iterative postorder growing of trees, unknown size of tree

[chickenandfries]

Given an input of a string, how do i put its characters in a binary tree in iterative postorder? The length of the string is one less than a power of 2 (e.g. 0, 1, 3, 7, 15..), so the resulting tree would be a "full binary tree". The number of nodes in the tree should be the length of the string, so there should be no "empty nodes". I'm using C. I've done everything i can. Thanks.

[CMPITG]

I think the heap data structure (using array) should be suitable to use. Linked list is good, too.