Push the right child before the left child so that the LIFO stack exposes the left child first:Let be the sequence of labels in the preorder traversal of . If the abstract pending stack, top first, is , the loop invariant is that the output already printed, followed by , is the required full output. Each pending root is non-null, and its subtree is still unvisited. This is the pending-work form of explicit-stack depth-first tree traversal.
def preorderIterative(t: Tree): Unit = {
val pending = new Stack
if (t != null) pending.push(t)
while (!pending.isEmpty) {
val u = pending.pop
println(u.datum)
if (u.right != null) pending.push(u.right)
if (u.left != null) pending.push(u.left)
}
}One iteration discharges the first root's own label and replaces its remaining obligation by the left subtree followed by the right subtree. The push order makes that precisely the new top-first pending order. Thus the loop invariant is preserved. The loop variant is the sum of the numbers of vertices in all pending subtrees; it decreases by exactly one per iteration, even if the number of stack entries increases. When the stack is empty there is no remaining output obligation, proving correctness and termination. This assumes a finite genuine binary tree and, as permitted, sufficient stack capacity. Each vertex is pushed and popped once, giving time and pending references for binary tree height .
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