面试题27：二叉搜索树与双向链表转换

1.输入一棵二叉搜索树，将该二叉搜索树转换成一个排序的双向链表，不能创建任何新的结点。只能调整树中结点指针的指向。

例如： 下面的二叉搜索树和对应的双向链表。



分析：在二叉搜索树中，每个节点都有两个指针，在双向链表中，也有两个指针，在二叉搜索树种，做节点的值总是小于父节点的值，右节点的值总是大于父节点的值。为了使得构造的双向链表有序，原先指向左节点的指针调整为指向前一个节点，原先指向右节点的指针指向链表中的下一个结点。而二叉搜索树的中序遍历出来的序列是从小打到排序的。所以采用中序遍历二叉树。当遍历到根节点的时候，如下图：



当遍历到根节点10
的时候，可以将树看成三个部分，根节点为6的左子树的部分和根节点为14 的右子树，按要求，值为10 的节点将和左子树的最大的一个节点8连接起来，同时还要和右子树值为12 的节点连接起来。

源码：

/**
* 功能说明：Description
* 作者：K0713
* 日期：2016-7-20
**/
#include<iostream>
#include<vector>
using namespace std;
//二叉树结构
struct BinaryTreeNode
{
int m_nValue;
BinaryTreeNode* m_pLeft;
BinaryTreeNode* m_pRight;
};
//创建结点
BinaryTreeNode* CreateBinaryTreeNode(int value);
//连接结点
void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight);
//打印树结点
void PrintTreeNode(BinaryTreeNode* pNode);
//打印二叉树
void PrintTree(BinaryTreeNode* pRoot);
//销毁二叉树
void DestroyTree(BinaryTreeNode* pRoot);
//树的深度
int TreeDepth(BinaryTreeNode* pRoot);
//-----------------//
//递归转换
void ConvertNode(BinaryTreeNode* pNode, BinaryTreeNode** pLastNodeInList);
//二叉树与双向链表转换，并返回链表头节点
BinaryTreeNode* Convert(BinaryTreeNode* pRootOfTree);
//打印双向链表
void PrintDoubleLinkedList(BinaryTreeNode* pHeadOfList);
//销毁链表
void DestroyList(BinaryTreeNode* pHeadOfList);
int main()
{
BinaryTreeNode* pNode10 = CreateBinaryTreeNode(10);
BinaryTreeNode* pNode6 = CreateBinaryTreeNode(6);
BinaryTreeNode* pNode14 = CreateBinaryTreeNode(14);
BinaryTreeNode* pNode4 = CreateBinaryTreeNode(4);
BinaryTreeNode* pNode8 = CreateBinaryTreeNode(8);
BinaryTreeNode* pNode12 = CreateBinaryTreeNode(12);
BinaryTreeNode* pNode16 = CreateBinaryTreeNode(16);
ConnectTreeNodes(pNode10, pNode6, pNode14);
ConnectTreeNodes(pNode6, pNode4, pNode8);
ConnectTreeNodes(pNode14, pNode12, pNode16);
PrintTree(pNode10);
BinaryTreeNode* pHeadOfList = Convert(pNode10);
PrintDoubleLinkedList(pHeadOfList);
DestroyList(pNode4);
system("PAUSE");
return 0;
}
//创建树结点
BinaryTreeNode* CreateBinaryTreeNode(int value)
{
BinaryTreeNode* pNode = new BinaryTreeNode();
pNode->m_nValue = value;
pNode->m_pLeft = NULL;
pNode->m_pRight = NULL;
return pNode;
}
//连接树结点
void ConnectTreeNodes(BinaryTreeNode* pParent, BinaryTreeNode* pLeft, BinaryTreeNode* pRight)
{
if (pParent != NULL)
{
pParent->m_pLeft = pLeft;
pParent->m_pRight = pRight;
}
}
//打印
void PrintTreeNode(BinaryTreeNode* pNode)
{
if (pNode != NULL)
{
cout << "value of this node is: " << pNode->m_nValue << endl;
if (pNode->m_pLeft != NULL)
cout << "value of its left child is: " << pNode->m_pLeft->m_nValue << endl;
else
cout << "left child is null.\n";
if (pNode->m_pRight != NULL)
cout << "value of its right child is:" << pNode->m_pRight->m_nValue << endl;
else
cout << "right child is null.\n";
}
else
{
cout << "this node is null.\n";
}
cout << endl;
}
void PrintTree(BinaryTreeNode* pRoot)
{
PrintTreeNode(pRoot);
if (pRoot != NULL)
{
if (pRoot->m_pLeft != NULL)
PrintTree(pRoot->m_pLeft);
if (pRoot->m_pRight != NULL)
PrintTree(pRoot->m_pRight);
}
}
//销毁
void DestroyTree(BinaryTreeNode* pRoot)
{
if (pRoot != NULL)
{
BinaryTreeNode* pLeft = pRoot->m_pLeft;
BinaryTreeNode* pRight = pRoot->m_pRight;
delete pRoot;
pRoot = NULL;
DestroyTree(pLeft);
DestroyTree(pRight);
}
}
//树的深度
int TreeDepth(BinaryTreeNode* pRoot)
{
if (pRoot == NULL)
return 0;
int nLeft = TreeDepth(pRoot->m_pLeft);
int nRight = TreeDepth(pRoot->m_pRight);
return (nLeft > nRight) ? (nLeft + 1) : (nRight + 1);
}
//二叉树与双向链表的转换
BinaryTreeNode* Convert(BinaryTreeNode* pRootOfTree)
{
BinaryTreeNode *pLastNodeInList = NULL;
ConvertNode(pRootOfTree, &pLastNodeInList);
// pLastNodeInList指向双向链表的尾结点，
// 我们需要返回头结点
BinaryTreeNode *pHeadOfList = pLastNodeInList;
while (pHeadOfList != NULL && pHeadOfList->m_pLeft != NULL)
pHeadOfList = pHeadOfList->m_pLeft;
return pHeadOfList;
}
//递归转换
void ConvertNode(BinaryTreeNode* pNode, BinaryTreeNode** pLastNodeInList)
{
if (pNode == NULL)
return;
BinaryTreeNode *pCurrent = pNode;
if (pCurrent->m_pLeft != NULL)
ConvertNode(pCurrent->m_pLeft, pLastNodeInList);
pCurrent->m_pLeft = *pLastNodeInList;
if (*pLastNodeInList != NULL)
(*pLastNodeInList)->m_pRight = pCurrent;
*pLastNodeInList = pCurrent;
if (pCurrent->m_pRight != NULL)
ConvertNode(pCurrent->m_pRight, pLastNodeInList);
}
//打印双向链表
void PrintDoubleLinkedList(BinaryTreeNode* pHeadOfList)
{
BinaryTreeNode* pNode = pHeadOfList;
printf("The nodes from left to right are:\n");
while (pNode != NULL)
{
printf("%d\t", pNode->m_nValue);
if (pNode->m_pRight == NULL)
break;
pNode = pNode->m_pRight;
}
printf("\nThe nodes from right to left are:\n");
while (pNode != NULL)
{
printf("%d\t", pNode->m_nValue);
if (pNode->m_pLeft == NULL)
break;
pNode = pNode->m_pLeft;
}
printf("\n");
}
void DestroyList(BinaryTreeNode* pHeadOfList)
{
BinaryTreeNode* pNode = pHeadOfList;
while (pNode != NULL)
{
BinaryTreeNode* pNext = pNode->m_pRight;
delete pNode;
pNode = pNext;
}
}

结果：