图的两种遍历方式

Posted 2020-09-25 NoviScl

图的遍历有两种：深度优先和广度优先。本文中，深度优先使用递归实现，每次递归找到第一个与当前结点相连且未输出过的结点继续往下递归，直至所有结点都已输出。广度优先将开始结点的所有邻接结点全部压入栈，当栈不为空时一直循环将栈首的结点的所有相邻结点压入栈。

具体代码实现如下：

  1 //邻接链表
  2 class Graph {
  3 private:
  4     //n: number of nodes
  5     int n;
  6     vector<int> *edges;
  7     bool *visited;
  8 public:
  9     Graph(int input_n) {
 10         n = input_n;
 11         edges = new vector<int>[n];
 12         visited=new bool[n];
 13         //size of bool=1
 14         memset(visited,0,n);
 15     }
 16     ~Graph() {
 17         delete[] edges;
 18         delete[] visited;
 19     }
 20     //no directions
 21     void insert(int x, int y) {
 22         edges[x].push_back(y);
 23         edges[y].push_back(x);
 24     }
 25 
 26     //visited will be changed after one traversal
 27     //so need to reset for new operations
 28     void reset_visited(){
 29         memset(visited,0,n);
 30     }
 31 
 32     void dfs(int vertex) {
 33         cout<<vertex<<endl;
 34         visited[vertex]=true;
 35         for(int adj_vertex: edges[vertex]){
 36             if(!visited[adj_vertex]){
 37                 dfs(adj_vertex);
 38             }
 39         }
 40     }
 41 
 42     void bfs(int start_vertex) {
 43         queue<int> bfs_queue;
 44         bfs_queue.push(start_vertex);
 45         visited[start_vertex]=true;
 46         while(!bfs_queue.empty()){
 47             int vertex=bfs_queue.front();
 48             cout<<vertex<<endl;
 49             bfs_queue.pop();
 50             for(int adj_vertex: edges[vertex]){
 51                 //if it has not been put into the queue yet
 52                 if(!visited[adj_vertex]){
 53                     visited[adj_vertex]=true;
 54                     bfs_queue.push(adj_vertex);
 55                 }
 56             }
 57         }
 58     }
 59 };
 60 
 61 
 62 
 63 
 64 //邻接矩阵
 65 class Graph {
 66 private:
 67     //指向邻接矩阵
 68     int **mat;
 69     //n为顶点个数, 注意这里顶点是从0开始编号的
 70     int n;
 71     bool *visited;
 72 public:
 73     Graph(int input_n) {
 74         n = input_n;
 75         mat = new int *[n];
 76         for (int i = 0; i < n; ++i) {
 77             mat[i] = new int[n];
 78             memset(mat[i], 0, sizeof(int) * n);
 79         }
 80         visited=new bool[input_n];
 81         memset(visited,0,input_n);
 82     }
 83     ~Graph() {
 84         for (int i = 0; i< n; ++i) {
 85             delete[] mat[i];
 86         }
 87         delete[] mat;
 88         delete[] visited;
 89     }
 90     //flag=0为有向图, flag=1为无向图
 91     void insert(int x,int y, int flag){
 92         mat[x][y]=1;
 93         if(flag==1){
 94             mat[y][x]=1;
 95         }
 96     }
 97     void output() {
 98         for(int i=0;i<n;i++){
 99             for(int j=0;j<n;j++){
100                 cout<<mat[i][j]<<" ";
101             }
102             cout<<endl;
103         }
104     }
105     
106     void reset_visited(){
107         memset(visited,0,n);
108     }
109     
110     void dfs(int cur_vertex){
111         cout<<cur_vertex<<endl;
112         visited[cur_vertex]=true;
113         for(int adj_ver=0;adj_ver<n;adj_ver++){
114             if((!visited[adj_ver]) && mat[cur_vertex][adj_ver]==1){
115                 dfs(adj_ver);
116             }
117         }
118     }
119     
120     
121     void bfs(int start_vertex){
122         queue<int> bfs_queue;
123         bfs_queue.push(start_vertex);
124         visited[start_vertex]=true;
125         while(!bfs_queue.empty()){
126             int cur_ver=bfs_queue.front();
127             bfs_queue.pop();
128             cout<<cur_ver<<endl;
129             for(int adj_ver=0; adj_ver<n; adj_ver++){
130                 if((!visited[adj_ver]) && mat[cur_ver][adj_ver]==1){
131                     bfs_queue.push(adj_ver);
132                     visited[adj_ver]=true;
133                 }
134             }
135         }
136     }
137 };