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49 lines
2.1 KiB
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49 lines
2.1 KiB
HTML
<p>You are given two integers <code>n</code> and <code>maxValue</code>, which are used to describe an <strong>ideal</strong> array.</p>
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<p>A <strong>0-indexed</strong> integer array <code>arr</code> of length <code>n</code> is considered <strong>ideal</strong> if the following conditions hold:</p>
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<ul>
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<li>Every <code>arr[i]</code> is a value from <code>1</code> to <code>maxValue</code>, for <code>0 <= i < n</code>.</li>
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<li>Every <code>arr[i]</code> is divisible by <code>arr[i - 1]</code>, for <code>0 < i < n</code>.</li>
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</ul>
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<p>Return <em>the number of <strong>distinct</strong> ideal arrays of length </em><code>n</code>. Since the answer may be very large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> n = 2, maxValue = 5
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<strong>Output:</strong> 10
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<strong>Explanation:</strong> The following are the possible ideal arrays:
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- Arrays starting with the value 1 (5 arrays): [1,1], [1,2], [1,3], [1,4], [1,5]
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- Arrays starting with the value 2 (2 arrays): [2,2], [2,4]
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- Arrays starting with the value 3 (1 array): [3,3]
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- Arrays starting with the value 4 (1 array): [4,4]
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- Arrays starting with the value 5 (1 array): [5,5]
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There are a total of 5 + 2 + 1 + 1 + 1 = 10 distinct ideal arrays.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> n = 5, maxValue = 3
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<strong>Output:</strong> 11
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<strong>Explanation:</strong> The following are the possible ideal arrays:
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- Arrays starting with the value 1 (9 arrays):
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- With no other distinct values (1 array): [1,1,1,1,1]
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- With 2<sup>nd</sup> distinct value 2 (4 arrays): [1,1,1,1,2], [1,1,1,2,2], [1,1,2,2,2], [1,2,2,2,2]
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- With 2<sup>nd</sup> distinct value 3 (4 arrays): [1,1,1,1,3], [1,1,1,3,3], [1,1,3,3,3], [1,3,3,3,3]
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- Arrays starting with the value 2 (1 array): [2,2,2,2,2]
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- Arrays starting with the value 3 (1 array): [3,3,3,3,3]
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There are a total of 9 + 1 + 1 = 11 distinct ideal arrays.
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</pre>
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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 <= n <= 10<sup>4</sup></code></li>
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<li><code>1 <= maxValue <= 10<sup>4</sup></code></li>
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</ul>
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