Dijkstra算法-单源最短路径（包括路径记录）

#include
#include
using namespace std;


#define MAX 999
#define BIG 101


int a[BIG][BIG];
int dist[BIG]; //储存起点到其他点的最短路径
int book[BIG]; //标记数组
int path[BIG];
stack pathout;


void output_path(int end)
{
int i = end;
int flag = 1;
int sum = 0;
while (flag == 1)
{
sum++;
pathout.push(i);             //压栈
if (path[i] == 0) flag = 2;
else i = path[i];           //指向该点的上一个点
}
cout << "前进路径为：";
while (!pathout.empty())
{
cout << pathout.top() << " "; //栈顶出栈
if (sum > 1)
{
sum--;
cout << "-> ";
}
pathout.pop();               // 移除栈顶
}
cout << endl;
}


void dijkstra(int sta, int end, int m,int n)  //dijkstra 核心代码
{
while (book[end] != 1)
{
int min_i;
int min = MAX;
//////////////
for (int i = 1; i <= m; i++)   //找出未标记的点中 里起点最近的
{


if (book[i] == 0 && dist[i] < min)
{
min = dist[i];
min_i = i;
}


}
/////////////////
book[min_i] = 1;
for (int i = 1; i <=m; i++) //松弛 
{
//cout <<"i="<< i << endl;
if (a[min_i][i] < MAX)
{
if (dist[i] > dist[min_i] + a[min_i][i])
{
dist[i] = dist[min_i] + a[min_i][i];
path[i] = min_i;
}
}


}
}
}




int main()
{
int m, n;
cout << "                                               欢迎使用路径规划系统" << endl << endl;;
while (cout << "输入地点和街道的数目：", cin >> m >> n)
{
if(m<2||n<(m-1||n>(m*(m-1)/2)))
{
cout << "输入有误" << endl << endl;
}
else
{
//以下是初始化
memset(dist, MAX, sizeof(dist));
memset(book, 0, sizeof(book));
memset(path, 0, sizeof(path));


for (int i = 0; i < BIG; i++)
{
for (int j = 0; j < BIG; j++)
{
if (i == j) a[i][j] = 0;
else a[i][j] = MAX;
}
}
//////////////////////////////////
int x, y, z;
cout << "输入街道的信息：" << endl;
for (int i = 1; i <= n; i++)
{
cin >> x >> y >> z;
a[x][y] = z;
}
int sta;
int end;
cout << "输入出发地点与目的地：" << endl;
cin >> sta >> end;
///////////////////////
int min_i = MAX;
for (int i = 1; i <= m; i++)
{
dist[i] = a[sta][i];  //起点与其余点的距离
if (dist[i] 0 && dist[i] < min_i) min_i = i;
}
path[min_i] = sta;
book[sta] = 1;


//////////////////////
dijkstra(sta, end,m,n);
//////////////////////
cout << "出发地点到目的地的最短距离为：" << dist[end] << endl;
output_path(end);
}
cout << "是否继续查询？ Y or N : ";
char c;
cin >> c;
if (c == 'N' || c == 'n')
{
cout << "                                               感谢使用！再见" << endl << endl;
getchar();
getchar();
return 0;
}

}


}