leetcode-problemset/leetcode-cn/originData/maximum-number-of-groups-with-increasing-length.json

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        "question": {
            "questionId": "2919",
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            "title": "Maximum Number of Groups With Increasing Length",
            "titleSlug": "maximum-number-of-groups-with-increasing-length",
            "content": "<p>You are given a <strong>0-indexed</strong> array <code>usageLimits</code> of length <code>n</code>.</p>\n\n<p>Your task is to create <strong>groups</strong> using numbers from <code>0</code> to <code>n - 1</code>, ensuring that each number, <code>i</code>, is used no more than <code>usageLimits[i]</code> times in total <strong>across all groups</strong>. You must also satisfy the following conditions:</p>\n\n<ul>\n\t<li>Each group must consist of <strong>distinct </strong>numbers, meaning that no duplicate numbers are allowed within a single group.</li>\n\t<li>Each group (except the first one) must have a length <strong>strictly greater</strong> than the previous group.</li>\n</ul>\n\n<p>Return <em>an integer denoting the <strong>maximum</strong> number of groups you can create while satisfying these conditions.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> <code>usageLimits</code> = [1,2,5]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> In this example, we can use 0 at most once, 1 at most twice, and 2 at most five times.\nOne way of creating the maximum number of groups while satisfying the conditions is: \nGroup 1 contains the number [2].\nGroup 2 contains the numbers [1,2].\nGroup 3 contains the numbers [0,1,2]. \nIt can be shown that the maximum number of groups is 3. \nSo, the output is 3. </pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> <code>usageLimits</code> = [2,1,2]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> In this example, we can use 0 at most twice, 1 at most once, and 2 at most twice.\nOne way of creating the maximum number of groups while satisfying the conditions is:\nGroup 1 contains the number [0].\nGroup 2 contains the numbers [1,2].\nIt can be shown that the maximum number of groups is 2.\nSo, the output is 2. \n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> <code>usageLimits</code> = [1,1]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> In this example, we can use both 0 and 1 at most once.\nOne way of creating the maximum number of groups while satisfying the conditions is:\nGroup 1 contains the number [0].\nIt can be shown that the maximum number of groups is 1.\nSo, the output is 1. \n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= usageLimits.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= usageLimits[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "长度递增组的最大数目",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始、长度为 <code>n</code> 的数组 <code>usageLimits</code> 。</p>\n\n<p>你的任务是使用从 <code>0</code> 到 <code>n - 1</code> 的数字创建若干组，并确保每个数字 <code>i</code> 在 <strong>所有组</strong> 中使用的次数总共不超过 <code>usageLimits[i]</code> 次。此外，还必须满足以下条件：</p>\n\n<ul>\n\t<li>每个组必须由 <strong>不同</strong> 的数字组成，也就是说，单个组内不能存在重复的数字。</li>\n\t<li>每个组（除了第一个）的长度必须 <strong>严格大于</strong> 前一个组。</li>\n</ul>\n\n<p>在满足所有条件的情况下，以整数形式返回可以创建的最大组数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<code><strong>输入：</strong>usageLimits</code> = [1,2,5]\n<strong>输出：</strong>3\n<strong>解释：</strong>在这个示例中，我们可以使用 0 至多一次，使用 1 至多 2 次，使用 2 至多 5 次。\n一种既能满足所有条件，又能创建最多组的方式是： \n组 1 包含数字 [2] 。\n组 2 包含数字 [1,2] 。\n组 3 包含数字 [0,1,2] 。 \n可以证明能够创建的最大组数是 3 。 \n所以，输出是 3 。 </pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<code><strong>输入：</strong></code><code>usageLimits</code> = [2,1,2]\n<strong>输出：</strong>2\n<strong>解释：</strong>在这个示例中，我们可以使用 0 至多 2 次，使用 1 至多 1 次，使用 2 至多 2 次。\n一种既能满足所有条件，又能创建最多组的方式是： \n组 1 包含数字 [0] 。 \n组 2 包含数字 [1,2] 。\n可以证明能够创建的最大组数是 2 。 \n所以，输出是 2 。 \n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<code><strong>输入：</strong></code><code>usageLimits</code> = [1,1]\n<strong>输出：</strong>1\n<strong>解释：</strong>在这个示例中，我们可以使用 0 和 1 至多 1 次。 \n一种既能满足所有条件，又能创建最多组的方式是：\n组 1 包含数字 [0] 。\n可以证明能够创建的最大组数是 1 。 \n所以，输出是 1 。 \n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= usageLimits.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= usageLimits[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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                "Can we solve this problem using sorting and binary search?\r\nSort the array in increasing order and run a binary search on the number of groups, x.\r\nTo determine if a value x is feasible, greedily distribute the numbers such that each group receives 1, 2, 3, ..., x numbers.",
                "Sort the array in increasing order and run a binary search on the number of groups, x.",
                "To determine if a value x is feasible, greedily distribute the numbers such that each group receives 1, 2, 3, ..., x numbers."
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