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48 lines
2.4 KiB
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48 lines
2.4 KiB
HTML
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<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.</p>
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<p>The <strong>average difference</strong> of the index <code>i</code> is the <strong>absolute</strong> <strong>difference</strong> between the average of the <strong>first</strong> <code>i + 1</code> elements of <code>nums</code> and the average of the <strong>last</strong> <code>n - i - 1</code> elements. Both averages should be <strong>rounded down</strong> to the nearest integer.</p>
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<p>Return<em> the index with the <strong>minimum average difference</strong></em>. If there are multiple such indices, return the <strong>smallest</strong> one.</p>
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<p><strong>Note:</strong></p>
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<ul>
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<li>The <strong>absolute difference</strong> of two numbers is the absolute value of their difference.</li>
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<li>The <strong>average</strong> of <code>n</code> elements is the <strong>sum</strong> of the <code>n</code> elements divided (<strong>integer division</strong>) by <code>n</code>.</li>
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<li>The average of <code>0</code> elements is considered to be <code>0</code>.</li>
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</ul>
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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> nums = [2,5,3,9,5,3]
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<strong>Output:</strong> 3
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<strong>Explanation:</strong>
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- The average difference of index 0 is: |2 / 1 - (5 + 3 + 9 + 5 + 3) / 5| = |2 / 1 - 25 / 5| = |2 - 5| = 3.
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- The average difference of index 1 is: |(2 + 5) / 2 - (3 + 9 + 5 + 3) / 4| = |7 / 2 - 20 / 4| = |3 - 5| = 2.
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- The average difference of index 2 is: |(2 + 5 + 3) / 3 - (9 + 5 + 3) / 3| = |10 / 3 - 17 / 3| = |3 - 5| = 2.
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- The average difference of index 3 is: |(2 + 5 + 3 + 9) / 4 - (5 + 3) / 2| = |19 / 4 - 8 / 2| = |4 - 4| = 0.
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- The average difference of index 4 is: |(2 + 5 + 3 + 9 + 5) / 5 - 3 / 1| = |24 / 5 - 3 / 1| = |4 - 3| = 1.
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- The average difference of index 5 is: |(2 + 5 + 3 + 9 + 5 + 3) / 6 - 0| = |27 / 6 - 0| = |4 - 0| = 4.
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The average difference of index 3 is the minimum average difference so return 3.
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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> nums = [0]
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<strong>Output:</strong> 0
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<strong>Explanation:</strong>
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The only index is 0 so return 0.
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The average difference of index 0 is: |0 / 1 - 0| = |0 - 0| = 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>1 <= nums.length <= 10<sup>5</sup></code></li>
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<li><code>0 <= nums[i] <= 10<sup>5</sup></code></li>
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</ul>
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