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图的广度优先搜索(BFS)与树的广度优先搜索类似。与树不同的是,图中可能存在循环。所我们可能会再次访问到同一个节点。为了表面多次处理同一个节点,我们要布尔变量数据记录节点有没有被访问过。为了简化,我们假设所有的节点都是从根节点可达的。
比如在下图中,我们从节点2出发。当我们访问到节点0时,我们寻找所有与他相邻的节点。节点2就是与0相邻的节点,如果我们不对已访问的节点做标记,那么节点2就会被重复访问。这样的话,算法将会一直进行下去。对下图进行广度优先搜索的结果是2,0,3,1.
以下C++程序是从给定节点进行广度优先搜索的一个简单实现。图的存储使用了邻接链表法。STL的list容器用来存储邻接节点以及与广度优先搜索需要的节点队列。
#include<list> #include<iostream> //Program to print BFS traversal from a given source vertex. BFS(int s) //traverses vertices reachable from s using namespace std; //The class represents a directed graph using adjacency lists class Graph { int V; //No. of vertices list<int> *adj; public: Graph(int V); //Constructor ~Graph(); //Destructor void addEdge(int v, int w); //function to add an edge to graph void BFS(int s); //print BFS traversal from a given source s }; Graph::Graph(int V) { this->V = V; adj = new list<int>[V]; } Graph::~Graph() { delete []adj; } void Graph::addEdge(int v, int w) { adj[v].push_back(w); } void Graph::BFS(int s) { //Mark all the vertices as not visited bool *visited = new bool[V]; for (int i = 0; i < V; i++) { visited[i] = false; } //Create a queue for BFS list<int> queue; //Mark the current node as visited and enqueue it visited[s] = true; queue.push_back(s); //"i" will be used to get all adjacent vertices of vertex list<int>::iterator i; while (!queue.empty()) { //Dequeue a vertex from queue and print it s = queue.front(); cout<<s<<" "; queue.pop_front(); //Get all adjacent vertices of the Dequeued vertex s //If a adjacent has not been visited, then mark it visited //and enqueue it for (i = adj[s].begin(); i != adj[s].end(); i++) { if (!visited[*i]) { visited[*i] = true; queue.push_back(*i); } } } delete []visited; } int main() { // Create a graph given in the above diagram Graph g(4); g.addEdge(0, 1); g.addEdge(0, 2); g.addEdge(1, 2); g.addEdge(2, 0); g.addEdge(2, 3); g.addEdge(3, 3); cout << "Following is Breadth First Traversal (starting from vertex 2) \n"; g.BFS(2); return 0; }
参考资料
1. http://www.geeksforgeeks.org/breadth-first-traversal-for-a-graph/
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原文地址:http://www.cnblogs.com/vincently/p/4769422.html