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67 lines
3.1 KiB
HTML
67 lines
3.1 KiB
HTML
<p>You are given an array <code>complexity</code> of length <code>n</code>.</p>
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<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>
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<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>
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<ul>
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<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>
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<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>
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</ul>
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<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>
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<p>Since the answer may be large, return it <strong>modulo</strong> 10<sup>9</sup> + 7.</p>
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<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>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">complexity = [1,2,3]</span></p>
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<p><strong>Output:</strong> <span class="example-io">2</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The valid permutations are:</p>
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<ul>
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<li>[0, 1, 2]
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<ul>
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<li>Unlock computer 0 first with root password.</li>
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<li>Unlock computer 1 with password of computer 0 since <code>complexity[0] < complexity[1]</code>.</li>
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<li>Unlock computer 2 with password of computer 1 since <code>complexity[1] < complexity[2]</code>.</li>
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</ul>
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</li>
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<li>[0, 2, 1]
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<ul>
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<li>Unlock computer 0 first with root password.</li>
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<li>Unlock computer 2 with password of computer 0 since <code>complexity[0] < complexity[2]</code>.</li>
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<li>Unlock computer 1 with password of computer 0 since <code>complexity[0] < complexity[1]</code>.</li>
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</ul>
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</li>
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</ul>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">complexity = [3,3,3,4,4,4]</span></p>
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<p><strong>Output:</strong> <span class="example-io">0</span></p>
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<p><strong>Explanation:</strong></p>
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<p>There are no possible permutations which can unlock all computers.</p>
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</div>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>2 <= complexity.length <= 10<sup>5</sup></code></li>
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<li><code>1 <= complexity[i] <= 10<sup>9</sup></code></li>
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</ul>
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