Depth First Search Reachability in C#

using System;
// Depth First Search Reachability in C#
//
// PURPOSE
// DFS follows a branch deeply before returning to pending branches. An explicit stack avoids
// language recursion limits for reachability exploration.
//
// METHOD
// Push the source and mark it. Pop a vertex, count it, then mark and push each unseen
// neighbor. Marking when pushed bounds stack entries to at most n.
//
// COMPLEXITY
// O(n squared) time with a matrix and O(n) auxiliary space. Adjacency lists reduce traversal
// to O(V+E).
//
// CONTRACT
// Flattened n by n 0/1 matrix, n >= 1, valid source. Returns the number of reachable
// vertices INCLUDING source. Directed edges supported.
// 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: 3.
// 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 dfs_reachable(ReadOnlySpan<int> graph, int n, int source) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((graph.Length == (n * n)));
            alg_require(((n >= 1) && (source >= 0) && (source < n)));
            int[] seen = new int[alg_size(n)];
            int[] stack = new int[alg_size(n)];
            int top = 1;
            int count = 0;
            int u = 0;
            int v = 0;
            stack[0] = source;
            seen[source] = 1;
            while ((top > 0)) {
                top = (top - 1);
                u = stack[top];
                count = (count + 1);
                v = 0;
                while ((v < n)) {
                    if (((graph[((u * n) + v)] != 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, 0, 0, 1, 0, 0, 0};
        int n = 3;
        int source = 0;
        int result = dfs_reachable(graph, n, source);
        Console.WriteLine(result);
    }
}