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58 lines
2.4 KiB
HTML
58 lines
2.4 KiB
HTML
<p>You are given 3 positive integers <code>zero</code>, <code>one</code>, and <code>limit</code>.</p>
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<p>A <span data-keyword="binary-array">binary array</span> <code>arr</code> is called <strong>stable</strong> if:</p>
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<ul>
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<li>The number of occurrences of 0 in <code>arr</code> is <strong>exactly </strong><code>zero</code>.</li>
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<li>The number of occurrences of 1 in <code>arr</code> is <strong>exactly</strong> <code>one</code>.</li>
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<li>Each <span data-keyword="subarray-nonempty">subarray</span> of <code>arr</code> with a size greater than <code>limit</code> must contain <strong>both </strong>0 and 1.</li>
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</ul>
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<p>Return the <em>total</em> number of <strong>stable</strong> binary arrays.</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">zero = 1, one = 1, limit = 2</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 two possible stable binary arrays are <code>[1,0]</code> and <code>[0,1]</code>.</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">zero = 1, one = 2, limit = 1</span></p>
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<p><strong>Output:</strong> <span class="example-io">1</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The only possible stable binary array is <code>[1,0,1]</code>.</p>
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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">zero = 3, one = 3, limit = 2</span></p>
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<p><strong>Output:</strong> <span class="example-io">14</span></p>
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<p><strong>Explanation:</strong></p>
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<p>All the possible stable binary arrays are <code>[0,0,1,0,1,1]</code>, <code>[0,0,1,1,0,1]</code>, <code>[0,1,0,0,1,1]</code>, <code>[0,1,0,1,0,1]</code>, <code>[0,1,0,1,1,0]</code>, <code>[0,1,1,0,0,1]</code>, <code>[0,1,1,0,1,0]</code>, <code>[1,0,0,1,0,1]</code>, <code>[1,0,0,1,1,0]</code>, <code>[1,0,1,0,0,1]</code>, <code>[1,0,1,0,1,0]</code>, <code>[1,0,1,1,0,0]</code>, <code>[1,1,0,0,1,0]</code>, and <code>[1,1,0,1,0,0]</code>.</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 <= zero, one, limit <= 1000</code></li>
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</ul>
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