武汉地铁站点最短路径搜索的实现（一）——Dijkstra算法（coding）

 

  1 #include <iostream>
  2 #include <string>
  3 #include <iomanip>
  4 using namespace std;
  5 
  6 void dijsktra(int n, int **arc);
  7 
  8 int main(){
  9     int n;//节点数
 10     int m;//边数
 11     int a, b, c;
 12     int **arc;//邻接矩阵
 13     cout << "输入图的节点个数和边的条数：" << endl;
 14     cin >> n >> m;
 15     //初始化邻接矩阵
 16     arc = new int*[n];
 17     for (int i = 0; i < n; i++){
 18         arc[i] = new int[n];
 19         for (int j = 0; j < n; j++){
 20             if (i == j) arc[i][j] = 0;
 21             else arc[i][j] = INT_MAX;
 22         }
 23     }
 24     //邻接矩阵赋值
 25     cout << "请输入每条边的起点和终点（节点编号从1开始）以及其权重" << endl;
 26     for (int i = 0; i < m; i++){
 27         cin >> a >> b >> c;
 28         arc[a - 1][b - 1] = c;
 29     }
 30     dijsktra(n, arc);
 31     //释放内存
 32     for (int i = 0; i < n; i++)
 33     {
 34         delete[] arc[i];
 35     }
 36     delete[] arc;
 37 }
 38 
 39 void dijsktra(int n, int **arc){
 40     bool *s = new bool[n];
 41     int *dis = new int[n];
 42     string *path = new string[n];
 43     //给定源点
 44     string path_s = "n1";
 45     s[0] = true;
 46     dis[0] = 0;
 47     path[0] = path_s + "→n1";
 48     //初始化s、dis、path
 49     for (int i = 1; i < n; i++)
 50     {
 51         s[i] = false;
 52         dis[i] = arc[0][i];
 53         path[i] = path_s + "→n" + to_string(i+1);
 54     }
 55 
 56     //打印邻接矩阵
 57     cout << "\n图的邻接矩阵初始化为：" << endl;
 58     int count_row = 0; //打印行的标签
 59     int count_col = 0; //打印列的标签
 60     while (count_row != n) {
 61         count_col = 0;
 62         while (count_col != n) {
 63             if (arc[count_row][count_col] == INT_MAX)
 64                 cout << "∞" << " ";//按住Alt键不放，依次按下小键盘中的“41438”，再放开Alt健，“∞”就显示在屏幕中了
 65             else
 66                 cout << arc[count_row][count_col] << " ";
 67             ++count_col;
 68         }
 69         cout << endl;
 70         ++count_row;
 71     }
 72 
 73     //开始迭代
 74     for (int i = 1; i < n; i++)
 75     {
 76         //搜索U中的dis最小值节点v_temp
 77         int dis_min = INT_MAX;//记录U中dis最小值
 78         int temp = 0;//记录dis最小节点下标
 79         for (int j = 0; j < n; j++)
 80         {
 81             if (s[j] == false && dis[j] < dis_min)
 82             {
 83                 temp = i;
 84                 dis_min = dis[j];
 85             }
 86         }
 87         s[temp] = true;//dis最小节点加入S
 88 
 89         //搜索v_temp出S外的邻接点做松弛操作
 90         for (int k = 1; k < n; k++)
 91         {
 92             if (s[k] == false && arc[temp][k] != INT_MAX)
 93             {//搜寻到v_temp到v_k得路径
 94                 if (dis[k]>dis[temp] + arc[temp][k])
 95                 {
 96                     dis[k] = dis[temp] + arc[temp][k];
 97                     path[k] = path[temp] + "→n" + to_string(k + 1);//箭头搜狗输入法符号大全
 98                 }
 99             }
100         }
101     }
102 
103     //输出最短路径搜索结果
104     cout << "\n" << "以n1" << "为起点的图的最短路径为：" << endl;
105     cout.flags(ios::left);
106     cout << setw(8) << "起点 " << setw(8) << "终点 " << setw(10) << "最短路径" << setw(10) << "节点序列" << endl;
107     for (int i = 0; i < n; i++){
108         //cout.flags(ios::left);
109         if (dis[i]!= INT_MAX)
110             cout << setw(8) << "n1" << "n" << setw(7) << (i + 1) << setw(10) << dis[i] << path[i] << endl;
111         else
112             cout << setw(8) << "n1" << "n" << setw(7) << (i + 1) << setw(10) << dis[i] << "无最短路径" << endl;
113     }
114 }