二叉查找树（二叉排序树）操作大全C++实现

￡神魔★判官ぃ 2022-05-15 13:09 218阅读 0赞

**// 链式二叉查找树的各种操作.cpp : Defines the entry point for the console application.  
//**

**\#include "stdafx.h"  
\#include<iostream>  
using namespace std;**

**struct BSTree  
\{  
int data;  
BSTree \*left;  
BSTree \*right;  
\};  
//标记在插入时，如果已存在，则为true ，表示不需要插入，否则为false  
bool flag = false;  
int a\[100\];  
//查找操作  
BSTree \*search(BSTree \*r,int x)  
\{  
if(r==NULL)  
return NULL;  
else  
\{  
if(r->data==x)  
return r;  
else if(r->data>x)  
return search(r->left,x);  
else  
return search(r->right,x);  
\}  
\}  
//返回最小值节点  
BSTree \*BSTMinNum(BSTree \*r)  
\{  
BSTree \*s=r;  
while(s->left!=NULL)  
\{  
s=s->left;  
\}  
return s;  
\}  
//返回最大值节点  
BSTree \*BSTMaxNum(BSTree \*r)  
\{  
BSTree \*s=r;  
while(s->right!=NULL)  
\{  
s=s->right;  
\}  
return s;  
\}  
//获得其父节点  
BSTree \*getFather(BSTree \*r, BSTree \*s)  
\{  
BSTree \*sf;  
if(r==NULL||r==s)  
sf=NULL;  
else  
\{  
if(s==r->left||s==r->right)  
sf= r;  
else if(s->data > r->data)  
sf=getFather(r->right,s);  
else  
sf=getFather(r->left,s);  
\}  
return sf;  
\}  
//获得节点中序的前趋节点  
//此操作不需要遍历树  
BSTree \*searchPreMidOrder(BSTree \*r,int val)  
\{  
BSTree \*s = search(r,val);  
if(s==NULL)  
return NULL;  
else  
\{  
//如果左儿子节点非空，则找到左子树的最大值节点  
if(s->left!=NULL)  
return BSTMaxNum(s->left);  
//如果左儿子节点空，则找到第一个有右儿子节点的其祖辈节点  
BSTree \*p = getFather(r,s);  
while(p!=NULL&&s==p->left)  
\{  
s=p;  
p=getFather(r,s);  
\}**

**return p;  
\}  
\}  
//获得节点中序的后继节点  
//此操作不需要遍历树  
BSTree \*searchPostMidOrder(BSTree \*r,int val)  
\{  
BSTree \*s = search(r,val);  
if(s==NULL)  
return NULL;  
else  
\{  
//如果右儿子节点非空，则找到右子树的最小值节点  
if(s->right!=NULL)  
\{  
return BSTMinNum(s->right);  
\}  
//如果右儿子节点为空，则找到第一个有左儿子节点的其祖辈节点  
BSTree \*p = getFather(r,s);  
while(p!=NULL&&s==p->right)  
\{  
s=p;  
p=getFather(r,s);  
\}  
return p;  
\}  
\}  
//插入操作  
BSTree\* insert(BSTree \*r,BSTree \*s)  
\{  
//首先查找树中是否已存在此节点  
BSTree \*p = search(r,s->data);  
if(p==NULL)  
\{  
flag = false;  
if(r==NULL)  
\{  
r=s;  
\}  
else if(s->data<r->data)  
r->left = insert(r->left,s);  
else if(s->data>r->data)  
r->right = insert(r->right,s);  
\}  
else  
flag = true;  
return r;  
\}  
//建树  
BSTree \* createBSTree(BSTree \*r,int \*a,int n)  
\{  
int i;  
BSTree \* t;  
t = r;  
for(i=0;i<n;i++)  
\{  
BSTree \*s = (BSTree\*)malloc(sizeof(BSTree));  
s->data=a\[i\];  
s->left=NULL;  
s->right=NULL;  
t = insert(t,s);  
\}  
return t;  
\}**

