二叉查找树解析及其C++实现(5)

template<class T>
BSTNode<T>* BSTree<T>::successor(BSTNode<T> *x)
{
 // 如果x存在右孩子，则"x的后继结点"为 "以其右孩子为根的子树的最小结点"。
 if(x->right!=NULL)
  return minimum(x->right);
 // 如果x没有右孩子。则x有以下两种可能：
    // (1) x是"一个左孩子"，则"x的后继结点"为 "它的父结点"。
    // (2) x是"一个右孩子"，则查找"x的最低的父结点，并且该父结点要具有左孩子"，找到的这个"最低的父结点"就是"x的后继结点"。
    BSTNode<T> *p = x->parent;
    while(p!=NULL && x==p->right)
    {
     x = p;
     p = p->parent;
 }
 return p;
}

template<class T>
void BSTree<T>::insert(BSTNode<T>* &tree, BSTNode<T> *z)
{
 BSTNode<T> *y = NULL;
 BSTNode<T> *x = tree;
 
 // 查找z的插入位置
 while(x!=NULL)
 {
  y = x;
  if(z->key < x->key)
   x = x->left;
  else // else if(z->key > x->key)
   x = x->right;
//  若禁止插入相同键值
//  else
//  {
//   free(z)；// 释放之前分配的结点
//   return;
//  }
 }
 z->parent = y;
 if(y==NULL)
  tree = z;
 else if(z->key<y->key)
  y->left = z;
 else
  y->right = z;
}

template<class T>
void BSTree<T>::insert(T key)
{
 BSTNode<T> *z = NULL;
 
 // 如果新建结点失败，则返回
 if((z=new BSTNode<T>(key,NULL,NULL,NULL))==NULL)
  return;
 
 insert(root,z);
}

template<class T>
BSTNode<T>* BSTree<T>::remove(BSTNode<T>* &tree, BSTNode<T> *z)
{
 BSTNode<T> *x = NULL;
 BSTNode<T> *y = NULL;
 
 if(z->left==NULL || z->right==NULL)
  y = z;
 else
  y = successor(z);
 
 if(y->left!=NULL)
  x = y->left;
 else
  x = y->right;
 
 if(x!=NULL)
  x->parent = y->parent;
 
 if(y->parent==NULL)
  tree = x;
 else if(y==y->parent->left)
  y->parent->left = x;
 else
  y->parent->right = x;
 
 if(y!=z)
  z->key = y->key;
 return y;
}

template<class T>
void BSTree<T>::remove(T key)
{
 BSTNode<T> *z, *node;
 
 if((z=search(root,key))!=NULL)
  if((node=remove(root,z))!=NULL)
   delete node;
}

template<class T>
void BSTree<T>::print(BSTNode<T> *&tree, T key, int direction)
{
 if(tree!=NULL)
 {
  if(direction==0)
   cout<<setw(2)<<tree->key<<"is root"<<endl;
  else
   cout<<setw(2)<<tree->key<<"is"<<setw(2)<<key<<"'s"<<setw(12)<<(direction==1 ? "right child":"left child")<<endl;
  print(tree->left,tree->key,-1);
  print(tree->right,tree->key,1);
 }
}

template<class T>
void BSTree<T>::print()
{
 if(root!=NULL)
  print(root,root->key,0);
}

template<class T>
void BSTree<T>::destroy(BSTNode<T> *&tree)
{
 if(tree==NULL)
  return ;
 if(tree->left!=NULL)
  return destroy(tree->left);
 if(tree->right!=NULL)
  return destroy(tree->right);
 
 delete tree;
 tree=NULL;
}

template<class T>
void BSTree<T>::destroy()
{
 destroy(root);
}

#endif

测试代码：BSTreeTest.cpp

#include<iostream>
#include "BSTree.h"
using namespace std;

static int arr[] = {1,5,4,3,2,6};

int main()
{
 int i,len;
 BSTree<int> *tree = new BSTree<int>();
 
 cout<<"依次添加：";
 len = sizeof(arr)/sizeof(arr[0]);
 for(i=0;i<len;++i)
 {
  cout<<arr[i]<<" ";
  tree->insert(arr[i]);
 }
 
 cout<<"\n前序遍历：";
 tree->preOrder();
 cout<<"\n中序遍历：";
 tree->inOrder();
 cout<<"\n后序遍历：";
 tree->postOrder();
 cout<<endl;
 
 cout<<"最小值："<<tree->minimum()<<endl;
 cout<<"最大值："<<tree->maximum()<<endl;
 cout<<"树的详细信息："<<endl;
 tree->print();
 
 cout<<" \n删除根节点："<<arr[3];
 tree->remove(arr[3]);
 
 cout<<"\n中序遍历：";
 tree->inOrder();
 cout<<endl;
 
 // 销毁二叉树
 tree->destroy();