Kahn Topological Cycle Detection in C#

using System;
// Kahn Topological Cycle Detection in C#
//
// PURPOSE
// Kahn algorithm repeatedly removes vertices with no incoming edges. A directed graph has a
// topological ordering exactly when all vertices can be removed this way.
//
// METHOD
// Compute indegrees, queue every zero-indegree vertex, then remove its outgoing edges.
// Enqueue a neighbor when its indegree becomes zero. Compare the number removed with n.
//
// COMPLEXITY
// O(n squared) time with an adjacency matrix and O(n) auxiliary space. Adjacency lists give
// O(V+E).
//
// CONTRACT
// Flattened n by n 0/1 directed matrix. Returns 1 for a DAG and 0 for a cycle. Empty graph
// is a DAG. This variant reports existence rather than returning an ordering.
// 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 is_dag(ReadOnlySpan<int> graph, int n) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((graph.Length == (n * n)));
            int[] indegree = new int[alg_size((n + 1))];
            int[] queue = new int[alg_size((n + 1))];
            int u = 0;
            int v = 0;
            int head = 0;
            int tail = 0;
            while ((u < n)) {
                v = 0;
                while ((v < n)) {
                    if ((graph[((u * n) + v)] != 0)) {
                        indegree[v] = (indegree[v] + 1);
                    }
                    v = (v + 1);
                }
                u = (u + 1);
            }
            v = 0;
            while ((v < n)) {
                if ((indegree[v] == 0)) {
                    queue[tail] = v;
                    tail = (tail + 1);
                }
                v = (v + 1);
            }
            while ((head < tail)) {
                u = queue[head];
                head = (head + 1);
                v = 0;
                while ((v < n)) {
                    if ((graph[((u * n) + v)] != 0)) {
                        indegree[v] = (indegree[v] - 1);
                        if ((indegree[v] == 0)) {
                            queue[tail] = v;
                            tail = (tail + 1);
                        }
                    }
                    v = (v + 1);
                }
            }
            if ((tail == n)) {
                return 1;
            }
            return 0;
        }
    }

    static void Main() {
        int[] graph = new int[] {0, 1, 0, 0, 0, 1, 0, 0, 0};
        int n = 3;
        int result = is_dag(graph, n);
        Console.WriteLine(result);
    }
}