Bellman Ford Shortest Path in C#

using System;
// Bellman Ford Shortest Path in C#
//
// PURPOSE
// Bellman-Ford permits negative edge weights and detects negative cycles reachable from the
// source. Repeated edge relaxation finds progressively longer optimal paths.
//
// METHOD
// Relax every edge up to n-1 times, stopping early if nothing changes. Perform one extra
// pass to detect a reachable negative cycle. Guard unreachable endpoints before adding
// weights.
//
// COMPLEXITY
// O(VE) time and O(V) auxiliary space.
//
// CONTRACT
// Edge arrays from_vertex, to_vertex, weight each have m entries; n >= 1. Finite distances
// and all relaxed sums stay strictly between -1,000,000,000 and 1,000,000,000. Returns
// distance, INF if unreachable, or -INF for any reachable negative cycle (even if it cannot
// reach target).
// 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 bellman_ford(ReadOnlySpan<int> from_vertex, ReadOnlySpan<int> to_vertex, ReadOnlySpan<int> weight, int n, int source, int target) {
        checked {
            int m = from_vertex.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require(((m >= 0) && (m <= 1000000)));
            alg_require((from_vertex.Length == m));
            alg_require((to_vertex.Length == m));
            alg_require((weight.Length == m));
            alg_require(((n >= 1) && (source >= 0) && (source < n)));
            alg_require(((target >= 0) && (target < n)));
            for (int alg_i = 0; alg_i < from_vertex.Length; alg_i++) {
                int alg_value = from_vertex[alg_i];
                alg_require(((alg_value >= 0) && (alg_value < n)));
            }
            for (int alg_i = 0; alg_i < to_vertex.Length; alg_i++) {
                int alg_value = to_vertex[alg_i];
                alg_require(((alg_value >= 0) && (alg_value < n)));
            }
            int[] distance = new int[alg_size(n)];
            int i = 0;
            int edge = 0;
            int iteration = 0;
            int changed = 0;
            int u = 0;
            int v = 0;
            while ((i < n)) {
                distance[i] = 1000000000;
                i = (i + 1);
            }
            distance[source] = 0;
            while ((iteration < (n - 1))) {
                changed = 0;
                edge = 0;
                while ((edge < m)) {
                    u = from_vertex[edge];
                    v = to_vertex[edge];
                    if (((distance[u] != 1000000000) && ((distance[u] + weight[edge]) < distance[v]))) {
                        distance[v] = (distance[u] + weight[edge]);
                        changed = 1;
                    }
                    edge = (edge + 1);
                }
                if ((changed == 0)) {
                    break;
                }
                iteration = (iteration + 1);
            }
            edge = 0;
            while ((edge < m)) {
                u = from_vertex[edge];
                v = to_vertex[edge];
                if (((distance[u] != 1000000000) && ((distance[u] + weight[edge]) < distance[v]))) {
                    return (-1000000000);
                }
                edge = (edge + 1);
            }
            return distance[target];
        }
    }

    static void Main() {
        int[] from_vertex = new int[] {0, 1, 0};
        int[] to_vertex = new int[] {1, 2, 2};
        int[] weight = new int[] {4, -2, 9};
        int n = 3;
        int source = 0;
        int target = 2;
        int result = bellman_ford(from_vertex, to_vertex, weight, n, source, target);
        Console.WriteLine(result);
    }
}