面试算法001-- 把二元查找树转变成排序的双向链表

问题：

输入一棵二元查找树，将该二元查找树转换成一个排序的双向链表， 

要求不能创建任何新的结点，只调整指针的指向 。

         10

        /     \
      6       14
     /  \       /   \

  4    8   12  16

  转换成 4->6->8->10->12->14->16

问题来源： 

本题是微软的面试题

问题分析：

一般与树有关的题目都可以用递归的思路来解决，本题我们也可以考虑用此思路来解决。

思路一：

每到一个节点时准备调整以该节点为根节点的子树（先调整其左子树，将左子树转换成一个排好序的左子链表，再调整其右子树，将其转换成右子链表，最后链接左子链表的最右端、当前节点、右子链表的最左端）。从树的根节点开始递归调整所有的节点。

思路二：

采用数的中序遍历整棵树。按这种方式比较小的节点会先被访问。如果我们每访问一个节点，假设之前访问过的节点已经调整成一个排序的双向链表，我们再把当前访问的阶段加入到其链表末尾。当所有的节点访问结束后，整棵树便变成了双向链表。

代码实现（Java）：

public class Node<T extends Comparable<T>> {private T data;private Node<T> lNode;private Node<T> rNode;public Node(T data){this.setData(data);this.setlNode(null);this.setrNode(null);}/** * @return the data */public T getData() {return data;}/** * @param data the data to set */public void setData(T data) {this.data = data;}/** * @return the lNode */public Node<T> getlNode() {return lNode;}/** * @param lNode the lNode to set */public void setlNode(Node<T> lNode) {this.lNode = lNode;}/** * @return the rNode */public Node<T> getrNode() {return rNode;}/** * @param rNode the rNode to set */public void setrNode(Node<T> rNode) {this.rNode = rNode;}}

/**  * @ClassName: BTree  * @Description: This class describe the binary tree * @author [e-mail]  * @date Mar 2, 2015 2:01:53 PM  *   */public class Tree<T extends Comparable<T>> {public Node<T> root = null;/** * @Title: addNode  * @Description: This method used to add a new node into the tree * @param @param data * @return void * @throws */public void addNode(T data){Node<T> node = new Node<T>(data);if(root == null){root = node;} else {Node<T> parent = root;Node<T> cur = root;boolean isLeft=true;while(cur != null){parent=cur;if(data.compareTo(cur.getData()) < 0) {isLeft = true;cur = cur.getlNode();} else {isLeft=false;cur = cur.getrNode();}}if(isLeft) {parent.setlNode(node);} elseparent.setrNode(node);}}/** * * @Title: display * @Description: display all the nodes in tree* @param @param node* @return void* @throws */public void display(Node<T> node){if(node != null){display(node.getlNode());System.out.print(node.getData() + "-->");display(node.getrNode());}}}

public class List<T extends Comparable<T>> {/** * * @Title: append * @Description: append two list* @param @param node1* @param @param node2* @param @return* @return Node<T>* @throws */public Node<T> append(Node<T> node1,Node<T> node2){if(node1==null)return node2;if(node2==null)return node1;Node<T> tail=node1;while(tail.getrNode()!=null) {tail=tail.getrNode();}tail.setrNode(node2);node2.setlNode(tail);return node1;}public void display(Node<T> node){while(node != null){System.out.print(node.getData() + "\t");node = node.getrNode();}}}

public interface TreeToLinkList<T extends Comparable<T>> {public Node<T> convert(Node<T> root);}

public class Test {/** * @param args */public static void main(String[] args) {Tree<Integer> tree=new Tree<Integer>();tree.addNode(49);tree.addNode(25);tree.addNode(55);tree.addNode(10);tree.addNode(51);tree.addNode(65);tree.display(tree.root);System.out.println();TreeToLinkList<Integer> solution = new TreeToLinkListImpl1<Integer>();Node<Integer> node = solution.convert(tree.root);List<Integer> list = new List<Integer>();list.display(node);TreeToLinkList<Integer> solution2 = new TreeToLinkListImpl2<Integer>();Node<Integer> node2 = solution2.convert(tree.root);List<Integer> list2 = new List<Integer>();list2.display(node2);}}

思路一代码：

public class TreeToLinkListImpl1<T extends Comparable<T>> implements TreeToLinkList<T>{/* (non-Javadoc) * <p>Title: convert</p>  * <p>Description: </p>  * @param tree  * @see Algorithm.Test.T001_TreeToLinkList.TreeToLinkList#convert(Algorithm.Test.T001_TreeToLinkList.Tree)  */@Overridepublic Node<T> convert(Node<T> root) {List<T> list = new List<T>();if(root != null){Node<T> left = convert(root.getlNode());Node<T> right = convert(root.getrNode());root.setlNode(null);root.setrNode(null);left = list.append(left, root);left = list.append(left, right);return left;} else {return null;}}}

思路二代码：

/**  * @ClassName: TreeToLinkListImpl1  * @Description: The class implements the algorithm that convert the tree to link list * @author [e-mail]  * @date Mar 2, 2015 4:24:31 PM  *   */public class TreeToLinkListImpl2<T extends Comparable<T>> implements TreeToLinkList<T>{public Node<T> firstListNode;/* (non-Javadoc) * <p>Title: convert</p>  * <p>Description: </p>  * @param tree  * @see Algorithm.Test.T001_TreeToLinkList.TreeToLinkList#convert(Algorithm.Test.T001_TreeToLinkList.Tree)  */@Overridepublic Node<T> convert(Node<T> root) {inOrder(root);return this.firstListNode;}public void inOrder(Node<T> root){List<T> list = new List<T>();if(root.getlNode()!=null){inOrder(root.getlNode());}this.firstListNode = list.append(this.firstListNode, new Node<T>(root.getData()));if(root.getrNode()!=null){inOrder(root.getrNode());}}}