Bipartite Graph Coloring in Python

from bisect import bisect_left

# Bipartite Graph Coloring in Python
#
# PURPOSE
# A graph is bipartite when its vertices can be colored with two colors so that each edge
# joins opposite colors.
#
# METHOD
# BFS every uncolored component. Give neighbors the opposite color and reject any edge
# joining equal colors.
#
# COMPLEXITY
# O(n squared) time with this dense matrix, O(n) auxiliary space.
#
# CONTRACT
# Symmetric flattened n by n 0/1 matrix. Returns 1 or 0. Self-loops make a graph non-
# bipartite.
# 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: 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 is_bipartite(graph: list[int], n: int) -> int:
    alg_require(isinstance(graph, (list, tuple)) 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)
    color: list[int] = [0] * alg_size(n + 1)
    queue: list[int] = [0] * alg_size(n + 1)
    source: int = 0
    head: int = 0
    tail: int = 0
    u: int = 0
    v: int = 0
    while source < n:
        if color[source] == 0:
            head = 0
            tail = 1
            queue[0] = source
            color[source] = 1
            while head < tail:
                u = queue[head]
                head += 1
                v = 0
                while v < n:
                    if graph[u * n + v] != 0:
                        if color[v] == color[u]:
                            return 0
                        if color[v] == 0:
                            color[v] = 3 - color[u]
                            queue[tail] = v
                            tail += 1
                    v += 1
        source += 1
    return 1

graph = [0, 1, 1, 0]
n = 2
result = is_bipartite(graph, n)
print(result)