mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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197 lines
23 KiB
JSON
197 lines
23 KiB
JSON
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"title": "Maximum Number of Groups Getting Fresh Donuts",
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"content": "<p>There is a donuts shop that bakes donuts in batches of <code>batchSize</code>. They have a rule where they must serve <strong>all</strong> of the donuts of a batch before serving any donuts of the next batch. You are given an integer <code>batchSize</code> and an integer array <code>groups</code>, where <code>groups[i]</code> denotes that there is a group of <code>groups[i]</code> customers that will visit the shop. Each customer will get exactly one donut.</p>\n\n<p>When a group visits the shop, all customers of the group must be served before serving any of the following groups. A group will be happy if they all get fresh donuts. That is, the first customer of the group does not receive a donut that was left over from the previous group.</p>\n\n<p>You can freely rearrange the ordering of the groups. Return <em>the <strong>maximum</strong> possible number of happy groups after rearranging the groups.</em></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> batchSize = 3, groups = [1,2,3,4,5,6]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> You can arrange the groups as [6,2,4,5,1,3]. Then the 1<sup>st</sup>, 2<sup>nd</sup>, 4<sup>th</sup>, and 6<sup>th</sup> groups will be happy.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> batchSize = 4, groups = [1,3,2,5,2,2,1,6]\n<strong>Output:</strong> 4\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= batchSize <= 9</code></li>\n\t<li><code>1 <= groups.length <= 30</code></li>\n\t<li><code>1 <= groups[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"translatedTitle": "得到新鲜甜甜圈的最多组数",
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"translatedContent": "<p>有一个甜甜圈商店，每批次都烤 <code>batchSize</code> 个甜甜圈。这个店铺有个规则，就是在烤一批新的甜甜圈时，之前 <strong>所有</strong> 甜甜圈都必须已经全部销售完毕。给你一个整数 <code>batchSize</code> 和一个整数数组 <code>groups</code> ，数组中的每个整数都代表一批前来购买甜甜圈的顾客，其中 <code>groups[i]</code> 表示这一批顾客的人数。每一位顾客都恰好只要一个甜甜圈。</p>\n\n<p>当有一批顾客来到商店时，他们所有人都必须在下一批顾客来之前购买完甜甜圈。如果一批顾客中第一位顾客得到的甜甜圈不是上一组剩下的，那么这一组人都会很开心。</p>\n\n<p>你可以随意安排每批顾客到来的顺序。请你返回在此前提下，<strong>最多</strong> 有多少组人会感到开心。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>batchSize = 3, groups = [1,2,3,4,5,6]\n<b>输出：</b>4\n<b>解释：</b>你可以将这些批次的顾客顺序安排为 [6,2,4,5,1,3] 。那么第 1，2，4，6 组都会感到开心。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>batchSize = 4, groups = [1,3,2,5,2,2,1,6]\n<b>输出：</b>4\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= batchSize <= 9</code></li>\n\t<li><code>1 <= groups.length <= 30</code></li>\n\t<li><code>1 <= groups[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"The maximum number of happy groups is the maximum number of partitions you can split the groups into such that the sum of group sizes in each partition is 0 mod batchSize. At most one partition is allowed to have a different remainder (the first group will get fresh donuts anyway).",
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"Suppose you have an array freq of length k where freq[i] = number of groups of size i mod batchSize. How can you utilize this in a dp solution?",
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"Make a DP state dp[freq][r] that represents \"the maximum number of partitions you can form given the current freq and current remainder r\". You can hash the freq array to store it more easily in the dp table.",
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"For each i from 0 to batchSize-1, the next DP state is dp[freq`][(r+i)%batchSize] where freq` is freq but with freq[i] decremented by 1. Take the largest of all of the next states and store it in ans. If r == 0, then return ans+1 (because you can form a new partition), otherwise return ans (continuing the current partition)."
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