mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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196 lines
28 KiB
JSON
196 lines
28 KiB
JSON
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"title": "Count the Number of Computer Unlocking Permutations",
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"content": "<p>You are given an array <code>complexity</code> of length <code>n</code>.</p>\n\n<p>There are <code>n</code> <strong>locked</strong> computers in a room with labels from 0 to <code>n - 1</code>, each with its own <strong>unique</strong> password. The password of the computer <code>i</code> has a complexity <code>complexity[i]</code>.</p>\n\n<p>The password for the computer labeled 0 is <strong>already</strong> decrypted and serves as the root. All other computers must be unlocked using it or another previously unlocked computer, following this information:</p>\n\n<ul>\n\t<li>You can decrypt the password for the computer <code>i</code> using the password for computer <code>j</code>, where <code>j</code> is <strong>any</strong> integer less than <code>i</code> with a lower complexity. (i.e. <code>j < i</code> and <code>complexity[j] < complexity[i]</code>)</li>\n\t<li>To decrypt the password for computer <code>i</code>, you must have already unlocked a computer <code>j</code> such that <code>j < i</code> and <code>complexity[j] < complexity[i]</code>.</li>\n</ul>\n\n<p>Find the number of <span data-keyword=\"permutation-array\">permutations</span> of <code>[0, 1, 2, ..., (n - 1)]</code> that represent a valid order in which the computers can be unlocked, starting from computer 0 as the only initially unlocked one.</p>\n\n<p>Since the answer may be large, return it <strong>modulo</strong> 10<sup>9</sup> + 7.</p>\n\n<p><strong>Note</strong> that the password for the computer <strong>with label</strong> 0 is decrypted, and <em>not</em> the computer with the first position in the permutation.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">complexity = [1,2,3]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The valid permutations are:</p>\n\n<ul>\n\t<li>[0, 1, 2]\n\t<ul>\n\t\t<li>Unlock computer 0 first with root password.</li>\n\t\t<li>Unlock computer 1 with password of computer 0 since <code>complexity[0] < complexity[1]</code>.</li>\n\t\t<li>Unlock computer 2 with password of computer 1 since <code>complexity[1] < complexity[2]</code>.</li>\n\t</ul>\n\t</li>\n\t<li>[0, 2, 1]\n\t<ul>\n\t\t<li>Unlock computer 0 first with root password.</li>\n\t\t<li>Unlock computer 2 with password of computer 0 since <code>complexity[0] < complexity[2]</code>.</li>\n\t\t<li>Unlock computer 1 with password of computer 0 since <code>complexity[0] < complexity[1]</code>.</li>\n\t</ul>\n\t</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">complexity = [3,3,3,4,4,4]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">0</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>There are no possible permutations which can unlock all computers.</p>\n</div>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= complexity.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= complexity[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"translatedTitle": "统计计算机解锁顺序排列数",
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"translatedContent": "<p>给你一个长度为 <code>n</code> 的数组 <code>complexity</code>。</p>\n\n<p>在房间里有 <code>n</code> 台 <strong>上锁的 </strong>计算机，这些计算机的编号为 0 到 <code>n - 1</code>，每台计算机都有一个 <strong>唯一 </strong>的密码。编号为 <code>i</code> 的计算机的密码复杂度为 <code>complexity[i]</code>。</p>\n\n<p>编号为 0 的计算机密码已经 <strong>解锁 </strong>，并作为根节点。其他所有计算机必须通过它或其他已经解锁的计算机来解锁，具体规则如下：</p>\n\n<ul>\n\t<li>可以使用编号为 <code>j</code> 的计算机的密码解锁编号为 <code>i</code> 的计算机，其中 <code>j</code> 是任何小于 <code>i</code> 的整数，且满足 <code>complexity[j] < complexity[i]</code>（即 <code>j < i</code> 并且 <code>complexity[j] < complexity[i]</code>）。</li>\n\t<li>要解锁编号为 <code>i</code> 的计算机，你需要事先解锁一个编号为 <code>j</code> 的计算机，满足 <code>j < i</code> 并且 <code>complexity[j] < complexity[i]</code>。</li>\n</ul>\n\n<p>求共有多少种 <code>[0, 1, 2, ..., (n - 1)]</code> 的排列方式，能够表示从编号为 0 的计算机（唯一初始解锁的计算机）开始解锁所有计算机的有效顺序。</p>\n\n<p>由于答案可能很大，返回结果需要对 <strong>10<sup>9</sup> + 7</strong> 取余数。</p>\n\n<p><strong>注意：</strong>编号为 0 的计算机的密码已解锁，而 <strong>不是 </strong>排列中第一个位置的计算机密码已解锁。</p>\n\n<p><strong>排列 </strong>是一个数组中所有元素的重新排列。</p>\n\n<p> </p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">complexity = [1,2,3]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>有效的排列有：</p>\n\n<ul>\n\t<li>[0, 1, 2]\n\t<ul>\n\t\t<li>首先使用根密码解锁计算机 0。</li>\n\t\t<li>使用计算机 0 的密码解锁计算机 1，因为 <code>complexity[0] < complexity[1]</code>。</li>\n\t\t<li>使用计算机 1 的密码解锁计算机 2，因为 <code>complexity[1] < complexity[2]</code>。</li>\n\t</ul>\n\t</li>\n\t<li>[0, 2, 1]\n\t<ul>\n\t\t<li>首先使用根密码解锁计算机 0。</li>\n\t\t<li>使用计算机 0 的密码解锁计算机 2，因为 <code>complexity[0] < complexity[2]</code>。</li>\n\t\t<li>使用计算机 0 的密码解锁计算机 1，因为 <code>complexity[0] < complexity[1]</code>。</li>\n\t</ul>\n\t</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">complexity = [3,3,3,4,4,4]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">0</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>没有任何排列能够解锁所有计算机。</p>\n</div>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 <= complexity.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= complexity[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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