Iterative Segment Tree Range Sum in Python

from bisect import bisect_left

# Iterative Segment Tree Range Sum in Python
#
# PURPOSE
# A segment tree range query combines the small number of disjoint nodes covering a half-
# open interval.
#
# METHOD
# Move both endpoints to leaves. Include a left endpoint when it is a right child and a
# right endpoint when it is about to cross a left child, then move both up.
#
# COMPLEXITY
# O(log n) time, O(1) auxiliary space.
#
# CONTRACT
# tree has 2*n entries; n>=1, 0<=left<=right<=n. Returns sum in [left,right). Empty range
# returns zero.
# 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: 5.
# 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_sum(tree: list[int], left: int, right: int) -> int:
    alg_require(isinstance(tree, (list, tuple)) and len(tree) <= 1000000)
    alg_require(type(left) is int and -2147483648 <= left <= 2147483647)
    alg_require(type(right) is int and -2147483648 <= right <= 2147483647)
    n: int = len(tree) // 2
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(tree) == 2 * n)
    alg_require(n >= 1 and left >= 0 and (left <= right) and (right <= n))
    left += n
    right += n
    total: int = 0
    while left < right:
        if left % 2 == 1:
            total += tree[left]
            left += 1
        if right % 2 == 1:
            right -= 1
            total += tree[right]
        left = left // 2
        right = right // 2
    return total

tree = [0, 10, 3, 7, 1, 2, 3, 4]
left = 1
right = 3
result = segment_sum(tree, left, right)
print(result)