[LeetCode] 2064. Minimized Maximum of Products Distributed to Any Store

CNoodle發表於2024-11-14
LeetCodeZed

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

分配給商店的最多商品的最小值。

給你一個整數 n ，表示有 n 間零售商店。總共有 m 種產品，每種產品的數目用一個下標從 0 開始的整數陣列 quantities 表示，其中 quantities[i] 表示第 i 種商品的數目。

你需要將 所有商品 分配到零售商店，並遵守這些規則：

  • 一間商店 至多 只能有 一種商品 ，但一間商店擁有的商品數目可以為 任意 件。
  • 分配後，每間商店都會被分配一定數目的商品（可能為 0 件）。用 x 表示所有商店中分配商品數目的最大值，你希望 x 越小越好。也就是說，你想 最小化 分配給任意商店商品數目的 最大值 。

請你返回最小的可能的 x 。

思路

思路是二分法，而且是有點類似875題那種在答案上二分的題目。題目是請我們把 m 種商品分配到 n 個商店裡且需要儘量讓每個商店分配商品數目的最大值越小越好。所以我們在做二分找 mid 的時候，mid 的意思是每個商店需要放多少件商品。如果按照 mid 的個數分配商品需要的商店個數 > n，則把 mid 改小；反之則把 mid 改大。

注意程式碼中 count 的計算方式，因為是計算需要的商店個數所以需要向上取整。

複雜度

時間O(nlogn)
空間O(1)

程式碼

Java實現

class Solution {
    public int minimizedMaximum(int n, int[] quantities) {
        int left = 1;
        int right = 100000;
        while (left < right) {
            int mid = left + (right - left) / 2;
            int count = 0;
            for (int q : quantities) {
                // count += (q + mid - 1) / mid;
                count += q / mid;
                if (q % mid != 0) {
                    count++;
                }
            }
            if (count > n) {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        return left;
    }
}

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