Binary Search Tree Lookup in Python

from bisect import bisect_left

# Binary Search Tree Lookup in Python
#
# PURPOSE
# A binary search tree chooses a branch by comparing the target with the current node key.
#
# METHOD
# At each node return on equality, otherwise follow the left child for a smaller target or
# the right child for a larger target.
#
# COMPLEXITY
# O(height) time and O(1) auxiliary space; height is O(log n) only when the tree is
# balanced.
#
# CONTRACT
# keys,left_child,right_child have n entries; -1 means absent. Must be a valid BST. Returns
# node ID or -1.
# 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: 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 bst_lookup(keys: list[int], left_child: list[int], right_child: list[int], root: int, target: int) -> int:
    alg_require(isinstance(keys, (list, tuple)) and len(keys) <= 1000000)
    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(type(target) is int and -2147483648 <= target <= 2147483647)
    n: int = len(keys)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(keys) == n)
    alg_require(len(left_child) == n)
    alg_require(len(right_child) == 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)
    while root != -1:
        if keys[root] == target:
            return root
        if target < keys[root]:
            root = left_child[root]
        else:
            root = right_child[root]
    return -1

keys = [4, 2, 6]
left_child = [1, -1, -1]
right_child = [2, -1, -1]
root = 0
target = 6
result = bst_lookup(keys, left_child, right_child, root, target)
print(result)