leetcode-problemset/leetcode-cn/originData/minimized-maximum-of-products-distributed-to-any-store.json

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        "question": {
            "questionId": "2188",
            "questionFrontendId": "2064",
            "categoryTitle": "Algorithms",
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            "title": "Minimized Maximum of Products Distributed to Any Store",
            "titleSlug": "minimized-maximum-of-products-distributed-to-any-store",
            "content": "<p>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 <strong>0-indexed</strong> integer array <code>quantities</code>, where <code>quantities[i]</code> represents the number of products of the <code>i<sup>th</sup></code> product type.</p>\n\n<p>You need to distribute <strong>all products</strong> to the retail stores following these rules:</p>\n\n<ul>\n\t<li>A store can only be given <strong>at most one product type</strong> but can be given <strong>any</strong> amount of it.</li>\n\t<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 <strong>minimize</strong> the <strong>maximum</strong> number of products that are given to any store.</li>\n</ul>\n\n<p>Return <em>the minimum possible</em> <code>x</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 6, quantities = [11,6]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> One optimal way is:\n- The 11 products of type 0 are distributed to the first four stores in these amounts: 2, 3, 3, 3\n- The 6 products of type 1 are distributed to the other two stores in these amounts: 3, 3\nThe maximum number of products given to any store is max(2, 3, 3, 3, 3, 3) = 3.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 7, quantities = [15,10,10]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> One optimal way is:\n- The 15 products of type 0 are distributed to the first three stores in these amounts: 5, 5, 5\n- The 10 products of type 1 are distributed to the next two stores in these amounts: 5, 5\n- The 10 products of type 2 are distributed to the last two stores in these amounts: 5, 5\nThe maximum number of products given to any store is max(5, 5, 5, 5, 5, 5, 5) = 5.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1, quantities = [100000]\n<strong>Output:</strong> 100000\n<strong>Explanation:</strong> The only optimal way is:\n- The 100000 products of type 0 are distributed to the only store.\nThe maximum number of products given to any store is max(100000) = 100000.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == quantities.length</code></li>\n\t<li><code>1 &lt;= m &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= quantities[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "分配给商店的最多商品的最小值",
            "translatedContent": "<p>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 <strong>0</strong>&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。</p>\n\n<p>你需要将 <strong>所有商品</strong>&nbsp;分配到零售商店，并遵守这些规则：</p>\n\n<ul>\n\t<li>一间商店 <strong>至多</strong>&nbsp;只能有 <strong>一种商品</strong> ，但一间商店拥有的商品数目可以为&nbsp;<strong>任意</strong>&nbsp;件。</li>\n\t<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 <strong>最小化</strong>&nbsp;分配给任意商店商品数目的 <strong>最大值</strong>&nbsp;。</li>\n</ul>\n\n<p>请你返回最小的可能的&nbsp;<code>x</code>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>n = 6, quantities = [11,6]\n<b>输出：</b>3\n<strong>解释： </strong>一种最优方案为：\n- 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 。\n- 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 。\n分配给所有商店的最大商品数目为 max(2, 3, 3, 3, 3, 3) = 3 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>n = 7, quantities = [15,10,10]\n<b>输出：</b>5\n<b>解释：</b>一种最优方案为：\n- 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 。\n- 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 。\n- 10 件种类为 2 的商品被分配到最后 2 间商店，数目为：5，5 。\n分配给所有商店的最大商品数目为 max(5, 5, 5, 5, 5, 5, 5) = 5 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>n = 1, quantities = [100000]\n<b>输出：</b>100000\n<b>解释：</b>唯一一种最优方案为：\n- 所有 100000 件商品 0 都分配到唯一的商店中。\n分配给所有商店的最大商品数目为 max(100000) = 100000 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>m == quantities.length</code></li>\n\t<li><code>1 &lt;= m &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= quantities[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                "There exists a monotonic nature such that when x is smaller than some number, there will be no way to distribute, and when x is not smaller than that number, there will always be a way to distribute.",
                "If you are given a number k, where the number of products given to any store does not exceed k, could you determine if all products can be distributed?",
                "Implement a function canDistribute(k), which returns true if you can distribute all products such that any store will not be given more than k products, and returns false if you cannot. Use this function to binary search for the smallest possible k."
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