Brian Kernighan Population Count in Python

from bisect import bisect_left

# Brian Kernighan Population Count in Python
#
# PURPOSE
# The expression n AND (n-1) clears the lowest set bit. Repeating it counts the ones in a
# nonnegative integer without visiting zero bits individually.
#
# METHOD
# Clear one set bit per iteration and increment the counter. The loop stops exactly when all
# original set bits have been removed.
#
# COMPLEXITY
# O(k) iterations for k set bits and O(1) auxiliary space under fixed-width arithmetic.
#
# CONTRACT
# n must be nonnegative. Negative integers have different width/sign behavior between
# languages and are excluded.
# 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.
# 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 population_count(n: int) -> int:
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    alg_require(n >= 0)
    count: int = 0
    while n != 0:
        n = n & n - 1
        count += 1
    return count

n = 0
result = population_count(n)
print(result)