图的最短路径（C++实现）

1 #include <iostream>
2 using namespace std ;
3
4 #define MAXVERTEXNUM 100
5 struct Graph
6 {
7   int VertexNum ;
8   char Vertex[MAXVERTEXNUM] ;
9   int AdjMatrix[MAXVERTEXNUM][MAXVERTEXNUM] ;
10 } ;
11
12 Graph MGraph ;
13
14
15 #define INFINITY 100
16 void CreateGraph (Graph *G)
17 {
18   int i , j ;
19
20   cin >> G-> VertexNum ;
21   for (i = 1 ; i <= G->VertexNum ; i++)
22   {
23     cin >> G->Vertex[i] ;
24   }
25   for (i = 1 ; i <= G->VertexNum ; i++)
26   {
27     for (j = 1 ; j <= G->VertexNum ; j++)
28     {
29       cin >> G->AdjMatrix[i][j] ;
30       if (G->AdjMatrix[i][j] == -1)
31       {
32         G->AdjMatrix[i][j] = INFINITY ;
33       }
34     }
35   }
36 }
37
38
39 void ShowGraph (Graph *G)
40 {
41   int i , j ;
42
43   for (i = 1 ; i <= G->VertexNum ; i++)
44   {
45     cout << G->Vertex[i] << " " ;
46   }
47   cout << endl ;
48
49   for (i = 1 ; i <= G->VertexNum ; i++)
50   {
51     for (j = 1 ; j <= G->VertexNum ; j++)
52     {
53       cout << G->AdjMatrix[i][j] << " " ;
54     }
55     cout << endl ;
56   }
57 }
58
59 char Path[MAXVERTEXNUM][MAXVERTEXNUM] ;
60 int Dest[MAXVERTEXNUM] ;
61 void ShortestPath (Graph *G , char StartVexChar)
62 {
63   int i , j , m , StartVex , CurrentVex , MinDest ;
64   int Final[MAXVERTEXNUM] ;
65
66
67   for (i = 1 ; j <= G->VertexNum ; i++)
68   {
69     if (G->Vertex[i] == StartVexChar)
70     {
71       StartVex = i ;
72       break ;
73     }
74   }
75
76   for (i = 1 ; i <= G->VertexNum ; i++)
77   {
78     Path[i][0] = 0 ;
79     Dest[i] = INFINITY ;
80     if (G->AdjMatrix[StartVex][i] < INFINITY)
81     {
82       Dest[i] = G->AdjMatrix[StartVex][i] ;
83       Path[i][1] = G->Vertex[StartVex] ;
84       Path[i][2] = G->Vertex[i] ;
85       Path[i][0] = 2 ;
86     }
87     Final[i] = 'F' ;
88   }
89   Dest[StartVex] = 0 ;
90   Final[StartVex] = 'T' ;
91   for (i = 1 ; i <= G->VertexNum ; i++)
92   {
93     MinDest = INFINITY ;
94     for (j = 1 ; j <= G->VertexNum ; j++)
95     {
96       if (Final[j] == 'F')
97       {
98         if (Dest[j] < MinDest)
99         {
100           CurrentVex = j ;
101           MinDest = Dest[j] ;
102         }
103       }
104     }
105     Final[CurrentVex] = 'T' ;
106     for (j = 1 ; j <= G->VertexNum ; j++)
107     {
108       if ((Final[j] == 'F') && (MinDest + G->AdjMatrix[CurrentVex][j] < Dest[j]))
109       {
110         Dest[j] = MinDest + G->AdjMatrix[CurrentVex][j] ;
111
112         for (m = 0 ; m <= Path[CurrentVex][0] ; m++)
113         {
114           Path[j][m] = Path[CurrentVex][m] ;
115         }
116         Path[j][0]++ ;
117         Path[j][Path[j][0]] = G->Vertex[j] ;
118       }
119     }
120   }
121 }
122
123 void ShowPath (Graph *G)
124 {
125   int i , j ;
126
127   for (i = 1 ; i <= G->VertexNum ; i++)
128   {
129     cout << G->Vertex[i] << "(" << Dest[i] << ") : " ;
130     if (Path[i][0] > 0)
131     {
132       for (j = 1 ; j < G->VertexNum ; j++)
133       {
134         cout << " " << Path[i][j] ;
135       }
136     }
137     cout << endl ;
138   }
139 }
140
141 int main ()
142 {
143   char StartVex ;
144
145   CreateGraph (&MGraph) ;
146   ShowGraph (&MGraph) ;
147
148   cin >> StartVex ;
149   ShortestPath (&MGraph , StartVex) ;
150   ShowPath (&MGraph) ;
151
152   return 0 ;
153
154 }