribution.
C#
Time Complexity: O(n), where n is the number of balls.
Space Complexity: O(n) for the frequency map.
| Approach | Complexity |
|---|---|
| Greedy Distribution Based on Frequency | Time Complexity: O(n), where n is the number of balls. |
| Balancing Frequency Distributions | Time Complexity: O(n), where n is the number of balls. |
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