1. 图上BFS
2. 图上DFS

图上BFS

将BFS扩展到图，从顶点0开始访问，逐层访问其邻居顶点，持续到访问完毕

最后获得序列：按照访问距离离起始顶点最近的所有顶点

按照该序列，访问到每个顶点后，就找到了达到该顶点的最短路径（适用于权值相等）

对相同距离邻居顶点，访问顺序不重要

同样可以使用队列实现

#include <bits/stdc++.h>
using namespace std;
const int N = 100;
bool vis[N]; // 访问标记数组
typedef char VertexType ;
typedef int EdgeType;
queue<int> q;
struct mat_grph{
  VertexType vertex[N];
  EdgeType arc[N][N];
  int vertex_num;
  int edge_num;
};
void create_graph(mat_grph* G){
  G->vertex_num = 9;
  G->edge_num = 15;
  G->vertex[0] = 'A';
  G->vertex[1] = 'B';
  G->vertex[2] = 'C';
  G->vertex[3] = 'D';
  G->vertex[4] = 'E';
  G->vertex[5] = 'F';
  G->vertex[6] = 'G';
  G->vertex[7] = 'H';
  G->vertex[8] = 'I';
  for (int i = 0;i<G->vertex_num;i++){
    for (int j = 0;j<G->vertex_num;j++){
      G->arc[i][j] = 0;
    }
  }
  G->arc[0][1] = 1;
  G->arc[0][5] = 1;
  G->arc[1][2] = 1;
  G->arc[1][6] = 1;
  G->arc[1][8] = 1;
  G->arc[2][3] = 1;
  G->arc[2][8] = 1;
  G->arc[3][4] = 1;
  G->arc[3][6] = 1;
  G->arc[3][7] = 1;
  G->arc[3][8] = 1;
  G->arc[4][5] = 1;
  G->arc[4][7] = 1;
  G->arc[5][6] = 1;
  G->arc[6][7] = 1;
  // 无向图，把对称的也复制过去
  for (int i = 0;i<G->vertex_num;i++){
    for (int j = 0;j<G->vertex_num;j++){
      G->arc[j][i] = G->arc[i][j];
    }
  }
}
void bfs(mat_grph &G){
  int i = 0;
  vis[i]=1;
  cout << G.vertex[i]<<endl;
  q.push(i);
  while(!q.empty()){
    i = q.front();
    q.pop();
    for (int j = 0;j<G.vertex_num;j++){
      if (!(vis[j])&&G.arc[i][j]==1){
        vis[j] = 1;
        cout << G.vertex[j]<<endl;
        q.push(j);
      }
    }
  }
}
int main(){
  mat_grph G;
  create_graph(&G);
  memset(vis, 0, sizeof vis);
  bfs(G);
  return 0;
}

图上DFS

#include <bits/stdc++.h>
using namespace std;
const int N = 100;
bool vis[N]; // 访问标记数组
typedef char VertexType ;
typedef int EdgeType;
struct mat_grph{
  VertexType vertex[N];
  EdgeType arc[N][N];
  int vertex_num;
  int edge_num;
};
void create_graph(mat_grph* G){
  G->vertex_num = 9;
  G->edge_num = 15;
  G->vertex[0] = 'A';
  G->vertex[1] = 'B';
  G->vertex[2] = 'C';
  G->vertex[3] = 'D';
  G->vertex[4] = 'E';
  G->vertex[5] = 'F';
  G->vertex[6] = 'G';
  G->vertex[7] = 'H';
  G->vertex[8] = 'I';
  for (int i = 0;i<G->vertex_num;i++){
    for (int j = 0;j<G->vertex_num;j++){
      G->arc[i][j] = 0;
    }
  }
  G->arc[0][1] = 1;
  G->arc[0][5] = 1;
  G->arc[1][2] = 1;
  G->arc[1][6] = 1;
  G->arc[1][8] = 1;
  G->arc[2][3] = 1;
  G->arc[2][8] = 1;
  G->arc[3][4] = 1;
  G->arc[3][6] = 1;
  G->arc[3][7] = 1;
  G->arc[3][8] = 1;
  G->arc[4][5] = 1;
  G->arc[4][7] = 1;
  G->arc[5][6] = 1;
  G->arc[6][7] = 1;
  // 无向图，把对称的也复制过去
  for (int i = 0;i<G->vertex_num;i++){
    for (int j = 0;j<G->vertex_num;j++){
      G->arc[j][i] = G->arc[i][j];
    }
  }
  
}
void dfs(mat_grph &G, int i){
  vis[i] = 1;
  cout << G.vertex[i]<<endl;
  for (int j = 0;j<G.vertex_num;j++){ // 寻找邻接矩阵中和第i个顶点间有边的顶点
    if ((!vis[j]) && G.arc[i][j]==1){ // 如果没被访问过且存在边，则从其对应的顶点开始搜索与其有边的顶点
      dfs(G, j);
    }
  }
}
int main(){
  mat_grph G;
  create_graph(&G);
  memset(vis, 0, sizeof vis);
  dfs(G, 0);
  return 0;
}

本作品采用知识共享署名-相同方式共享 4.0 国际许可协议进行许可

红魔咖啡馆

【图论】图上BFS/DFS

图上BFS

图上DFS