Watch 9 video solutions for Minimum Number of Groups to Create a Valid Assignment, a medium level problem involving Array, Hash Table, Greedy. This walkthrough by Abhinav Awasthi has 2,875 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
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] <= 109Problem Overview: You are given an array of integers and must split elements into groups so that each group contains identical values and the size difference between any two groups is at most 1. The goal is to minimize the total number of groups. Since elements with different values cannot mix, the problem reduces to analyzing the frequency of each value and distributing those counts into valid group sizes.
Approach 1: Greedy Distribution Based on Frequency (O(n + m * k) time, O(m) space)
Start by counting occurrences of each value using a hash map. If a value appears f times, you must split those f elements into groups whose sizes differ by at most 1. The greedy insight is to try the smallest feasible base group size derived from the minimum frequency across all values. For a candidate size k, check whether every frequency f can be expressed using groups of size k or k+1. Iterate possible k values from the minimum frequency downward and compute the required number of groups using integer division. This approach relies heavily on frequency counting via a hash table and a greedy choice that minimizes total groups while keeping group sizes balanced.
Approach 2: Balancing Frequency Distributions (O(n + m * k) time, O(m) space)
This method focuses on balancing the number of groups each frequency contributes. After building a frequency map, you treat each frequency as needing to be decomposed into several nearly equal groups. For a candidate base size x, compute how many groups are required if each group contains either x or x+1 elements. If a frequency cannot be distributed under that constraint, the candidate size is invalid and you try the next smaller size. The balancing step ensures the difference between group sizes never exceeds one. This approach combines ideas from greedy algorithms and counting techniques on arrays to systematically minimize the group count.
Recommended for interviews: The greedy frequency distribution approach is what most interviewers expect. It demonstrates that you can convert the problem into a frequency analysis task and reason about valid group sizes mathematically. A brute-force attempt to simulate group creation shows basic understanding, but the optimized greedy check shows stronger algorithmic insight and clean reasoning about constraints.
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Greedy Distribution Based on Frequency | O(n + m * k) | O(m) | General case; efficient when using frequency counting and testing valid group sizes |
| Balancing Frequency Distributions | O(n + m * k) | O(m) | Useful when reasoning about equalized group sizes and validating distributions mathematically |