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65 lines
2.2 KiB
HTML
65 lines
2.2 KiB
HTML
<p>You are given three integers <code>n</code>, <code>m</code>, <code>k</code>. A <strong>good array</strong> <code>arr</code> of size <code>n</code> is defined as follows:</p>
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<ul>
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<li>Each element in <code>arr</code> is in the <strong>inclusive</strong> range <code>[1, m]</code>.</li>
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<li><em>Exactly</em> <code>k</code> indices <code>i</code> (where <code>1 <= i < n</code>) satisfy the condition <code>arr[i - 1] == arr[i]</code>.</li>
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</ul>
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<p>Return the number of <strong>good arrays</strong> that can be formed.</p>
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<p>Since the answer may be very large, return it <strong>modulo </strong><code>10<sup>9 </sup>+ 7</code>.</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">n = 3, m = 2, k = 1</span></p>
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<p><strong>Output:</strong> <span class="example-io">4</span></p>
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<p><strong>Explanation:</strong></p>
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<ul>
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<li>There are 4 good arrays. They are <code>[1, 1, 2]</code>, <code>[1, 2, 2]</code>, <code>[2, 1, 1]</code> and <code>[2, 2, 1]</code>.</li>
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<li>Hence, the answer is 4.</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">n = 4, m = 2, k = 2</span></p>
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<p><strong>Output:</strong> <span class="example-io">6</span></p>
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<p><strong>Explanation:</strong></p>
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<ul>
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<li>The good arrays are <code>[1, 1, 1, 2]</code>, <code>[1, 1, 2, 2]</code>, <code>[1, 2, 2, 2]</code>, <code>[2, 1, 1, 1]</code>, <code>[2, 2, 1, 1]</code> and <code>[2, 2, 2, 1]</code>.</li>
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<li>Hence, the answer is 6.</li>
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</ul>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 5, m = 2, k = 0</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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<ul>
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<li>The good arrays are <code>[1, 2, 1, 2, 1]</code> and <code>[2, 1, 2, 1, 2]</code>. Hence, the answer is 2.</li>
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</ul>
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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>1 <= n <= 10<sup>5</sup></code></li>
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<li><code>1 <= m <= 10<sup>5</sup></code></li>
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<li><code>0 <= k <= n - 1</code></li>
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</ul>
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