弗洛伊德算法

弗洛伊德算法

求最短路径

#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 Path[MVNum][MVNum];						//最短路径上顶点vj的前一顶点的序号
int D[MVNum][MVNum];						//记录顶点vi和vj之间的最短路径长度

//------------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，创建有向网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){  
			if(j != i)
				G.arcs[i][j] = MaxInt;  
			else
				G.arcs[i][j] = 0;
		}//for
	}//for

	cout << "输入边依附的顶点及权值，如a b 3" << 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 
	}//for
}//CreateUDN 

void ShortestPath_Floyed(AMGraph G){ 
    //用Floyd算法求有向网G中各对顶点i和j之间的最短路径 
	int i , j , k ;
    for (i = 0; i < G.vexnum; ++i)          		//各对结点之间初始已知路径及距离 
        for(j = 0; j < G.vexnum; ++j){ 
            D[i][j] = G.arcs[i][j]; 
            if(D[i][j] < MaxInt && i != j)  Path[i][j]=i;  	//如果i和j之间有弧，则将j的前驱置为i 
            else Path [i][j] = -1;              		//如果i和j之间无弧，则将j的前驱置为-1 
		}//for
		for(k = 0; k < G.vexnum; ++k) 
			for(i = 0; i < G.vexnum; ++i) 
				for(j = 0; j < G.vexnum; ++j)
					if(D[i][k] + D[k][j] < D[i][j]){   		//从i经k到j的一条路径更短 
						D[i][j] = D[i][k]+D[k][j];    		//更新D[i][j] 
						Path[i][j] = Path[k][j];       			//更改j的前驱为k 
					}//if 
}//ShortestPath_Floyed

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

int main(){
	cout << "************算法6.11　弗洛伊德算法**************" << endl << endl;
	AMGraph G;
	char start , destination;
	int num_start , num_destination;

	CreateUDN(G);
	
	cout <<endl;
	cout << "有向网G创建完成！" << endl;
	ShortestPath_Floyed(G);

	cout << "请依次输入路径的起点与终点的名称：";
	cin >> start >> destination;
	num_start = LocateVex(G , start);
	num_destination = LocateVex(G , destination);

	DisplayPath(G , num_start , num_destination);
	cout << G.vexs[num_destination] << endl;
	cout << "最短路径的长度为：" << D[num_start][num_destination] << endl;
	cout <<endl;
}//main