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2064. Minimized Maximum of Products Distributed to Any Store

Difficulty Topics

Description

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

Solution

minimized-maximum-of-products-distributed-to-any-store.py
class Solution:
    def minimizedMaximum(self, n: int, quantities: List[int]) -> int:
        total = sum(quantities)

        def good(x):
            return sum(ceil(quantity / x) for quantity in quantities) <= n

        left, right = 1, max(quantities)

        while left < right:
            mid = left + (right - left) // 2
            x = good(mid)

            if x:
                right = mid
            else:
                left = mid + 1

        return left