Iterative Segment Tree Point Assignment in Python

from bisect import bisect_left

# Iterative Segment Tree Point Assignment in Python
#
# PURPOSE
# A point assignment changes a leaf and recomputes only its ancestors.
#
# METHOD
# Write the new leaf value, move upward by dividing the index by two, and recompute each
# parent from its children.
#
# COMPLEXITY
# O(log n) time, O(1) auxiliary space.
#
# CONTRACT
# tree is an existing iterative sum tree of length 2*n; n>=1, 0<=index<n. Mutates tree;
# returns 0.
# 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, 17, 10, 7, 1, 9, 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_set(tree: list[int], index: int, value: int) -> int:
    alg_require(isinstance(tree, list) and len(tree) <= 1000000)
    alg_require(type(index) is int and -2147483648 <= index <= 2147483647)
    alg_require(type(value) is int and -2147483648 <= value <= 2147483647)
    n: int = len(tree) // 2
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(tree) == 2 * n)
    alg_require(n >= 1 and index >= 0 and (index < n))
    index += n
    tree[index] = value
    index = index // 2
    while index > 0:
        tree[index] = tree[2 * index] + tree[2 * index + 1]
        index = index // 2
    return 0

tree = [0, 10, 3, 7, 1, 2, 3, 4]
index = 1
value = 9
result = segment_set(tree, index, value)
print(result)
# Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
print(tree)