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46 lines
1.6 KiB
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46 lines
1.6 KiB
HTML
<p>You are given an integer array <code>nums</code> of length <code>n</code> which represents a permutation of all the integers in the range <code>[0, n - 1]</code>.</p>
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<p>The number of <strong>global inversions</strong> is the number of the different pairs <code>(i, j)</code> where:</p>
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<ul>
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<li><code>0 <= i < j < n</code></li>
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<li><code>nums[i] > nums[j]</code></li>
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</ul>
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<p>The number of <strong>local inversions</strong> is the number of indices <code>i</code> where:</p>
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<ul>
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<li><code>0 <= i < n - 1</code></li>
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<li><code>nums[i] > nums[i + 1]</code></li>
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</ul>
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<p>Return <code>true</code> <em>if the number of <strong>global inversions</strong> is equal to the number of <strong>local inversions</strong></em>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,0,2]
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<strong>Output:</strong> true
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<strong>Explanation:</strong> There is 1 global inversion and 1 local inversion.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,2,0]
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<strong>Output:</strong> false
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<strong>Explanation:</strong> There are 2 global inversions and 1 local inversion.
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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 == nums.length</code></li>
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<li><code>1 <= n <= 10<sup>5</sup></code></li>
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<li><code>0 <= nums[i] < n</code></li>
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<li>All the integers of <code>nums</code> are <strong>unique</strong>.</li>
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<li><code>nums</code> is a permutation of all the numbers in the range <code>[0, n - 1]</code>.</li>
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</ul>
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