图-迪杰斯特拉算法

//算法6.10　迪杰斯特拉算法

#include <iostream>
using namespace std;

#define MaxInt 32767                    					
#define MVNum 100                       					
typedef char VerTexType;              						
typedef int ArcType;                  						

int *D=new int[MVNum];	                    				
bool *S=new bool[MVNum];          							
int *Path=new int[MVNum];									


typedef struct{ 
	VerTexType vexs[MVNum];            						
	ArcType arcs[MVNum][MVNum];      						
	int vexnum,arcnum;                						 
}AMGraph;

int LocateVex(AMGraph G , VerTexType v){
	for(int i = 0; i < G.vexnum; ++i)
		if(G.vexs[i] == v)
			return i;
   return -1;
}

void CreateUDN(AMGraph &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;							
	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];                        			
	}
	cout << endl;
    for(i = 0; i < G.vexnum; ++i)                			
		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){							
		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;								
		i = LocateVex(G, v1);  j = LocateVex(G, v2);		
		G.arcs[i][j] = w;									
		G.arcs[j][i] = G.arcs[i][j];						
	}
}

void ShortestPath_DIJ(AMGraph G, int v0){ 
   
    int v , i , w , min;
	int n = G.vexnum;                    					

	for(v = 0; v < n; ++v){             					
		S[v] = false;                  						
		D[v] = G.arcs[v0][v];           					
		if(D[v] < MaxInt)  Path [v] = v0;  					
		else Path [v] = -1;               					
	}

	S[v0]=true;                    							
	D[v0]=0;                      							 

	for(i = 1;i < n; ++i){									
        min= MaxInt; 
        for(w = 0; w < n; ++w) 
			if(!S[w] && D[w] < min){						
				v = w; 
				min = D[w];
			}         	
		S[v]=true;                   						
		for(w = 0;w < n; ++w)           					
			if(!S[w] && (D[v] + G.arcs[v][w] < D[w])){ 
				D[w] = D[v] + G.arcs[v][w];   				
				Path [w] = v;              					
			}
    }  
}

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]] << "-->";
	}
}

int main()
{
	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;
			}
		}
	}
	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;
}