Dijstra(C#)

支持有向与无向图

DijistraSeach.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Dijistra
{
    public static class DijistraSeach
    {
        public class SearchResult
        {
            public int Distance { get; private set; }
            public int[] Route { get; set; }
            public SearchResult(int distance, int[] route)
            {
                Distance = distance;
                Route = route;
            }
        }

        /// <summary>
        /// 获取正确的顺序<para/>
        /// 比如footPrint为<para/>
        /// [0] = 0<para/>
        /// [1] = 0<para/>
        /// [2] = 3<para/>
        /// [3] = 0<para/>
        /// [4] = 2<para/>
        /// 从最后一行开始，[4] = 2，意味着[4]的前一个节点为[2]，然后看[2] = 3这一行，2的前节点为3，如此循环直到起点。
        /// </summary>
        /// <param name="footPrint">value -> index</param>
        /// <param name="startPoint"></param>
        /// <returns></returns>
        private static int[] findRoute(int[] footPrint, int startPoint = 0)
        {
            var mapSize = footPrint.Length;
            // 反向路径
            var reversedRoute = new int[mapSize];
            // 反向路径中的当前操作序号
            int routeIndex = 0;

            // 添加终点
            reversedRoute[routeIndex] = mapSize - 1;

            routeIndex++;

            // 找到最末节点的前节点
            int previousIndex = footPrint[mapSize - 1];

            // 如果不是起点的话
            while (previousIndex != startPoint)
            {
                // 路径不存在
                if (previousIndex == -1)
                    return null;

                // 记录此节点并继续查找前节点
                reversedRoute[routeIndex] = previousIndex;
                routeIndex++;
                previousIndex = footPrint[previousIndex];
            }

            // 添加起点
            reversedRoute[routeIndex] = startPoint;

            // 将反向路径反向
            var route = new List<int>(mapSize);
            for (int i = routeIndex; i >= 0; i--)
            {
                route.Add(reversedRoute[i]);
            }
            return route.ToArray();
        }

        /// <summary>
        /// search for the shortest route.
        /// </summary>
        /// <param name="routes">an array which contains {pointA, pointB, distance}
        /// <para/>e.g.
        /// <para/>var map = new[] {
        /// <para/>    new []{0,1,10},
        /// <para/>    new []{0,3,30},
        /// <para/>    new []{0,4,100},
        /// <para/>    new []{1,2,50},
        /// <para/>    new []{2,4,10},
        /// <para/>    new []{3,2,20},
        /// <para/>    new []{3,4,60},
        /// <para/>};
        /// </param>
        /// <param name="mapSize">size</param>
        /// <param name="startPoint"></param>
        /// <param name="directional"></param>
        /// <returns></returns>
        public static SearchResult Search(int[][] routes, int mapSize, int startPoint , bool directional)
        {
            // record all minIndex found during the searching progress.
            var footPrint = new int[mapSize];
            // to avoid dead searching loop.
            var visted = new bool[mapSize];
            // accumulated distance from startPoint to each index.
            var milestones = new int[mapSize];

            // initialize map.
            var map = new int[mapSize, mapSize];
            for (int i = 0; i < mapSize; i++)
            {
                for (int j = 0; j < mapSize; j++)
                {
                    map[i, j] = i == j? 0 : int.MaxValue;
                }
            }

            // build map.
            foreach (var route in routes)
            {
                map[route[0], route[1]] = route[2];

                if (!directional)
                {
                    // make the map non-directional.
                    map[route[1], route[0]] = route[2];
                }
            }

            // initialize milestones by distance between each node and startPoint.
            for (int i = 0; i < mapSize; i++)
            {
                milestones[i] = map[startPoint, i];
                // wether i is connected to startPoint or not;
                if (milestones[i] != int.MaxValue)
                {
                    footPrint[i] = startPoint;
                }
                else
                {
                    footPrint[i] = -1;
                }
            }

            // start searching.
            for (int j = 0; j < mapSize; j++)
            {
                // find the nearest from this index.
                // milestones has already been updated to fit the minIndex.
                int localMin = int.MaxValue, minIndex = startPoint;
                for (int i = 0; i < mapSize; i++)
                {
                    if (!visted[i] && milestones[i] < localMin)
                    {
                        minIndex = i;
                        localMin = milestones[i];
                    }
                }

                visted[minIndex] = true;

                // update milestones.
                for (int i = 0; i < mapSize; i++)
                {
                    // index not connected to minIndex is not connected to 
                    if (map[minIndex, i] == int.MaxValue) continue;
                    if (visted[i]) continue;

                    // accumulate distance from startPoint to minIndex;
                    var newDis = milestones[minIndex] + map[minIndex, i];
                    if ((newDis < milestones[i]))
                    {
                        milestones[i] = newDis;
                        footPrint[i] = minIndex;
                    }
                }
            }

            // the end is beyond reach.
            if (milestones[mapSize - 1] == int.MaxValue)
                return null;

            var resultRoute = findRoute(footPrint, startPoint);
            var result = new SearchResult(milestones[mapSize - 1], resultRoute);
            return result;
        }
    }
}

Main.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Dijistra
{
    class Program
    {
        static void Main(string[] args)
        {
            // 无向图
            // 使用此外图时，需将DijistraSeach.Search的directional参数设为false，mapSize=5
            var nonDirectionalMap = new[] {
                new []{0,1,10},
                new []{0,3,30},
                new []{0,4,100},
                new []{1,2,50},
                new []{2,4,10},
                new []{3,2,20},
                new []{3,4,60},
            };

            // 有向图
            // 使用此外图时，需将DijistraSeach.Search的directional参数设为true，mapSize=2
            var directionalMap = new[]{
                new []{1, 0, 10},
                new []{0, 1, 11},
            };

            var result = DijistraSeach.Search(
                routes: nonDirectionalMap,
                mapSize: 5,
                startPoint: 0,
                directional: false
                );

            if (result == null)
            {
                Console.WriteLine("Can't find the route.");
            }
            else
            {
                Console.WriteLine(
                "Shortest distance is {0}
route : {1}
",
                result.Distance,
                String.Join("->", result.Route)
                );
            }
            
        }
    }
}