最短路径多源点Flod-Warshall算法

#include<iostream>
#include<vector>
#include<set>
#include<stack>
#include<stdlib.h>

using namespace std;

const int MaxNumber=1e10;
struct EdgeType //边的类型
{
 int fromvertex; //边的起点
 int tovertex;  //边的终点
 double weight; //边上的权值
};

template<class vertexType>
class DirectedGraphofMatrix //邻接矩阵存储的有向图
{
 private:
  vector<vertexType>vertex; //顶点向量
  int vertexnum; //顶点数目
  vector<EdgeType>edge; //边向量
  int edgenum; //边的数目
  double **Distance; //Distance[i][j]表示第i个顶点到第j个顶点的最短路径长度,初始值为顶点i,j之间的权值
  vector<int> **Path; //Path[i][j]表示第i个顶点到第j个顶点之间最短路径经过的顶点序列
  
  int getposofvertex(vertexType& v); //求出顶点v在图中的位置
  vertexType getvertex(int i); //求出顶点i代表的元素
  double getWeight(int fromvertex,int tovertex); //获取顶点fromvertex到tovertex之间的权值
  void Initializationwork(); //在求最短路径前的初始化工作
  void UpdateDistanceAndPath(); //更新数组Distance和Path
 public:
  DirectedGraphofMatrix(int n,int m);
  ~DirectedGraphofMatrix();
  void showGraph() const;
  void PrintShortestPath(vertexType& one,vertexType& other); //打印顶点one到顶点other之间的最短路径
};

bool checkInputFormat(istream& is) //检查输入格式是否正确
{
 if(!is.good())
 {
  cerr<<"输入格式错误!"<<endl;
  return false;
 }
 else return true;
}

template<class vertexType>
DirectedGraphofMatrix<vertexType>::DirectedGraphofMatrix(int n=0,int m=0):vertexnum(n),edgenum(m)
{
 int i;
 vertexType v;
 EdgeType e;
 for(i=0;i<n;i++)
 {
  cout<<"请输入第"<<i<<"个顶点:";
  cin>>v;
  if(!checkInputFormat(cin)) return;
  else this->vertex.push_back(v);
 }
 for(i=0;i<m;i++)
 {
  cout<<" 请输入第"<<i<<"条边的起点:";
  cin>>e.fromvertex;
  cout<<" 请输入第"<<i<<"条边的终点:";
  cin>>e.tovertex;
  cout<<" 请输入第"<<i<<"条边的权值:";
  cin>>e.weight;
  this->edge.push_back(e);
 }
 this->Distance=new double* [this->vertexnum];  //为数组Distance,Path分配内存
 if(!this->Distance) exit(0);
 for(i=0;i<this->vertexnum;i++)
 {
  this->Distance[i]=new double[this->vertexnum];
  if(!this->Distance[i]) exit(0);
 }
 this->Path=new vector<int>* [this->vertexnum];
 if(!this->Path) exit(0);
 for(i=0;i<this->vertexnum;i++)
 {
  this->Path[i]=new vector<int>[this->vertexnum];
  if(!this->Path[i]) exit(0);
 }
}

template<class vertexType>
DirectedGraphofMatrix<vertexType>::~DirectedGraphofMatrix()
{
 int i;
 for(i=0;i<this->vertexnum;i++)
 {
  delete []this->Distance[i];
  delete []this->Path[i];
 }
}

template<class vertexType>
void DirectedGraphofMatrix<vertexType>::showGraph() const
{
 int i;
 for(i=0;i<this->vertexnum;i++)
 {
  cout<<" 第"<<i<<"个顶点是:"<<this->vertex[i]<<endl;
 }
 for(i=0;i<this->edgenum;i++)
 {
  cout<<" 第"<<i<<"条边的起点是:"<<this->edge[i].fromvertex<<endl;
  cout<<" 第"<<i<<"条边的终点是:"<<this->edge[i].tovertex<<endl;
  cout<<" 第"<<i<<"条边的权值是:"<<this->edge[i].weight<<endl;
 }
}

template<class vertexType>
int DirectedGraphofMatrix<vertexType>::getposofvertex(vertexType& v)
{
 int i;
 for(i=0;i<this->vertexnum;i++)
 {
  if(v==this->vertex[i]) return i;
 }
 return -1;
}

template<class vertexType>
vertexType DirectedGraphofMatrix<vertexType>::getvertex(int i)
{
 int j;
 for(j=0;j<vertexnum;j++)
 {
  if(i==j) return this->vertex[i];
 }
}

template<class vertexType>
double DirectedGraphofMatrix<vertexType>::getWeight(int fromvertex,int tovertex)
{
 int i;
 for(i=0;i<edgenum;i++)
 {
  if(this->edge[i].fromvertex==fromvertex && this->edge[i].tovertex==tovertex)
  {
   return this->edge[i].weight;
  }
 }
 return MaxNumber;
}

template<class vertexType>
void DirectedGraphofMatrix<vertexType>::Initializationwork() //在求最短路径前的初始化工作
{
 int i,j;
 for(i=0;i<this->vertexnum;i++)
 {
  for(j=0;j<this->vertexnum;j++) this->Distance[i][j]=this->getWeight(i,j);
 }
}

template<class vertexType>
void DirectedGraphofMatrix<vertexType>::UpdateDistanceAndPath()
{
 Initializationwork();
 int i,j,k;
 for(i=0;i<this->vertexnum;i++)
 {
  for(j=0;j<this->vertexnum;j++)
  {
   for(k=0;k<this->vertexnum;k++)
   {
    if(this->Distance[j][k]>this->Distance[j][i]+this->Distance[i][k])
  // 将顶点i加入第j个顶点和第k个顶点的之间,如果Distance[j][k]>Distance[j][i]+Distance[i][k]
  // 则说明第i个顶点是顶点i到顶点j的最短路径上的第i个顶点
    {
     this->Distance[j][k]=this->Distance[j][i]+this->Distance[i][k];
     this->Path[j][k].push_back(i);
    }
   }
  }
 }
}


template<class vertexType>
void DirectedGraphofMatrix<vertexType>::PrintShortestPath(vertexType& one,vertexType& other)
{
 int i,j;
 i=this->getposofvertex(one);
 if(i==-1) exit(0);
 j=this->getposofvertex(other);
 if(j==-1) exit(0);
 this->UpdateDistanceAndPath();
 double d=this->Distance[i][j];
 vector<int>::const_iterator it;
 cout<<" 顶点"<<one<<"到顶点"<<other<<"的最短路径长度是:"<<d<<endl;
 cout<<"顶点"<<one<<"到顶点"<<other<<"的最短路径是:"<<one<<" ";
 for(it=this->Path[i][j].begin();it!=this->Path[i][j].end();it++)
 {
  cout<<this->getvertex(*it)<<" ";
 }
 cout<<other<<endl;
}

void main()
{
 int n,m;
 cout<<"请输入顶点个数:";
 cin>>n;
 cout<<"请输入边的个数:";
 cin>>m;
 DirectedGraphofMatrix<char>g(n,m);
 g.showGraph();
 char one,other;
 cout<<"请输入源点:";
 cin>>one;
 cout<<" 请输入目标点:";
 cin>>other;
 g.PrintShortestPath(one,other);
}