最优路径的一种算法（原创）

问题来自博问：http://q.cnblogs.com/q/28763/

给定的测试矩阵：

测试矩阵数据

1. public int[,] InitMap()
2. {
3.     //x-1,??-2,??-3,??????
4.     return new int[Width,Height]
5.                {
6.                    {-2, 1, 5, 2, 4, 5, 8, 2, 1},
7.                    {1, 5, 2, 4, 5, 8, 2, -1, 5},
8.                    {2, 7, 5, 2, 4, 5, -1, 2, 1},
9.                    {2, 1, 3, 2, -1, 0, 8, 7, 3},
10.                    {2, 1, 5, 1, 9, 5, 2, 2, 1},
11.                    {4, 8, 4, 3, 4, 2, 8, 2, 3},
12.                    {2, 1, 5, 6, 4, 5, 7, 4, 1},
13.                    {2, 8, 7, 2, 4, 5, 8, 2, 1},
14.                    {1, 5, 5, 4, 5, 6, 2, 2, -3}
15.                };
16. }

递归路径查找：

Code Snippet

1. public bool NextStep(int x,int y )
2. {
3.     if (x < 0 || x >=Width)
4.         return false;
5.     if(y<0||y>=Height)
6.         return false;
7.  
8.     //?????????1
9.     if(CurRoad.Count==KKCatStep+1)
10.         return false;
11.  
12.     int curScore = map[x, y];
13.     //?
14.     if(curScore==-1)
15.         return false;
16.     //??????
17.     if (CurRoad.Any(c => c.X == x && c.Y == y))
18.         return false;
19.  
20.     CurRoad.Push(new Coord(x,y));
21.  
22.     //?????????
23.     if (curScore == -3)
24.     {
25.         var score = CurRoad.Skip(1).Take(CurRoad.Count - 2).Sum(c => map[c.X, c.Y]);
26.         if(score>LastScore)
27.         {
28.             LastScore = score;
29.             var road = CurRoad.ToList();
30.             road.Reverse();
31.             NiceRoads.Add(road);
32.         }
33.  
34.         return true;
35.     }
36.     
37.     //???
38.  
39.     if (NextStep(x + 1, y))
40.         CurRoad.Pop();
41.     if(NextStep(x, y + 1))
42.         CurRoad.Pop();
43.     if(NextStep(x - 1, y))
44.         CurRoad.Pop();
45.     if(NextStep(x, y - 1))
46.         CurRoad.Pop();
47.     return true;
48. }

效率还不是很高，特别对更大的地图时算法还有待优化。

以下是完整的代码：

Code Snippet

1. using System;
2. using System.Collections.Generic;
3. using System.Linq;
4. using System.Text;
5. using Xunit;
6.  
7. namespace KKCatWalking
8. {
9.     public class Walking
10.     {
11.         protected int[,] map;
12.         const int Width= 9, Height = 9;
13.         private Stack<Coord> CurRoad = new Stack<Coord>();
14.         private List<List<Coord>> NiceRoads = new List<List<Coord>>();
15.         private int KKCatStep = 19;
16.         private int LastScore=0;
17.         public Walking()
18.         {
19.             map = InitMap();
20.  
21.         }
22.  
23.         [Fact]
24.         public void FindWays()
25.         {
26.             NextStep(0, 0);
27.             NiceRoads.TrimExcess();
28.             Console.WriteLine("KKCatStep:{0}\tTotal Roads:{1} MaxScore:{2}",KKCatStep,NiceRoads.Count,NiceRoads.Max(r=>r.Skip(1).Take(r.Count-2).Sum(c=>map[c.X,c.Y])));
29.             foreach(var r in NiceRoads.OrderByDescending(r=>r.Skip(1).Take(r.Count-2).Sum(c=>map[c.X,c.Y])).Take(20))
30.             {
31.                 int sum = 0;
32.                 foreach (var c in r)
33.                 {
34.                     Console .Write("{0},{1}\t",c.X,c.Y);
35.                     sum += map[c.X, c.Y];
36.                 }
37.                 Console.WriteLine("Score:{0}\t", sum+5);
38.                 Console.WriteLine();
39.             }
40.         }
41.  
42.         public bool NextStep(int x,int y )
43.         {
44.             if (x < 0 || x >=Width)
45.                 return false;
46.             if(y<0||y>=Height)
47.                 return false;
48.  
49.             //?????????1
50.             if(CurRoad.Count==KKCatStep+1)
51.                 return false;
52.  
53.             int curScore = map[x, y];
54.             //?
55.             if(curScore==-1)
56.                 return false;
57.             //??????
58.             if (CurRoad.Any(c => c.X == x && c.Y == y))
59.                 return false;
60.  
61.             CurRoad.Push(new Coord(x,y));
62.  
63.             //?????????
64.             if (curScore == -3)
65.             {
66.                 var score = CurRoad.Skip(1).Take(CurRoad.Count - 2).Sum(c => map[c.X, c.Y]);
67.                 if(score>LastScore)
68.                 {
69.                     LastScore = score;
70.                     var road = CurRoad.ToList();
71.                     road.Reverse();
72.                     NiceRoads.Add(road);
73.                 }
74.  
75.                 return true;
76.             }
77.             
78.             //???
79.  
80.             if (NextStep(x + 1, y))
81.                 CurRoad.Pop();
82.             if(NextStep(x, y + 1))
83.                 CurRoad.Pop();
84.             if(NextStep(x - 1, y))
85.                 CurRoad.Pop();
86.             if(NextStep(x, y - 1))
87.                 CurRoad.Pop();
88.             return true;
89.         }
90.  
91.         public int[,] InitMap()
92.         {
93.             //x-1,??-2,??-3,??????
94.             return new int[Width,Height]
95.                        {
96.                            {-2, 1, 5, 2, 4, 5, 8, 2, 1},
97.                            {1, 5, 2, 4, 5, 8, 2, -1, 5},
98.                            {2, 7, 5, 2, 4, 5, -1, 2, 1},
99.                            {2, 1, 3, 2, -1, 0, 8, 7, 3},
100.                            {2, 1, 5, 1, 9, 5, 2, 2, 1},
101.                            {4, 8, 4, 3, 4, 2, 8, 2, 3},
102.                            {2, 1, 5, 6, 4, 5, 7, 4, 1},
103.                            {2, 8, 7, 2, 4, 5, 8, 2, 1},
104.                            {1, 5, 5, 4, 5, 6, 2, 2, -3}
105.                        };
106.         }
107.         public struct Coord
108.         {
109.             public Coord(int x,int y)
110.             {
111.                 X = x;
112.                 Y = y;
113.             }
114.  
115.             public int X;
116.             public int Y;
117.         }
118.     }
119.     public enum MapEnum
120.     {
121.         Hole = -1,
122.         Start = -2,
123.         End = -3
124.     }
125. }