Kosaraju Strongly Connected Components in C#

using System;
// Kosaraju Strongly Connected Components in C#
//
// PURPOSE
// Strongly connected components group vertices that can reach each other in both directions.
//
// METHOD
// First perform iterative DFS to record finishing order. Traverse vertices in reverse
// finishing order using incoming edges, counting each newly discovered component.
//
// COMPLEXITY
// O(n squared) time for the dense matrix and O(n) auxiliary space.
//
// CONTRACT
// Flattened n by n directed 0/1 matrix. Returns number of components; empty graph returns
// zero.
// 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: 2.
// 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 scc_count(ReadOnlySpan<int> graph, int n) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((graph.Length == (n * n)));
            int[] seen = new int[alg_size((n + 1))];
            int[] stack = new int[alg_size((n + 1))];
            int[] next_vertex = new int[alg_size((n + 1))];
            int[] order = new int[alg_size((n + 1))];
            int source = 0;
            int top = 0;
            int finished = 0;
            int u = 0;
            int v = 0;
            int count = 0;
            while ((source < n)) {
                if ((seen[source] == 0)) {
                    stack[0] = source;
                    top = 1;
                    seen[source] = 1;
                    while ((top > 0)) {
                        u = stack[(top - 1)];
                        if ((next_vertex[u] == n)) {
                            order[finished] = u;
                            finished = (finished + 1);
                            top = (top - 1);
                        } else {
                            v = next_vertex[u];
                            next_vertex[u] = (next_vertex[u] + 1);
                            if (((graph[((u * n) + v)] != 0) && (seen[v] == 0))) {
                                seen[v] = 1;
                                stack[top] = v;
                                top = (top + 1);
                            }
                        }
                    }
                }
                source = (source + 1);
            }
            source = 0;
            while ((source < n)) {
                seen[source] = 0;
                source = (source + 1);
            }
            while ((finished > 0)) {
                finished = (finished - 1);
                source = order[finished];
                if ((seen[source] == 0)) {
                    count = (count + 1);
                    stack[0] = source;
                    top = 1;
                    seen[source] = 1;
                    while ((top > 0)) {
                        top = (top - 1);
                        u = stack[top];
                        v = 0;
                        while ((v < n)) {
                            if (((graph[((v * n) + u)] != 0) && (seen[v] == 0))) {
                                seen[v] = 1;
                                stack[top] = v;
                                top = (top + 1);
                            }
                            v = (v + 1);
                        }
                    }
                }
            }
            return count;
        }
    }

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