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"title": "Minimized Maximum of Products Distributed to Any Store",
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"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> </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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == quantities.length</code></li>\n\t<li><code>1 <= m <= n <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= quantities[i] <= 10<sup>5</sup></code></li>\n</ul>\n",
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"code": "class Solution(object):\n def minimizedMaximum(self, n, quantities):\n \"\"\"\n :type n: int\n :type quantities: List[int]\n :rtype: int\n \"\"\"\n ",
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"code": "impl Solution {\n pub fn minimized_maximum(n: i32, quantities: Vec<i32>) -> i32 {\n \n }\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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