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    <p>You can solve your problem like that:</p> <p>You can find the median in <code>O(n)</code>, w.g. using the <code>O(n)</code> <a href="http://www.cplusplus.com/reference/algorithm/nth_element/" rel="nofollow">nth_element algorithm</a>.</p> <p>You loop through all elements substutiting each with a pair: <code>&lt;the absolute difference to the median&gt;, &lt;element's value&gt;</code>. Once more you do nth_element with <code>n</code> = <code>k</code>. after applying this algorithm you are guaranteed to have the <code>k</code> smallest elements in absolute difference first in the new array. You take their indices and DONE!</p> <p>Your algorithm, on the other hand uses sorting, and this makes it <code>O(nlogn)</code>.</p> <p><strong>EDIT</strong>: The requested example:</p> <p>Let the array be <code>[14, 6, 7, 8, 10, 13, 21, 16, 23]</code>.</p> <ul> <li>After the step for finding the median it will be reordered to, say: <code>[8, 7, 9, 10, 13, 16, 23, 14, 21]</code>, notice that the array is not sorted, but still the median (13) is exactly in the middle.</li> <li>Now let's do the pair substitution that got you confused: we create a new array of pairs: <code>[&lt;abs(14-13), 14&gt;, &lt;abs(6-13), 6&gt;, &lt;abs(7-13), 7&gt;, &lt;abs(8-13), 8&gt;, &lt;abs(10-13), 10&gt;, &lt;abs(13-13), 13&gt;, &lt;abs(21-13), 21&gt;, &lt;abs(16-13), 16&gt;, &lt;abs(23-13), 23&gt;</code>. Thus we obtain the array: <code>[&lt;1, 14&gt;, &lt;7, 6&gt;, &lt;6, 7&gt;, &lt;5, 8&gt;, &lt;3, 10&gt;, &lt;0, 13&gt;, &lt;8, 21&gt;, &lt;3, 16&gt;, &lt;10, 23&gt;</code></li> <li>If e.g. <code>k</code> is 4 we make once more nth_element(using the first element of each pair for comparisons) and obtain: <code>[&lt;1, 14&gt;, &lt;3, 16&gt;, &lt;0, 13&gt;, &lt;3, 10&gt;, &lt;8, 21&gt;, &lt;7, 6&gt;, &lt;10, 23&gt;, &lt;6, 7&gt;, &lt;5, 8&gt;]</code> so the numbers you search for are the second elements of the first 4 pairs: <code>14</code>, <code>16</code>, <code>13</code> and <code>10</code></li> </ul>
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    1. POHow do I calculate the k nearest numbers to the median?
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    1. USBoris Strandjev
    1. USBoris Strandjev
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    1. COCan you show me a example? Because i can't get "the substutiting with a pair" how to do so ?
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      1. USRat565
    2. CO@Rat565 Example added
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      1. USBoris Strandjev
    3. CO@Boris: your description says "element's index", but your worked example uses the element's value. Either is fine (if you use the index then you can look it up at the end in the original input array, assuming that the step 1 partition was done on a copy), but you probably want them to be the same. Also, if all you need at the end is the value then you can simplify a bit and do it all in place, just run nth_element using a comparator that compares the abs difference from the median.
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      1. USSteve Jessop
 

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