Fenwick Prefix Sum in Python

from bisect import bisect_left

# Fenwick Prefix Sum in Python
#
# PURPOSE
# A Fenwick prefix query combines disjoint stored partial sums covering the requested
# prefix.
#
# METHOD
# Starting from the exclusive prefix endpoint, add the current partial sum and clear its
# lowest set bit to move to the preceding block.
#
# COMPLEXITY
# O(log n) time, O(1) auxiliary space.
#
# CONTRACT
# tree length is n+1, 0<=end<=n. Returns sum of original values in [0,end). Empty prefix
# 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: 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 fenwick_sum(tree: list[int], end: int) -> int:
    alg_require(isinstance(tree, (list, tuple)) and len(tree) <= 1000000)
    alg_require(type(end) is int and -2147483648 <= end <= 2147483647)
    n: int = len(tree) - 1
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(tree) == n + 1)
    alg_require(end >= 0 and end <= n)
    total: int = 0
    while end > 0:
        total += tree[end]
        end -= end & -end
    return total

tree = [0, 1, 3, 3, 10]
end = 3
result = fenwick_sum(tree, end)
print(result)