广度优先搜索算法（breadth First Search, BFS)

                                    广度优先( Breadth-First-Search, BFS)

这是一种图形搜索算法，彻底地搜索整张图，直到找到结果为止。

一般的实现里，其邻居节点尚未被检验过的节点会被放置在一个称为open 容器里面，而未检验过的节点则

会被放置在称为closed的容器中，形成张open-closed表。

算法描述如下：

1. 将顶点入队列

2.当队列为非空时，继续执行，否则算法结束

a. 出队列取得队列头顶点V；访问并标记为已访问

b.查找顶点V的第一个邻接顶点W

c.若V的邻接顶点W未被访问过的，则W入队列

d.继续查找顶点V的另一个新的邻接顶点W，转到步骤2。

设置两个链表

closedList  存放已经访问过的节点

openList   存放即将访问的节点

广度优先算法可以总结为，按层次来遍历的，先是根节点，然后是第二层子节点，依次是第三层子节点，将节点分别放入队列中，每次从队列中探出首元素，遍历后的点放入closed表中，还未遍历的店放入open表中，当open表为空时，则整个数遍历完全。

实现的代码如下：

import java.util.Iterator;import java.util.LinkedList;import java.util.List;public class breadthFirstSearch {public static class Node{List neighbors;Node pathParent;String name;public Node(String name){this.name = name;neighbors = new LinkedList();}public String toString(){return name;}}public static void main(String[] args){Node nodeA = new Node("A");Node nodeB = new Node("B");Node nodeC = new Node("C");Node nodeD = new Node("D");Node nodeE = new Node("E");Node nodeF = new Node("F");Node nodeG = new Node("G");Node nodeH = new Node("H");/* * Construct Trees */nodeA.neighbors.add(nodeC);nodeA.neighbors.add(nodeD);nodeA.neighbors.add(nodeE);nodeB.neighbors.add(nodeE);nodeC.neighbors.add(nodeA);nodeC.neighbors.add(nodeD);nodeC.neighbors.add(nodeF);nodeD.neighbors.add(nodeA);nodeD.neighbors.add(nodeC);nodeE.neighbors.add(nodeA);nodeE.neighbors.add(nodeB);nodeE.neighbors.add(nodeG);nodeF.neighbors.add(nodeC);nodeF.neighbors.add(nodeH);nodeG.neighbors.add(nodeE);nodeH.neighbors.add(nodeC);nodeH.neighbors.add(nodeF);breadthFirstSearch bfs = new breadthFirstSearch();System.out.println("From A to B:" + bfs.search(nodeA,nodeF));}public List search(Node startNode,Node goalNode){LinkedList closedList = new LinkedList();LinkedList openList = new LinkedList();openList.add(startNode);startNode.pathParent = null;while(!openList.isEmpty()){Node node = (Node)openList.removeFirst();if(node == goalNode){//return constructPath(goalNode);//路径就是closed表中的顺序return constructPath(closedList);}else{closedList.add(node);Iterator i = node.neighbors.iterator();while(i.hasNext()){Node neighborNode = (Node)i.next();if(!closedList.contains(neighborNode) &&!openList.contains(neighborNode)){neighborNode.pathParent = node;openList.add(neighborNode);}}}}return null;}public List constructPath(LinkedList list){//LinkedList path = new LinkedList();System.out.println("广度优先路径：" + list.toString());//while(node.pathParent != null){//path.addFirst(node);//node = node.pathParent;//}return list;}}