Prefix Sum Range Query in Python

from bisect import bisect_left

# Prefix Sum Range Query in Python
#
# PURPOSE
# Prefix sums turn a range sum into a subtraction. The preprocessed prefix at index i stores
# the sum of all elements before i.
#
# METHOD
# Build prefix[i+1] = prefix[i] + a[i]. For inclusive bounds left and right, subtract
# prefix[left] from prefix[right+1]. Build once and reuse the prefix for many queries in a
# real application.
#
# COMPLEXITY
# O(n) preprocessing and O(n) space; each query after preprocessing is O(1). This self-
# contained function includes preprocessing on every call.
#
# CONTRACT
# 0 <= left <= right < n. Returns the inclusive range sum. All prefix totals 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: 6.
# 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 range_sum(a: list[int], left: int, right: int) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    alg_require(type(left) is int and -2147483648 <= left <= 2147483647)
    alg_require(type(right) is int and -2147483648 <= right <= 2147483647)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    alg_require(left >= 0 and left <= right and (right < n))
    prefix: list[int] = [0] * alg_size(n + 1)
    i: int = 0
    while i < n:
        prefix[i + 1] = prefix[i] + a[i]
        i += 1
    return prefix[right + 1] - prefix[left]

a = [2, 4, -1, 3]
left = 1
right = 3
result = range_sum(a, left, right)
print(result)