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POArray movement from a1,..,an,b1,..,bn to a1,b1,..,an,bn
 

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    <p>Today, I met a question which is really puzzled me</p> <p><strong>Question</strong></p> <p>I have array just like:<code>arr[a1, a2, a3....an, b1, b2, b3.....bn]</code>, how to move the elements of the array to transfer it into <code>arr[a1, b1, a2, b2......an,bn]</code>, And you should do the movement in-place（<code>space complexity should be constant</code>）.</p> <p>I tried my best to think it over and get an ugly algorithm just like bubble-sort:</p> <pre><code>b1 moves forward by n - 1; b2 moves forward by n - 2; . . bn-1 moves forward by 1; </code></pre> <p>But the time complexity is O(n<sup>2</sup>), who can give me a better algorithm? I find another better method just like quick-Sort:</p> <pre><code>First we swap the element from a(n/2) to a(n) with the elements from b1 to b(n/2);now we get two independent sub problems,So we can solve it by recursion. T(n) = 2T(n/2) + O(n) the time complexity is O(nlgn) </code></pre> <p>here are whole codes:</p> <pre><code>void swapArray(int *arr, int left, int right) { int mid = (left + right) &gt;&gt; 1; int temp = mid + 1; while(left &lt;= mid) { swap(arr[left++], arr[temp++]); } } void arrayMove(int *arr, int lb, int le, int rb, int re) { if(le - lb &lt;= 0 || re - rb &lt;= 0) return; int mid = (lb + le + 1) &gt;&gt; 1; int len = le - mid; if(rb + len &gt;= re) { swapArray(arr, mid + 1, rb); } else { swapArray(arr, mid, rb + len); } arrayMove(arr, lb, mid - 1, mid, le); arrayMove(arr, rb, rb + len, rb + 1 + len, re); } </code></pre>
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    1. COHint: [In-place matrix transposition](http://en.wikipedia.org/wiki/In-place_matrix_transposition)
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