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60 lines
2.5 KiB
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60 lines
2.5 KiB
HTML
<p>You are given a <strong>0-indexed</strong> array of <code>n</code> integers <code>differences</code>, which describes the <strong>differences </strong>between each pair of <strong>consecutive </strong>integers of a <strong>hidden</strong> sequence of length <code>(n + 1)</code>. More formally, call the hidden sequence <code>hidden</code>, then we have that <code>differences[i] = hidden[i + 1] - hidden[i]</code>.</p>
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<p>You are further given two integers <code>lower</code> and <code>upper</code> that describe the <strong>inclusive</strong> range of values <code>[lower, upper]</code> that the hidden sequence can contain.</p>
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<ul>
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<li>For example, given <code>differences = [1, -3, 4]</code>, <code>lower = 1</code>, <code>upper = 6</code>, the hidden sequence is a sequence of length <code>4</code> whose elements are in between <code>1</code> and <code>6</code> (<strong>inclusive</strong>).
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<ul>
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<li><code>[3, 4, 1, 5]</code> and <code>[4, 5, 2, 6]</code> are possible hidden sequences.</li>
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<li><code>[5, 6, 3, 7]</code> is not possible since it contains an element greater than <code>6</code>.</li>
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<li><code>[1, 2, 3, 4]</code> is not possible since the differences are not correct.</li>
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</ul>
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</li>
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</ul>
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<p>Return <em>the number of <strong>possible</strong> hidden sequences there are.</em> If there are no possible sequences, return <code>0</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> differences = [1,-3,4], lower = 1, upper = 6
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> The possible hidden sequences are:
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- [3, 4, 1, 5]
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- [4, 5, 2, 6]
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Thus, we return 2.
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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> differences = [3,-4,5,1,-2], lower = -4, upper = 5
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<strong>Output:</strong> 4
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<strong>Explanation:</strong> The possible hidden sequences are:
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- [-3, 0, -4, 1, 2, 0]
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- [-2, 1, -3, 2, 3, 1]
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- [-1, 2, -2, 3, 4, 2]
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- [0, 3, -1, 4, 5, 3]
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Thus, we return 4.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> differences = [4,-7,2], lower = 3, upper = 6
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<strong>Output:</strong> 0
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<strong>Explanation:</strong> There are no possible hidden sequences. Thus, we return 0.
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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>n == differences.length</code></li>
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<li><code>1 <= n <= 10<sup>5</sup></code></li>
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<li><code>-10<sup>5</sup> <= differences[i] <= 10<sup>5</sup></code></li>
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<li><code>-10<sup>5</sup> <= lower <= upper <= 10<sup>5</sup></code></li>
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</ul>
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