【Data structure & Algorithm】把二元查找树转变成排序的双向链表

把二元查找树转变成排序的双向链表

题目：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节点，只调整指针指向。

比如将二元查找树

10

/       \

6        14

/  \        /     \

4   8   12   16

转换成双向链表4=6=8=10=12=14=16

分析：

思路一：当到达某一节点准备调整以该节点为根节点的子树时，先调整其左子树将左子树转换成一个排好序的左子链表，再调整其右子树转换右子链表。最近链接左子链表的最右节点（左子树的最大节点）、当前节点和有子链表的最左节点（右子树的最小节点）。从树的根节点开始递归调整所有节点。

首先定义二元查找树的数据结构如下：

structBSTreeNode

{

int m_nValue;

BSTreeNode *m_pLeft;

BSTreeNode *m_pRight;

}

BSTreeNode*ConvertNode(BSTreeNode* pNode, bool asRight)
{
       if (!pNode)
              returnNULL;
       BSTreeNode *pLeft = NULL;
       BSTreeNode* pRight = NULL;
 
       //Convert the left sub-tree
       if(pNode -> m_pLeft)
              pLeft = ConvertNode(pNode ->m_pLeft, false);
 
       //Convert the greatest node in the leftsub-tree to the current node
       if (pLeft)
       {
              pLeft -> m_pRight = pNode;
              pNode -> m_pLeft = pLeft;
}
 
//Convert the right sub-tree
if (pNode -> m_pRight)
   	pRight= ConvertNode (pNode -> m_pRight, true);
 
//Connect the least node in the rightsub-tree to the current node
if (pRight)
{
       pNode-> m_pRight = pRight;
       pRight-> m_pLeft = pNode;
}
 
BSTreeNode *pTemp = pNode;
 
//If the current node is the right child ofits parent, return the least node in the tree whose root is the current node
if (asRight)
{
       while(pTemp -> m_pLeft)
             pTemp= pTemp -> m_pLeft;
}
//if the current node is the left child ofits parent, return the greatest node in the tree whose root is the current node
else
{
       while(pTemp -> m_pRight)
             pTemp= pTemp -> m_pRight;
}
return pTemp;
 
//Convert a BSTree into a sorteddouble-linked list
BSTreeNode* Convert(BSTreeNode* pHeadOfTree)
{
       returnConvertNode(pHeadOfTree, true);
}

思路二：中序遍历二叉树。较小节点先访问。如果访问一个节点，假设之前访问过的节点已经调整成一个排序的双向链表，再把调整当前节点的指针将其连接到链表末尾，当所有节点都访问过之后，整棵树也就转换为一个排序的双向链表了。

voidConvertNode(BSTreeNode* pNode, BSTreeNode*& pLastNodeInList)
{
       if(pNode ==NULL)
              return;
       BSTreeNode *pCurrent = pNode;
 
       //Convert the left sub-tree
       if (pCurrent -> m_pLeft !=NULL)
              ConvertNode(pCurrent-> m_pLeft, pLastNodeInList);
 
       //Put the current node into thedouble-linked list
       pCurrent -> m_pLeft = pLastNodeInList;
       if(pLastNodeInList != NULL)
       pLastNodeInList-> m_pRight = pCurrent;
 
pLastNodeInList = pCurrent;
 
//Convert the right sub-tree
if (pCurrent -> m_pRight != NULL)
       ConvertNode(pCurrent-> m_pRight, pLastNodeInList);
 
//Convert a BSTree into a sorteddouble-linked list
BSTreeNode* Convert_Solution(BSTreeNode*pHeadOfTree)
{
       BSTreeNode*pLastNodeInList = NULL;
       ConvertNode(pHeadOfTree,pLastNodeInList);
 
       //Getthe head of the double-linked list
       BSTreeNode*pHeadOfList = pLastNodeInList;
       while(pHeadOfList && pHeadOfList -> m_pLeft)
              pHeadOfList= pHeadOfList -> m_pLeft;
 
       return pHeadOfList;
}
}