Breadth First Search Shortest Path in C#

using System;
// Breadth First Search Shortest Path in C#
//
// PURPOSE
// BFS explores an unweighted graph one distance layer at a time. The first discovery of a
// vertex gives its shortest number of edges from the source.
//
// METHOD
// Put the source into a FIFO queue and mark its distance zero. Remove vertices in order and
// enqueue each undiscovered neighbor with distance one greater. Mark on enqueue so each
// vertex enters at most once.
//
// COMPLEXITY
// O(n squared) time with this adjacency matrix and O(n) auxiliary space. An adjacency-list
// implementation is O(V+E).
//
// CONTRACT
// graph is a flattened n by n 0/1 adjacency matrix, n >= 1, source and target are valid
// vertices. Directed edges are supported. Returns distance or -1.
// 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 bfs_distance(ReadOnlySpan<int> graph, int n, int source, int target) {
        checked {
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((graph.Length == (n * n)));
            alg_require(((n >= 1) && (source >= 0) && (source < n)));
            alg_require(((target >= 0) && (target < n)));
            int[] distance = new int[alg_size(n)];
            int[] queue = new int[alg_size(n)];
            int v = 0;
            int u = 0;
            int head = 0;
            int tail = 1;
            while ((v < n)) {
                distance[v] = (-1);
                v = (v + 1);
            }
            distance[source] = 0;
            queue[0] = source;
            while ((head < tail)) {
                u = queue[head];
                head = (head + 1);
                v = 0;
                while ((v < n)) {
                    if (((graph[((u * n) + v)] != 0) && (distance[v] == (-1)))) {
                        distance[v] = (distance[u] + 1);
                        queue[tail] = v;
                        tail = (tail + 1);
                    }
                    v = (v + 1);
                }
            }
            return distance[target];
        }
    }

    static void Main() {
        int[] graph = new int[] {0, 1, 0, 0, 0, 1, 0, 0, 0};
        int n = 3;
        int source = 0;
        int target = 2;
        int result = bfs_distance(graph, n, source, target);
        Console.WriteLine(result);
    }
}