Directed Cycle Detection by DFS in Python

from bisect import bisect_left

# Directed Cycle Detection by DFS in Python
#
# PURPOSE
# DFS detects a directed cycle when an edge points to a vertex still active in the current
# search path.
#
# METHOD
# Use an explicit stack and per-vertex next-neighbor positions. Mark vertices active on
# entry and finished on exit. An edge to an active vertex is a back edge.
#
# COMPLEXITY
# O(n squared) matrix traversal time and O(n) auxiliary space.
#
# CONTRACT
# Flattened n by n 0/1 directed adjacency matrix; returns 1 if a cycle exists, otherwise 0.
# 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 directed_cycle(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)
    stack: list[int] = [0] * alg_size(n + 1)
    next_vertex: list[int] = [0] * alg_size(n + 1)
    source: int = 0
    top: int = 0
    u: int = 0
    v: int = 0
    while source < n:
        if color[source] == 0:
            top = 1
            stack[0] = source
            color[source] = 1
            while top > 0:
                u = stack[top - 1]
                if next_vertex[u] == n:
                    color[u] = 2
                    top -= 1
                else:
                    v = next_vertex[u]
                    next_vertex[u] += 1
                    if graph[u * n + v] != 0:
                        if color[v] == 1:
                            return 1
                        if color[v] == 0:
                            color[v] = 1
                            stack[top] = v
                            top += 1
        source += 1
    return 0

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