Complete Binary Search Tree

Given a list of numbers, we could create a complete binary search tree.

• Sort A.
• Pick i as the appropriate halfway point. Let i be the root.
• Make a complete binary search tree out of A[1] through A[i-1] and make it the left subtree. Do the same with A[i+1] through A[n] and make it the right subtree.

Extra credit: Give a rule for picking i. Show that resulting tree is complete (i.e., deepest level is ``left justified''.)

Running time?