用BFS找最短路，并打印路径

转自：http://lingyibin.javaeye.com/blog/849828

 

我想大部分人都用Floyd或者Dijstra算法，甚至dfs算过最短路吧。

其实BFS也可以计算最短路。(补充：本文只针对无权图，有权图很难用BFS)

当我们用BFS找端对端最短路时，从出发点开始，第一次遍历到终点时过的那条路径就是最短的路径。（读者可以思考一下为什么！）

下面就用邻接表来实现一下BFS最短路，并把路径打出来。

 

#include<iostream>
#include<fstream>
#include<queue>
using namespace std;

const int MAX = 50;

struct link
{
 int data;
 link *next;
};
struct Node
{
 int v;     //顶点相关的信息
 link *next;
};
struct Graph
{
  Node node[MAX+1]; //所有的结点
  int nodeCnt; //用来记录图中结点的数目，这里假设用的是连通图。假设不连通，稍微改一下本程序就行了，具体操作留给读者思考！
};

int visited[MAX+1]; //标志数组
int pa[MAX+1];

/* 读取文件中的数据，构造一个邻接表来表示图 */
Graph readGraph()
{
    ifstream cin("c://graph.txt");

    //表的初始化
    Graph graph;
    int i ;
    for(i = 1; i < MAX; i ++)
    {
        graph.node[i].v = i;
        graph.node[i].next = NULL;
    }

    int n1 = 0,n2 = 0;
    link *s;
    graph.nodeCnt = 1;//把结点数初始化为1
    while(cin>>n1>>n2)
    {
        if(graph.nodeCnt < n1) graph.nodeCnt=n1;
        if(graph.nodeCnt < n2) graph.nodeCnt=n2;
        s = new link;
        s->data = n2;
        s->next=graph.node[n1].next;
        graph.node[n1].next=s; //从尾部插入
        //delete(s);

        s=new link;
        s->data = n1;
        s->next=graph.node[n2].next;
        graph.node[n2].next=s; //反过来也赋值，说明本程序测试的是无向图，如果是有向图的话读者应该知道怎么改了吧！
        //delete(s);
    }
    return graph;
}

/* 打印邻接表 */
void printGraph(Graph graph)
{
  link *p;
  for(int i = 1; i <= graph.nodeCnt; i ++)
  {
      cout<<graph.node[i].v<<" -- ";

      p=graph.node[i].next;
      while(p!=NULL)
      {
          cout<<p->data;
          p=p->next;
          if(p != NULL)
              cout<<",";
      }
      cout<<endl;
  }
}

/* 用BFS求最短路径 */
void shortestPath(Graph graph, int s, int d)
{
    cout<<"从"<<s<<"到"<<d<<"的bfs最短路求解过程如下："<<endl;
    queue<int> que ;
    link * p = NULL;
    //int cnt = 0;
    int parents = s;
    memset(visited,0,sizeof(visited));
    memset(pa,0,sizeof(pa));
    visited[s] = 1;
    pa[s] = -1;
    que.push(s);
    while(!que.empty()){
        p = graph.node[que.front()].next;
        parents = que.front();
        que.pop();
        //cnt ++;
        while(p != NULL)
        {
            if(!visited[p->data])
            {
                visited[p->data] = 1;
                pa[p->data] = parents;
                cout<<"访问："<<p->data<<endl;
                if(p->data == d) //找到了目标结点
                {
                    //cout<<"在第"<<cnt<<"层找到目标结点！（出发点算第一层）"<<endl;
                    break;
                }
                que.push(p->data);
            }
            p = p->next;
        }
    }
    cout<<"路径如下："<<endl;
    parents = d;
    //cout<<parents<<" <- ";
    while(pa[parents] != -1)
    {
        cout<<parents<<" <- ";
        parents = pa[parents];
    }
    cout<<parents<<endl;
}

int main()
{
    int s,d;
    Graph graph = readGraph();
    printGraph(graph);
    while(true)
    {
        cout<<"请输入起点和终点:"<<endl;
        cin>>s>>d;
        shortestPath(graph, s , d);
    }
    return 0;
}

