Convert Binary Search Tree to an Ordered Double Linked List

输入: 一棵二叉查找树

输出: 与二叉查找树对应的有序双向链表

要求：不允许额外生成节点，只允许调整指针指向。例如：

10

/ /

6 1

/ / / /

4 8 12 16

要求变换后输出

4=6=8=10=12=14=16

个人思路：

考虑到对二叉排序树进行中序遍历可以实现元素的排序，不妨在中序遍历过程中实现对各个节点指针的调整。那么到底先动节点的左指针还是右指针呢？仔细思考一下，如果先动节点的右指针，在递归的过程中所有的右子树都会丢失。而先动左儿子指针的话，因为中序遍历是先左儿子，再根节点最后再右子树，这样一旦结束左子树的遍历，当前根节点的左儿子指针就不再需要了，因而可以通过左指针来记录中序遍历的顺序。这样将整棵树遍历一次后，就会形成一个以最大数为首节点的单向链表。为了产生双向链表， 需要将产生的单向链表再遍历一次，使得各节点的右儿子指针指向各自的前向节点。按照上述思路，算法的最坏时间复杂度为O(n)。

核心代码：

void BSTree::Inorder(BSTreeNode* &root) {
if(root) {
Inorder(root->left);
root->left = prev;
prev = root;
Inorder(root->right);
}
}
BSTreeNode* BSTree::ToDoubleLinkedList() {
Inorder(root);

BSTreeNode *p = Max(root), *q;
while(p) {
q = p->left;
if(q == NULL)
break;
q->right = p;
p = p ->left;
}
return p;
}

以下C++代码完整实现建立二叉树，到链表的转换以及测试的过程。

#include <cstdlib>
#include <ctime>
#include <iostream>
#include <set>
using namespace std;
/* private member access control and destructor are omitted in favor of simplicity */
struct BSTreeNode {
BSTreeNode(int d = 0):data(d), left(0), right(0) {}
int data;
BSTreeNode *left, *right;
};
struct BSTree {
BSTree():root(0), prev(0) {}
BSTreeNode* Insert(int d, BSTreeNode* &r);
BSTreeNode* Max(BSTreeNode *r);
void Inorder(BSTreeNode* &r);
BSTreeNode* ToDoubleLinkedList();
BSTreeNode *root, *prev;
};
BSTreeNode* BSTree::Insert(int d, BSTreeNode *&r) {
if(r == NULL)
return r = new BSTreeNode(d);
if(r->data > d)
return Insert(d, r->left);
else
return Insert(d, r->right);
}
BSTreeNode* BSTree::Max(BSTreeNode *root) {
if(root == NULL) return NULL;
while(root->right)
root = root->right;
return root;
}
/* in-order search on BST */
void BSTree::Inorder(BSTreeNode* &root) {
if(root) {
Inorder(root->left);
root->left = prev;
prev = root;
Inorder(root->right);
}
}
BSTreeNode* BSTree::ToDoubleLinkedList() {
Inorder(root);

BSTreeNode *p = Max(root), *q;
while(p) {
q = p->left;
if(q == NULL)
break;
q->right = p;
p = p ->left;
}
return p;
}
int main(void) {
srand((unsigned)time(0));

/*	10 different random integers ranging from 0 to 99 */
set<int> s;
for(int i = 0; i < 10; ++i) {
int rd = rand() % 100;
while(s.count(rd)) rd = rand() % 100;
s.insert(rd);
}
/*	build a Binary Search Tree */
BSTree tree;
for(set<int>::const_iterator it = s.begin(); it != s.end(); ++it) {
tree.Insert(*it, tree.root);
}

/* convert the Binary Search Tree to a Double Linked List */
BSTreeNode *p = tree.ToDoubleLinkedList();
/* linear search on the resulting list */
while(p) {
cout << p->data << endl;
p = p->right;
}
}