I don’t know how to work on clojure, but I think I understand what you are looking for.
Here is some pseudo code. The stack in my pseudo-code looks like a stateful object, but it's possible to use an immutable one. It uses something like O (tree depth * max children per bunch of node).
walk_tree(TreeNode node) {
stack = new Stack<Pair<TreeNode, Boolean>>();
push(Pair(node, True), stack)
walk_tree_aux(stack);
}
walk_tree_aux(Stack<Pair<TreeNode, Boolean>> stack) { -- this should be tail-recursive
if stack is empty, return;
let (topnode, topflag) = pop(stack);
if (topflag is true) {
push Pair(topnode, False) onto stack);
for each child of topnode, in reverse order:
push(Pair(child, True)) onto stack
walk_tree_aux(stack);
} else { -- topflag is false
process(topnode)
walk_tree_aux(stack);
}
}
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