title: Sorted list to complete BST array representation
body: <p>I'm wondering whether there is a mapping between a sorted array (e.g., [1, 2, 3, 4, 5, 6]) and the representation that one obtains when one constructs a complete binary search tree from this sorted array, and expresses said binary search tree as an array (e.g., [4, 2, 6, 1, 3, 5], see graphic below)?</p>
  
  <pre><code>     4
    2     6
  1   3  5
  </code></pre>
  
  <p>Here's some more context: It is well known that one can take a sorted array and construct a complete binary search tree from it (there is a unique representation). A recursive algorithm is: find the appropriate mid (this is actually quite tricky), treat it as the root, then
  recurse on left subarray and right subarray. From the resulting BST, one can perform a level-order traversal (basically breadth first search) to construct the array representation of the complete BST. </p>
  
  <p>The reason I ask this is that this mapping is independent of the content of the array: it depends only on its length. Therefore I get the feeling that it should be possible to concisely express both arrays as a function of each other.</p>
  
  <p>Any thoughts?</p>