Warshall Transitive Closure in C#

using System;
// Warshall Transitive Closure in C#
//
// PURPOSE
// Transitive closure records whether every vertex can reach every other vertex. Warshall is
// the Boolean counterpart of Floyd-Warshall.
//
// METHOD
// Mark each vertex reachable from itself. For every intermediate k, mark i-to-j reachable
// whenever i reaches k and k reaches j. The matrix accumulates reachability through the
// processed intermediates.
//
// COMPLEXITY
// O(n cubed) time and O(1) auxiliary space beyond the caller-owned matrix.
//
// CONTRACT
// Mutates a flattened n by n 0/1 adjacency matrix to reflexive transitive closure. Returns
// 0. A vertex reaches itself via a path of zero edges.
// 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: 0.
// Expected graph after call: [1, 1, 1, 0, 1, 1, 0, 0, 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 transitive_closure(Span<int> graph, int n) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((graph.Length == (n * n)));
            int i = 0;
            int j = 0;
            int k = 0;
            while ((i < n)) {
                graph[((i * n) + i)] = 1;
                i = (i + 1);
            }
            while ((k < n)) {
                i = 0;
                while ((i < n)) {
                    j = 0;
                    while ((j < n)) {
                        if (((graph[((i * n) + k)] != 0) && (graph[((k * n) + j)] != 0))) {
                            graph[((i * n) + j)] = 1;
                        }
                        j = (j + 1);
                    }
                    i = (i + 1);
                }
                k = (k + 1);
            }
            return 0;
        }
    }

    static void Main() {
        int[] graph = new int[] {0, 1, 0, 0, 0, 1, 0, 0, 0};
        int n = 3;
        int result = transitive_closure(graph, n);
        Console.WriteLine(result);
        Console.WriteLine("[" + string.Join(", ", graph) + "]");
        // Expected graph: [1, 1, 1, 0, 1, 1, 0, 0, 1]
    }
}