#include<iostream>
#include<fstream>
#include<queue>
using namespace std;

const int MAX = 50;

struct link
{
 int data;
 link *next;
};
struct Node
{
 int v;     //顶点相关的信息
 link *next;
};
struct Graph
{
  Node node[MAX+1]; //所有的结点
  int nodeCnt; //用来记录图中结点的数目，这里假设用的是连通图。假设不连通，稍微改一下本程序就行了，具体操作留给读者思考！
};

int visited[MAX+1]; //标志数组
int pa[MAX+1];

/* 读取文件中的数据，构造一个邻接表来表示图 */ 
Graph readGraph()
{
	ifstream cin("c://graph.txt");

	//表的初始化
	Graph graph;
	int i ;
	for(i = 1; i < MAX; i ++)
	{
		graph.node[i].v = i;
		graph.node[i].next = NULL;
	}

	int n1 = 0,n2 = 0;
	link *s;
	graph.nodeCnt = 1;//把结点数初始化为1
	while(cin>>n1>>n2)
	{
		if(graph.nodeCnt < n1) graph.nodeCnt=n1;
		if(graph.nodeCnt < n2) graph.nodeCnt=n2;
		s = new link;
		s->data = n2;
		s->next=graph.node[n1].next;
		graph.node[n1].next=s; //从尾部插入
		//delete(s);

		s=new link;
		s->data = n1;
		s->next=graph.node[n2].next;
		graph.node[n2].next=s; //反过来也赋值，说明本程序测试的是无向图，如果是有向图的话读者应该知道怎么改了吧！
		//delete(s);
	}
	return graph;
}

/* 打印邻接表 */ 
void printGraph(Graph graph)
{
  link *p;
  for(int i = 1; i <= graph.nodeCnt; i ++)
  {
	  cout<<graph.node[i].v<<" -- ";

	  p=graph.node[i].next;
	  while(p!=NULL)
	  {
		  cout<<p->data;
		  p=p->next;
		  if(p != NULL) 
			  cout<<",";
	  }
	  cout<<endl;
  }
}

/* 用BFS求最短路径 */ 
void shortestPath(Graph graph, int s, int d)
{
	cout<<"从"<<s<<"到"<<d<<"的bfs最短路求解过程如下："<<endl;
	queue<int> que ;
	link * p = NULL;
	//int cnt = 0;
	int parents = s;
	memset(visited,0,sizeof(visited));
	memset(pa,0,sizeof(pa));
	visited[s] = 1;
	pa[s] = -1;
	que.push(s);
	while(!que.empty()){
		p = graph.node[que.front()].next;
		parents = que.front();
		que.pop();
		//cnt ++;
		while(p != NULL)
		{
			if(!visited[p->data])
			{
				visited[p->data] = 1;
				pa[p->data] = parents;
				cout<<"访问："<<p->data<<endl;
				if(p->data == d) //找到了目标结点
				{
					//cout<<"在第"<<cnt<<"层找到目标结点！（出发点算第一层）"<<endl;
					break;
				}
				que.push(p->data);
			}
			p = p->next;
		}
	}
	cout<<"路径如下："<<endl;
	parents = d;
	//cout<<parents<<" <- ";
	while(pa[parents] != -1)
	{
		cout<<parents<<" <- ";
		parents = pa[parents];
	}
	cout<<parents<<endl;
}

int main()
{
	int s,d;
	Graph graph = readGraph();
	printGraph(graph);
	while(true)
	{
		cout<<"请输入起点和终点:"<<endl;
		cin>>s>>d;
		shortestPath(graph, s , d);
	}
	return 0;
}

 

 

输入文件graph.txt里数据格式如下：

 

1 2
1 3
1 4
2 4