Iterative Binary Tree Preorder in Python

from bisect import bisect_left

# Iterative Binary Tree Preorder in Python
#
# PURPOSE
# Preorder traversal visits each binary-tree node once without recursion.
#
# METHOD
# Keep a stack of nodes and visit states. State zero descends left, state one descends
# right, and state two exits. Emit the node at the traversal-specific state.
#
# COMPLEXITY
# O(n) time and O(n) allocated stack space; live stack usage is O(tree height).
#
# CONTRACT
# Parallel left_child and right_child arrays contain -1 or node IDs. root=-1 means empty.
# The structure must be a valid tree, not cyclic or shared. output has n entries; writes
# node IDs and returns visited count.
# Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
# counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
# Sorted order, correct tree topology, and caller-owned data-structure invariants are
# preconditions; checking them on every query would change query complexity.
# Scalar and shape checks are included. Value-range checks are included where needed to
# prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
# workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
# uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
# partly updated after arithmetic failure. These are single-threaded, in-memory
# implementations.
#
# LANGUAGE DETAILS
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 3.
# Expected output after call: [0, 1, 2].
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def tree_preorder(left_child: list[int], right_child: list[int], root: int, output: list[int]) -> int:
    alg_require(isinstance(left_child, (list, tuple)) and len(left_child) <= 1000000)
    alg_require(isinstance(right_child, (list, tuple)) and len(right_child) <= 1000000)
    alg_require(type(root) is int and -2147483648 <= root <= 2147483647)
    alg_require(isinstance(output, list) and len(output) <= 1000000)
    n: int = len(left_child)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(left_child) == n)
    alg_require(len(right_child) == n)
    alg_require(len(output) == n)
    alg_require(root >= -1 and root < n)
    for value in left_child:
        alg_require(value >= -1 and value < n)
    for value in right_child:
        alg_require(value >= -1 and value < n)
    stack: list[int] = [0] * alg_size(n + 1)
    state: list[int] = [0] * alg_size(n + 1)
    top: int = 0
    u: int = 0
    phase: int = 0
    count: int = 0
    if root == -1:
        return 0
    stack[0] = root
    top = 1
    while top > 0:
        u = stack[top - 1]
        phase = state[top - 1]
        if phase == 0:
            output[count] = u
            count += 1
        if phase == 0:
            state[top - 1] = 1
            if left_child[u] != -1:
                stack[top] = left_child[u]
                state[top] = 0
                top += 1
        elif phase == 1:
            state[top - 1] = 2
            if right_child[u] != -1:
                stack[top] = right_child[u]
                state[top] = 0
                top += 1
        else:
            top -= 1
    return count

left_child = [1, -1, -1]
right_child = [2, -1, -1]
root = 0
output = [0, 0, 0]
result = tree_preorder(left_child, right_child, root, output)
print(result)
# Expected output: [0, 1, 2]
print(output)