Directed Cycle Detection by DFS in C#

using System;
// Directed Cycle Detection by DFS in C#
//
// 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
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 1.
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int directed_cycle(ReadOnlySpan<int> graph, int n) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((graph.Length == (n * n)));
            int[] color = new int[alg_size((n + 1))];
            int[] stack = new int[alg_size((n + 1))];
            int[] next_vertex = new int[alg_size((n + 1))];
            int source = 0;
            int top = 0;
            int u = 0;
            int v = 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 = (top - 1);
                        } else {
                            v = next_vertex[u];
                            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 = (top + 1);
                                }
                            }
                        }
                    }
                }
                source = (source + 1);
            }
            return 0;
        }
    }

    static void Main() {
        int[] graph = new int[] {0, 1, 1, 0};
        int n = 2;
        int result = directed_cycle(graph, n);
        Console.WriteLine(result);
    }
}