Dijkstra Shortest Path in C#

using System;
// Dijkstra Shortest Path in C#
//
// PURPOSE
// Dijkstra repeatedly settles the unsettled vertex with smallest tentative distance.
// Nonnegative edge weights ensure that distance can never improve later.
//
// METHOD
// Initialize source distance zero. Select the unused minimum-distance vertex by scanning,
// stop if none is reachable, and relax all its outgoing edges.
//
// COMPLEXITY
// O(n squared) time and O(n) auxiliary space for this dense-graph matrix version. A heap
// plus adjacency lists gives a different bound.
//
// CONTRACT
// Flattened n by n weight matrix; -1 means no edge, other weights >= 0. n >= 1. Every finite
// path must be < 1,000,000,000; additions must fit. Returns -1 if unreachable.
// 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: 6.
// 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 dijkstra(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)));
            alg_require((n >= 1));
            for (int alg_i = 0; alg_i < graph.Length; alg_i++) {
                int alg_value = graph[alg_i];
                alg_require(((alg_value >= (-1)) && (alg_value < 1000000000)));
            }
            int[] distance = new int[alg_size(n)];
            int[] used = new int[alg_size(n)];
            int i = 0;
            int v = 0;
            int u = 0;
            int best = 0;
            while ((i < n)) {
                distance[i] = 1000000000;
                i = (i + 1);
            }
            distance[source] = 0;
            i = 0;
            while ((i < n)) {
                u = (-1);
                best = 1000000000;
                v = 0;
                while ((v < n)) {
                    if (((used[v] == 0) && (distance[v] < best))) {
                        best = distance[v];
                        u = v;
                    }
                    v = (v + 1);
                }
                if ((u == (-1))) {
                    break;
                }
                used[u] = 1;
                v = 0;
                while ((v < n)) {
                    if ((graph[((u * n) + v)] >= 0)) {
                        distance[v] = Math.Min(distance[v], (distance[u] + graph[((u * n) + v)]));
                    }
                    v = (v + 1);
                }
                i = (i + 1);
            }
            if ((distance[target] == 1000000000)) {
                return (-1);
            }
            return distance[target];
        }
    }

    static void Main() {
        int[] graph = new int[] {0, 4, 10, -1, 0, 2, -1, -1, 0};
        int n = 3;
        int source = 0;
        int target = 2;
        int result = dijkstra(graph, n, source, target);
        Console.WriteLine(result);
    }
}