//算法6.10　迪杰斯特拉算法

#include <iostream>
using namespace std;

#define MaxInt 32767                    					//表示极大值，即∞
#define MVNum 100                       					//最大顶点数
typedef char VerTexType;              						//假设顶点的数据类型为字符型 
typedef int ArcType;                  						//假设边的权值类型为整型

int *D=new int[MVNum];	                    				//用于记录最短路的长度
bool *S=new bool[MVNum];          							//标记顶点是否进入S集合
int *Path=new int[MVNum];									//用于记录最短路顶点的前驱

//------------图的邻接矩阵-----------------
typedef struct{ 
	VerTexType vexs[MVNum];            						//顶点表 
	ArcType arcs[MVNum][MVNum];      						//邻接矩阵 
	int vexnum,arcnum;                						//图的当前点数和边数 
}AMGraph;

int LocateVex(AMGraph G , VerTexType v){
	//确定点v在G中的位置
	for(int i = 0; i < G.vexnum; ++i)
		if(G.vexs[i] == v)
			return i;
   return -1;
}//LocateVex

void CreateUDN(AMGraph &G){ 
    //采用邻接矩阵表示法，创建无向网G 
	int i , j , k;
	cout <<"请输入总顶点数，总边数，以空格隔开:";
    cin >> G.vexnum >> G.arcnum;							//输入总顶点数，总边数
	cout << endl;

	cout << "输入点的名称:，如a" << endl;

    for(i = 0; i < G.vexnum; ++i){   
		cout << "请输入第" << (i+1) << "个点的名称:";
		cin >> G.vexs[i];                        			//依次输入点的信息 
	}
	cout << endl;
    for(i = 0; i < G.vexnum; ++i)                			//初始化邻接矩阵，边的权值均置为极大值MaxInt 
		for(j = 0; j < G.vexnum; ++j)   
			G.arcs[i][j] = MaxInt; 
	cout << "输入边依附的顶点及权值，如a b 7" << endl;
	for(k = 0; k < G.arcnum;++k){							//构造邻接矩阵 
		VerTexType v1 , v2;
		ArcType w;
		cout << "请输入第" << (k + 1) << "条边依附的顶点及权值:";
		cin >> v1 >> v2 >> w;								//输入一条边依附的顶点及权值
		i = LocateVex(G, v1);  j = LocateVex(G, v2);		//确定v1和v2在G中的位置，即顶点数组的下标 
		G.arcs[i][j] = w;									//边<v1, v2>的权值置为w 
		G.arcs[j][i] = G.arcs[i][j];						//置<v1, v2>的对称边<v2, v1>的权值为w 
	}//for
}//CreateUDN

void ShortestPath_DIJ(AMGraph G, int v0){ 
    //用Dijkstra算法求有向网G的v0顶点到其余顶点的最短路径 
    int v , i , w , min;
	int n = G.vexnum;                    					//n为G中顶点的个数 

	for(v = 0; v < n; ++v){             					//n个顶点依次初始化 
		S[v] = false;                  						//S初始为空集 
		D[v] = G.arcs[v0][v];           					//将v0到各个终点的最短路径长度初始化为弧上的权值 
		if(D[v] < MaxInt)  Path [v] = v0;  					//如果v0和v之间有弧，则将v的前驱置为v0 
		else Path [v] = -1;               					//如果v0和v之间无弧，则将v的前驱置为-1 
	}//for 

	S[v0]=true;                    							//将v0加入S 
	D[v0]=0;                      							//源点到源点的距离为0 

	/*―初始化结束，开始主循环，每次求得v0到某个顶点v的最短路径，将v加到S集―*/ 
	for(i = 1;i < n; ++i){									//对其余n-1个顶点，依次进行计算 
        min= MaxInt; 
        for(w = 0; w < n; ++w) 
			if(!S[w] && D[w] < min){						//选择一条当前的最短路径，终点为v 
				v = w; 
				min = D[w];
			}//if         	
		S[v]=true;                   						//将v加入S 
		for(w = 0;w < n; ++w)           					//更新从v0出发到集合V?S上所有顶点的最短路径长度 
			if(!S[w] && (D[v] + G.arcs[v][w] < D[w])){ 
				D[w] = D[v] + G.arcs[v][w];   				//更新D[w] 
				Path [w] = v;              					//更改w的前驱为v 
			}//if 
    }//for  
}//ShortestPath_DIJ

void DisplayPath(AMGraph G , int begin ,int temp ){
	//显示最短路
	if(Path[temp] != -1){
		DisplayPath(G , begin ,Path[temp]);
		cout << G.vexs[Path[temp]] << "-->";
	}
}//DisplayPath

void main()
{
	cout << "************算法6.10　迪杰斯特拉算法**************" << endl << endl;
	AMGraph G; 
	int i , j ,num_start , num_destination;
	VerTexType start , destination;
	CreateUDN(G);
	cout <<endl;
	cout << "*****无向网G创建完成！*****" << endl;
	
	for(i = 0 ; i < G.vexnum ; ++i){
		for(j = 0; j < G.vexnum; ++j){
			if(j != G.vexnum - 1){
				if(G.arcs[i][j] != MaxInt)
					cout << G.arcs[i][j] << "\t";
				else
					cout << "∞" << "\t";
			}
			else{
				if(G.arcs[i][j] != MaxInt)
					cout << G.arcs[i][j] <<endl;
				else
					cout << "∞" <<endl;
			}
		}
	}//for
	cout << endl;
	cout << "请依次输入起始点、终点名称：";
	cin >> start >> destination;
	num_start = LocateVex(G , start);
	num_destination = LocateVex(G , destination);
	ShortestPath_DIJ(G , num_start);
	cout << endl <<"最短路径为：";
	DisplayPath(G , num_start , num_destination);
	cout << G.vexs[num_destination]<<endl;
}//main