Iterative Segment Tree Build in Python

from bisect import bisect_left

# Iterative Segment Tree Build in Python
#
# PURPOSE
# An iterative sum segment tree stores leaves in the second half of a flat array and parents
# in the first half.
#
# METHOD
# Copy values into tree[n+i], then compute every internal node from its two children in
# descending index order.
#
# COMPLEXITY
# O(n) time and O(1) auxiliary space beyond caller-owned tree.
#
# CONTRACT
# n>=1, tree length is 2*n. Build once and reuse for point assignments and half-open range
# queries. Sums must fit.
# 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: 0.
# Expected tree after call: [0, 10, 3, 7, 1, 2, 3, 4].
# 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 segment_build(a: list[int], tree: list[int]) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    alg_require(isinstance(tree, list) and len(tree) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    alg_require(len(tree) == 2 * n)
    alg_require(n >= 1)
    i: int = 0
    tree[0] = 0
    while i < n:
        tree[n + i] = a[i]
        i += 1
    i = n - 1
    while i > 0:
        tree[i] = tree[2 * i] + tree[2 * i + 1]
        i -= 1
    return 0

a = [1, 2, 3, 4]
tree = [0, 0, 0, 0, 0, 0, 0, 0]
result = segment_build(a, tree)
print(result)
# Expected tree: [0, 10, 3, 7, 1, 2, 3, 4]
print(tree)