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70 lines
2.5 KiB
HTML
70 lines
2.5 KiB
HTML
<p>You are given a <code>m x n</code> matrix <code>mat</code> of positive integers.</p>
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<p>Return an integer denoting the number of ways to choose <strong>exactly one</strong> integer from each row of <code>mat</code> such that the <strong>greatest common divisor</strong> of all chosen integers is 1.</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">mat = [[1,2],[3,4]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">3</span></p>
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<p><strong>Explanation:</strong></p>
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<table style="border: 1px solid black;">
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<tbody>
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<tr>
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<th align="center" style="border: 1px solid black;">Chosen integer in the first row</th>
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<th align="center" style="border: 1px solid black;">Chosen integer in the second row</th>
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<th align="center" style="border: 1px solid black;">Greatest common divisor of chosen integers</th>
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</tr>
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<tr>
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<td align="center" style="border: 1px solid black;">1</td>
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<td align="center" style="border: 1px solid black;">3</td>
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<td align="center" style="border: 1px solid black;">1</td>
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</tr>
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<tr>
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<td align="center" style="border: 1px solid black;">1</td>
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<td align="center" style="border: 1px solid black;">4</td>
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<td align="center" style="border: 1px solid black;">1</td>
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</tr>
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<tr>
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<td align="center" style="border: 1px solid black;">2</td>
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<td align="center" style="border: 1px solid black;">3</td>
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<td align="center" style="border: 1px solid black;">1</td>
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</tr>
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<tr>
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<td align="center" style="border: 1px solid black;">2</td>
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<td align="center" style="border: 1px solid black;">4</td>
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<td align="center" style="border: 1px solid black;">2</td>
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</tr>
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</tbody>
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</table>
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<p>3 of these combinations have a greatest common divisor of 1. Therefore, the answer is 3.</p>
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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">mat = [[2,2],[2,2]]</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>Every combination has a greatest common divisor of 2. Therefore, the answer is 0.</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>1 <= m == mat.length <= 150</code></li>
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<li><code>1 <= n == mat[i].length <= 150</code></li>
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<li><code>1 <= mat[i][j] <= 150</code></li>
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</ul>
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