【数据结构】图的广度优先搜索

　　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();
     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;

    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();
        visited[s] = true;

        //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]) {
                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) 
";
    g.BFS(2);
 
    return 0;
}

参考资料

　　1. http://www.geeksforgeeks.org/breadth-first-traversal-for-a-graph/