Warshall Transitive Closure in Python

from bisect import bisect_left

# Warshall Transitive Closure in Python
#
# PURPOSE
# Transitive closure records whether every vertex can reach every other vertex. Warshall is
# the Boolean counterpart of Floyd-Warshall.
#
# METHOD
# Mark each vertex reachable from itself. For every intermediate k, mark i-to-j reachable
# whenever i reaches k and k reaches j. The matrix accumulates reachability through the
# processed intermediates.
#
# COMPLEXITY
# O(n cubed) time and O(1) auxiliary space beyond the caller-owned matrix.
#
# CONTRACT
# Mutates a flattened n by n 0/1 adjacency matrix to reflexive transitive closure. Returns
# 0. A vertex reaches itself via a path of zero edges.
# 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 graph after call: [1, 1, 1, 0, 1, 1, 0, 0, 1].
# 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 transitive_closure(graph: list[int], n: int) -> int:
    alg_require(isinstance(graph, list) and len(graph) <= 1000000)
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(graph) == n * n)
    i: int = 0
    j: int = 0
    k: int = 0
    while i < n:
        graph[i * n + i] = 1
        i += 1
    while k < n:
        i = 0
        while i < n:
            j = 0
            while j < n:
                if graph[i * n + k] != 0 and graph[k * n + j] != 0:
                    graph[i * n + j] = 1
                j += 1
            i += 1
        k += 1
    return 0

graph = [0, 1, 0, 0, 0, 1, 0, 0, 0]
n = 3
result = transitive_closure(graph, n)
print(result)
print(graph)
# Expected graph: [1, 1, 1, 0, 1, 1, 0, 0, 1]