最短路径:Dijkstra算法 C#

    class Program
    {
        const int u = 10000;

        static void Main(string[] args)
        {
            Console.WriteLine("各点距离矩阵如下:");
            Console.WriteLine("   A  B  C  D  E");
            Console.WriteLine("A  0  2  3  /  /");
            Console.WriteLine("B  2  0  3  5  2");
            Console.WriteLine("C  3  3  0  2  4");
            Console.WriteLine("D  /  5  2  0  1");
            Console.WriteLine("E  /  2  4  1  0");
            int[,] matrix = new int[5, 5] { { 0, 2, 3, u, u }, { 2, 0, 3, 5, 2 }, { 3, 3, 0, 2, 4 }, { u, 5, 2, 0, 1 }, { u, 2, 4, 1, 0 } };
            while (true)
            {
                Console.WriteLine("请输入要计算的起始点：");
                string a = Console.ReadLine();
                int start;
                switch (a.ToLower())
                {
                    default:
                    case "a":
                        start = 0;
                        break;
                    case "b":
                        start = 1;
                        break;
                    case "c":
                        start = 2;
                        break;
                    case "d":
                        start = 3;
                        break;
                    case "e":
                        start = 4;
                        break;
                }
                var list = Dijkstra(matrix, start);

                for (int i = 0; i < list.Count; i++)
                {
                    Console.WriteLine("从" + a.ToUpper() + "出发到" + i.IndexToChar() + "的最短距离为:" + list[i].Distance + ",最短路径为:" + list[i].Path);
                }
            }
        }

        public static List<ShortPath> Dijkstra(int[,] matrix, int start)
        {
            int n = matrix.GetLength(0);
            int[] visited = new int[n];
            var list = new List<ShortPath>();

            for (int i = 0; i < n; i++)
            {
                list.Add(new ShortPath() { Index = i, Name = start.IndexToChar() + "->" + i.IndexToChar(), Path = start.IndexToChar() + "->" + i.IndexToChar(), Distance = 0 });
            }
            visited[start] = 1;
            for (int i = 1; i < n; i++)
            {
                int k = -1;
                int dmin = u;
                for (int j = 0; j < n; j++)
                {
                    if (visited[j] == 0 && matrix[start, j] < dmin)
                    {
                        dmin = matrix[start, j];
                        k = j;
                    }
                }

                list[k].Distance = dmin;

                visited[k] = 1;
                for (int j = 0; j < n; j++)
                {
                    if (visited[j] == 0 && matrix[start, k] + matrix[k, j] < matrix[start, j])
                    {
                        matrix[start, j] = matrix[start, k] + matrix[k, j];
                        list[j].Path = list[k].Path + "->" + j.IndexToChar();
                    }
                }
            }

            return list;
        }
    }

    public static class Common
    {
        /// <summary>
        /// 索引转换字母
        /// </summary>
        /// <param name="index">当前索引</param>
        /// <param name="startIndex">起始索引 默认0</param>
        /// <returns></returns>
        public static char IndexToChar(this int index, int startIndex = 0)
        {
            return (char)('A' + index - startIndex);
        }
    }

    public class ShortPath
    {
        private int index;
        private string name;
        private string path;
        private int distance;

        public string Path { get => path; set => path = value; }
        public int Distance { get => distance; set => distance = value; }
        public string Name { get => name; set => name = value; }
        public int Index { get => index; set => index = value; }
    }