2188 Minimized Maximum Of Products Distributed To Any Store

Minimized Maximum of Products Distributed to Any Store

You are given an integer n indicating there are n specialty retail stores. There are m product types of varying amounts, which are given as a 0-indexed integer array quantities, where quantities[i] represents the number of products of the ith product type.

You need to distribute all products to the retail stores following these rules:

A store can only be given **at most one product type** but can be given **any** amount of it.
After distribution, each store will have been given some number of products (possibly 0). Let x represent the maximum number of products given to any store. You want x to be as small as possible, i.e., you want to **minimize** the **maximum** number of products that are given to any store.

Return the minimum possible x.

 

Example 1:

**Input:** n = 6, quantities = [11,6]
**Output:** 3
**Explanation:** One optimal way is:
- The 11 products of type 0 are distributed to the first four stores in these amounts: 2, 3, 3, 3
- The 6 products of type 1 are distributed to the other two stores in these amounts: 3, 3
The maximum number of products given to any store is max(2, 3, 3, 3, 3, 3) = 3.

Example 2:

**Input:** n = 7, quantities = [15,10,10]
**Output:** 5
**Explanation:** One optimal way is:
- The 15 products of type 0 are distributed to the first three stores in these amounts: 5, 5, 5
- The 10 products of type 1 are distributed to the next two stores in these amounts: 5, 5
- The 10 products of type 2 are distributed to the last two stores in these amounts: 5, 5
The maximum number of products given to any store is max(5, 5, 5, 5, 5, 5, 5) = 5.

Example 3:

**Input:** n = 1, quantities = [100000]
**Output:** 100000
**Explanation:** The only optimal way is:
- The 100000 products of type 0 are distributed to the only store.
The maximum number of products given to any store is max(100000) = 100000.

 

Constraints:

m == quantities.length
1 <= m <= n <= 105
1 <= quantities[i] <= 105

from typing import List
from math import ceil

class Solution:
    def minimizedMaximum(self, n: int, quantities: List[int]) -> int:
        # Binary search to find the minimum possible maximum quantity per store
        left, right = 1, max(quantities)
        
        def canDistribute(maxQuantity: int) -> bool:
            # Calculate the number of stores needed if maxQuantity is the maximum each store can have
            stores_needed = sum(ceil(q / maxQuantity) for q in quantities)
            return stores_needed <= n
        
        while left < right:
            mid = (left + right) // 2
            if canDistribute(mid):
                right = mid  # Try for a smaller maximum
            else:
                left = mid + 1  # Increase the maximum quantity
        
        return left