minimized-maximum-of-products-distributed-to-any-store

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Algorithms

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

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

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

Return the minimum possible <code>x</code>.

&nbsp;
Example 1:

<pre>
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.
</pre>

Example 2:

<pre>
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.
</pre>

Example 3:

<pre>
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.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>m == quantities.length</code></li>
	<li><code>1 &lt;= m &lt;= n &lt;= 105</code></li>
	<li><code>1 &lt;= quantities[i] &lt;= 105</code></li>
</ul>

minimizedMaximum

Minimized Maximum of Products Distributed to Any Store

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Greedy

Array

Binary Search

给你一个整数&nbsp;<code>n</code>&nbsp;，表示有&nbsp;<code>n</code>&nbsp;间零售商店。总共有&nbsp;<code>m</code>&nbsp;种产品，每种产品的数目用一个下标从 0&nbsp;开始的整数数组&nbsp;<code>quantities</code>&nbsp;表示，其中&nbsp;<code>quantities[i]</code>&nbsp;表示第&nbsp;<code>i</code>&nbsp;种商品的数目。

你需要将 所有商品&nbsp;分配到零售商店，并遵守这些规则：

<ul>
	<li>一间商店 至多&nbsp;只能有 一种商品 ，但一间商店拥有的商品数目可以为&nbsp;任意&nbsp;件。</li>
	<li>分配后，每间商店都会被分配一定数目的商品（可能为 <code>0</code>&nbsp;件）。用&nbsp;<code>x</code>&nbsp;表示所有商店中分配商品数目的最大值，你希望 <code>x</code>&nbsp;越小越好。也就是说，你想 最小化&nbsp;分配给任意商店商品数目的 最大值&nbsp;。</li>
</ul>

请你返回最小的可能的&nbsp;<code>x</code>&nbsp;。

&nbsp;

示例 1：

<pre>
输入：n = 6, quantities = [11,6]
输出：3
解释： 一种最优方案为：
- 11 件种类为 0 的商品被分配到前 4 间商店，分配数目分别为：2，3，3，3 。
- 6 件种类为 1 的商品被分配到另外 2 间商店，分配数目分别为：3，3 。
分配给所有商店的最大商品数目为 max(2, 3, 3, 3, 3, 3) = 3 。
</pre>

示例 2：

<pre>
输入：n = 7, quantities = [15,10,10]
输出：5
解释：一种最优方案为：
- 15 件种类为 0 的商品被分配到前 3 间商店，分配数目为：5，5，5 。
- 10 件种类为 1 的商品被分配到接下来 2 间商店，数目为：5，5 。
- 10 件种类为 2 的商品被分配到最后 2 间商店，数目为：5，5 。
分配给所有商店的最大商品数目为 max(5, 5, 5, 5, 5, 5, 5) = 5 。
</pre>

示例 3：

<pre>
输入：n = 1, quantities = [100000]
输出：100000
解释：唯一一种最优方案为：
- 所有 100000 件商品 0 都分配到唯一的商店中。
分配给所有商店的最大商品数目为 max(100000) = 100000 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>m == quantities.length</code></li>
	<li><code>1 &lt;= m &lt;= n &lt;= 105</code></li>
	<li><code>1 &lt;= quantities[i] &lt;= 105</code></li>
</ul>