图的最短路径（C++实现）

#include <iostream>
using namespace std ;

#define MAXVERTEXNUM 100
struct Graph
{
  int VertexNum ;
  char Vertex[MAXVERTEXNUM] ;
  int AdjMatrix[MAXVERTEXNUM][MAXVERTEXNUM] ;
} ;

Graph MGraph ;


#define INFINITY 100
void CreateGraph (Graph *G)
{
  int i , j ;

  cin >> G-> VertexNum ;
  for (i = 1 ; i <= G->VertexNum ; i++)
  {
    cin >> G->Vertex[i] ;
  }
  for (i = 1 ; i <= G->VertexNum ; i++)
  {
    for (j = 1 ; j <= G->VertexNum ; j++)
    {
      cin >> G->AdjMatrix[i][j] ;
      if (G->AdjMatrix[i][j] == -1)
      {
        G->AdjMatrix[i][j] = INFINITY ;
      }
    }
  }
}


void ShowGraph (Graph *G)
{
  int i , j ;

  for (i = 1 ; i <= G->VertexNum ; i++)
  {
    cout << G->Vertex[i] << " " ;
  }
  cout << endl ;

  for (i = 1 ; i <= G->VertexNum ; i++)
  {
    for (j = 1 ; j <= G->VertexNum ; j++)
    {
      cout << G->AdjMatrix[i][j] << " " ;
    }
    cout << endl ;
  }
}

char Path[MAXVERTEXNUM][MAXVERTEXNUM] ;
int Dest[MAXVERTEXNUM] ;
void ShortestPath (Graph *G , char StartVexChar)
{
  int i , j , m , StartVex , CurrentVex , MinDest ;
  int Final[MAXVERTEXNUM] ;


  for (i = 1 ; j <= G->VertexNum ; i++)
  {
    if (G->Vertex[i] == StartVexChar)
    {
      StartVex = i ;
      break ;
    }
  }

  for (i = 1 ; i <= G->VertexNum ; i++)
  {
    Path[i][0] = 0 ;
    Dest[i] = INFINITY ;
    if (G->AdjMatrix[StartVex][i] < INFINITY)
    {
      Dest[i] = G->AdjMatrix[StartVex][i] ;
      Path[i][1] = G->Vertex[StartVex] ;
      Path[i][2] = G->Vertex[i] ;
      Path[i][0] = 2 ;
    }
    Final[i] = 'F' ;
  }
  Dest[StartVex] = 0 ;
  Final[StartVex] = 'T' ;
  for (i = 1 ; i <= G->VertexNum ; i++)
  {
    MinDest = INFINITY ;
    for (j = 1 ; j <= G->VertexNum ; j++)
    {
      if (Final[j] == 'F')
      {
        if (Dest[j] < MinDest)
        {
          CurrentVex = j ;
          MinDest = Dest[j] ;
        }
      }
    }
    Final[CurrentVex] = 'T' ;
    for (j = 1 ; j <= G->VertexNum ; j++)
    {
      if ((Final[j] == 'F') && (MinDest + G->AdjMatrix[CurrentVex][j] < Dest[j]))
      {
        Dest[j] = MinDest + G->AdjMatrix[CurrentVex][j] ;

        for (m = 0 ; m <= Path[CurrentVex][0] ; m++)
        {
          Path[j][m] = Path[CurrentVex][m] ;
        }
        Path[j][0]++ ;
        Path[j][Path[j][0]] = G->Vertex[j] ;
      }
    }
  }
}

void ShowPath (Graph *G)
{
  int i , j ;

  for (i = 1 ; i <= G->VertexNum ; i++)
  {
    cout << G->Vertex[i] << "(" << Dest[i] << ") : " ;
    if (Path[i][0] > 0)
    {
      for (j = 1 ; j < G->VertexNum ; j++)
      {
        cout << " " << Path[i][j] ;
      }
    }
    cout << endl ;
  }
}

int main ()
{
  char StartVex ;

  CreateGraph (&MGraph) ;
  ShowGraph (&MGraph) ;

  cin >> StartVex ;
  ShortestPath (&MGraph , StartVex) ;
  ShowPath (&MGraph) ;

  return 0 ;

}