数据结构(6) -- 构建二叉搜索树

//BinTree.h
#ifndef BINTREE_H_
#define BINTREE_H_
#define ElemType int
typedef struct _PNode
{
ElemType data;
_PNode *left;
_PNode *right;
}PNode;

class BinTree
{
private:
PNode *root;
public:
BinTree();
~BinTree();
PNode* GetRoot();    //获得根节点
void SetRoot(PNode *p) { root = p; }    //设置根节点
PNode* Find(ElemType x , PNode *p);        //查找元素x所在位置
PNode* FindMin(PNode *p);    //查找二叉搜索树的最小值
PNode* FindMax(PNode *p);    //查找二叉搜索树的最大值
PNode* Insert(ElemType x, PNode *p);  //构建二叉搜索树，所插入的元素按二叉搜索树排列
PNode* Delete(ElemType x, PNode *p);  //删除二叉搜索树的元素
//遍历二叉树
void PreOrder(PNode *p);  //先序遍历
void CenOrder(PNode *p);  //中序遍历
void Trave(PNode *p);     //层次遍历
};
#endif

/////////////////////////////////////////////////////////////////////
//BinTree.cpp
#include "BinTree.h"
#include <iostream>
#include <queue>

BinTree::BinTree()
{
root = NULL;
}

BinTree::~BinTree(){}

PNode* BinTree::GetRoot()
{
return root;
}
PNode* BinTree::Find(ElemType x, PNode *p)
{
/*
//尾递归实现
if (p == NULL)
return NULL;
if (x > p->data)
return Find(x, p->right);
else if (x < p->data)
return Find(x, p->left);
else
return p;*/
while (p != NULL)
{
if (x > p->data)
p = p->right;
else if (x < p->data)
p = p->left;
else
return p;
}
return NULL;
}

PNode* BinTree::FindMin(PNode *p)
{
//递归查找
if (p == NULL)
return NULL;
else if (p->left == NULL)
return p;
else
return FindMin(p->left);
}

PNode* BinTree::FindMax(PNode *p)
{
if (p != NULL)
while (p->right != NULL)
p = p->right;
return p;
}

//遍历二叉树
void BinTree::PreOrder(PNode *p)
{
if (p == NULL)
return;
std::cout << p->data << " ";
PreOrder(p->left);
PreOrder(p->right);
}

void BinTree::CenOrder(PNode *p)
{
if (p == NULL)
return;
CenOrder(p->left);
std::cout << p->data << " ";
CenOrder(p->right);
}

PNode* BinTree::Insert(ElemType x, PNode *p)
{
if (p == NULL)
{
p = new PNode();
p->data = x;
p->left = p->right = NULL;
}
else
{
if (x < p->data)
p->left = Insert(x, p->left);
else if (x > p->data)
p->right = Insert(x, p->right);
}
return p;
}

PNode* BinTree::Delete(ElemType x, PNode *p)
{
PNode *tmp;
if (p == NULL)
std::cout << "要删除的元素未找到" << std::endl;
else if (x < p->data)  //查找要删除的节点
p->left = Delete(x, p->left);
else if (x > p->data)
p->right = Delete(x, p->right);
else
{
//删除的元素左右节点都在,删除右子树的最小节点
if (p->left != NULL && p->right != NULL)
{
tmp = FindMin(p->right);  //查找右子树的最小节点
p->data = tmp->data;          //将右字数的最小值与当前节点的值互换
p->right = Delete(p->data, p->right);    //删除右字数最小节点
}
else
{//删除的元素只有左节点，或只有右节点，或是叶子节点
tmp = p;
if (p->left == NULL)  //只有右节点，直接用右节点替换要删除节点
p = p->right;
else if(p->right == NULL) //只有左节点，直接用左节点替换要删除节点
p = p->left;
delete tmp;    //如果删除节点是叶子节点，直接删除当前节点
}
}
return p;
}

void BinTree::Trave(PNode *p)    //层次遍历
{
std::queue<PNode*> q;
q.push(p);
while (!q.empty())
{
PNode *s = q.front();
std::cout << s->data << " ";
if (s->left != NULL)
q.push(s->left);
if (s->right != NULL)
q.push(s->right);
q.pop();
}
}

////////////////////////////////////////////////////////
//测试
#include <iostream>
#include "BinTree.h"
using namespace std;

int main()
{
BinTree bt;
//构造二分查找树
bt.SetRoot(bt.Insert(4, bt.GetRoot())); //注意跟新根节点
bt.SetRoot(bt.Insert(3, bt.GetRoot()));
bt.SetRoot(bt.Insert(5, bt.GetRoot()));
bt.SetRoot(bt.Insert(6, bt.GetRoot()));
bt.SetRoot(bt.Insert(7, bt.GetRoot()));
bt.SetRoot(bt.Insert(8, bt.GetRoot()));
cout << "先序遍历: " << endl;
bt.PreOrder(bt.GetRoot());
cout << endl;
cout << "中序遍历: " << endl;
bt.CenOrder(bt.GetRoot());
cout << endl;
cout << "层次遍历：" << endl;
bt.Trave(bt.GetRoot());
cout << endl;
cout << "最小值:" << bt.FindMin(bt.GetRoot())->data << endl;
cout << "最大值:" << bt.FindMax(bt.GetRoot())->data << endl;
///////////////////////////////////////////////////////////////////
cout << endl << "删除节点 5 " << endl;
bt.Delete(4, bt.GetRoot());
cout << "先序遍历: " << endl;
bt.PreOrder(bt.GetRoot());
cout << endl;
cout << "中序遍历: " << endl;
bt.CenOrder(bt.GetRoot());
cout << endl;
cout << "层次遍历：" << endl;
bt.Trave(bt.GetRoot());
cout << endl;
cout << "最小值:" << bt.FindMin(bt.GetRoot())->data << endl;
cout << "最大值:" << bt.FindMax(bt.GetRoot())->data << endl;
system("pause");
return 0;
}