DAG Shortest Path in C#

using System;
// DAG Shortest Path in C#
//
// PURPOSE
// A directed acyclic graph permits shortest-path relaxation in topological order even when
// weights are negative.
//
// METHOD
// Use Kahn ordering and relax each outgoing edge when removing its source. Detect a cycle if
// not all vertices are processed.
//
// COMPLEXITY
// O(n squared) time with a dense matrix and O(n) auxiliary space.
//
// CONTRACT
// Flattened matrix uses INF=1000000000 for missing edges. Diagonal must be INF (no self-
// loops). Finite sums stay strictly between -INF and INF. Returns INF if unreachable, -INF
// if cyclic.
// 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 dag_shortest_path(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[] degree = new int[alg_size(n)];
            int[] distance = new int[alg_size(n)];
            int[] queue = new int[alg_size(n)];
            int head = 0;
            int tail = 0;
            int u = 0;
            int v = 0;
            while ((u < n)) {
                distance[u] = 1000000000;
                v = 0;
                while ((v < n)) {
                    if ((graph[((u * n) + v)] != 1000000000)) {
                        degree[v] = (degree[v] + 1);
                    }
                    v = (v + 1);
                }
                u = (u + 1);
            }
            distance[source] = 0;
            v = 0;
            while ((v < n)) {
                if ((degree[v] == 0)) {
                    queue[tail] = v;
                    tail = (tail + 1);
                }
                v = (v + 1);
            }
            while ((head < tail)) {
                u = queue[head];
                head = (head + 1);
                v = 0;
                while ((v < n)) {
                    if ((graph[((u * n) + v)] != 1000000000)) {
                        if ((distance[u] != 1000000000)) {
                            distance[v] = Math.Min(distance[v], (distance[u] + graph[((u * n) + v)]));
                        }
                        degree[v] = (degree[v] - 1);
                        if ((degree[v] == 0)) {
                            queue[tail] = v;
                            tail = (tail + 1);
                        }
                    }
                    v = (v + 1);
                }
            }
            if ((tail != n)) {
                return (-1000000000);
            }
            return distance[target];
        }
    }

    static void Main() {
        int[] graph = new int[] {1000000000, 4, 10, 1000000000, 1000000000, -2, 1000000000, 1000000000, 1000000000};
        int n = 3;
        int source = 0;
        int target = 2;
        int result = dag_shortest_path(graph, n, source, target);
        Console.WriteLine(result);
    }
}