**//删除操作  
BSTree \* deleteNode(BSTree \*r,BSTree \*s)  
\{  
//BSTNODE \* temp, \* tfather, \* pf;  
BSTree \*temp,\*father,\*sf;  
//pf = getfather(p, r);  
sf=getFather(r,s);  
//被删除结点是叶子结点, 不是根结点  
if(s->left==NULL&&s->right==NULL&&sf!=NULL)  
//  
if(sf->left==s)  
sf->left=NULL;  
//  
else  
sf->right=NULL;  
//被删除结点是叶子结点,又是根结点  
else if(s->left==NULL&&s->right==NULL&&sf==NULL)  
r=NULL;  
//被删除结点有右孩子,无左孩子.被删结点是根结点  
else if(s->left==NULL&&s->right!=NULL&&sf!=NULL)  
if(sf->left==s)  
sf->left=s->right;  
else  
sf->right=s->right;  
//被删除结点有右孩子,无左孩子.被删结点是根结点  
else if(s->left==NULL&&s->right!=NULL&&sf==NULL)  
r=s->right;  
//被删结点有左孩子,无右孩子.被删结点不是根结点  
else if(s->left!=NULL&&s->right==NULL&&sf!=NULL)  
if(sf->left==s)  
sf->left=s->left;  
else  
sf->right=s->left;  
//被删结点有左孩子,无右孩子.被删结点是根结点  
else if(s->left!=NULL&&s->right==NULL&&sf==NULL)  
r=s->left;  
else if(s->left!=NULL&&s->right!=NULL)  
\{  
temp = s->left;  
father = s;  
//找出左子树最大的节点  
while(temp->right!=NULL)  
\{  
father=temp;  
temp=temp->right;  
\}  
s->data = temp->data;  
if(father!=s)  
father->right = temp->left;  
else  
father->left=temp->left;  
\}  
if(r==NULL)  
cout<<"删除之后，二叉排序树为空！"<<endl;  
else  
cout<<"删除成功！"<<endl;  
return r;  
\}  
//前序输出  
void preOrder(BSTree \*r)  
\{  
if(r==NULL)  
return;  
else  
\{  
cout<<r->data<<" ";  
preOrder(r->left);  
preOrder(r->right);  
\}  
\}  
//中序输出  
void inOrder(BSTree \*r)  
\{  
if(r==NULL)  
return ;  
else  
\{  
inOrder(r->left);  
cout<<r->data<<" ";  
inOrder(r->right);  
\}  
\}  
//后续输出  
void postOrder(BSTree \*r)  
\{  
if(r==NULL)  
return ;  
else  
\{  
postOrder(r->left);  
postOrder(r->right);  
cout<<r->data<<" ";  
\}  
\}**

**int \_tmain(int argc, \_TCHAR\* argv\[\])  
\{  
int cases;  
cout<<"请输入案例个数："<<endl;  
cin>>cases;  
while(cases--)  
\{  
memset(a,0,sizeof(a));  
int n;  
flag = false;  
BSTree \*root=NULL;  
cout<<"请输入元素个数："<<endl;  
cin>>n;  
int i;  
cout<<"请输入这些元素："<<endl;  
for(i=0;i<n;i++)  
cin>>a\[i\];  
cout<<"建立二叉排序树!"<<endl;  
root = createBSTree(root,a,n);  
if(root!=NULL)  
cout<<"二叉排序树建立成功！"<<endl;  
else  
\{  
cout<<"二叉排序树建立失败！"<<endl;  
return 0;  
\}  
cout<<"此二叉树根的值为："<<endl;  
cout<<root->data<<endl;  
cout<<"请选择您要进行的操作："<<endl;  
cout<<"1.插入(I/i)"<<endl;  
cout<<"2.查找(S/s)"<<endl;  
cout<<"3.删除(D/d)"<<endl;  
cout<<"4.先序输出(P/p)"<<endl;  
cout<<"5.中序输出(M/m)"<<endl;  
cout<<"6.后序输出(L/l)"<<endl;  
cout<<"7.退出(E/e)"<<endl;  
char s;  
cin>>s;  
while(1)  
\{  
if(s=='E'||s=='e')  
break;  
else if(s=='I'||s=='i')  
\{  
cout<<"请输入您要插入的值："<<endl;  
int x;  
cin>>x;  
BSTree \*p =(BSTree\*)malloc(sizeof(BSTree));  
p->data = x;  
p->left = NULL;  
p->right = NULL;  
root = insert(root,p);  
if(flag==false)  
cout<<"插入成功！"<<endl;  
else  
\{  
cout<<"此二叉树中已存在此值！"<<endl;  
flag=false;//恢复原值  
\}  
\}  
else if(s=='S'||s=='s')  
\{  
cout<<"请问您需要查询哪种信息？"<<endl;  
cout<<"1.此值的相关信息(1)："<<endl;  
cout<<"2.二叉排序树最小值(2)："<<endl;  
cout<<"3.二叉排序树最大值(3)："<<endl;  
cout<<"4.此值的中序前趋节点值(4)："<<endl;  
cout<<"5.此值的中序后继节点值(5)："<<endl;  
cout<<"6.退出查询(6)："<<endl;  
int cs;  
cin>>cs;  
while(1)  
\{  
if(cs==1)  
\{  
cout<<"请输入您要查找的值："<<endl;  
int x;  
cin>>x;  
BSTree \*p=search(root,x);  
BSTree \*pfather=getFather(root,p);  
cout<<"查找的值为："<<p->data<<endl;  
if(pfather!=NULL)  
cout<<"其父节点的值为："<<pfather->data<<endl;  
else  
cout<<"它是根节点，没有父节点！"<<endl;  
if(p->left==NULL&&p->right==NULL)  
cout<<"它是叶子节点，没有子节点"<<endl;  
else  
\{  
if(p->left != NULL)  
cout<<"其左儿子节点的值为："<<p->left->data<<endl;  
else  
cout<<"其左儿子节点为空！"<<endl;  
if(p->right != NULL)  
cout<<"其右儿子的值为："<<p->right->data<<endl;  
else  
cout<<"其右儿子节点为空！"<<endl;  
\}  
\}  
else if(cs==2)  
\{  
BSTree \* node = BSTMinNum(root);  
cout<<"此二叉排序树的最小值为："<<node->data<<endl;  
\}  
else if(cs==3)  
\{  
BSTree \* node = BSTMaxNum(root);  
cout<<"此二叉排序树的最大值为："<<node->data<<endl;  
\}  
else if(cs==4)  
\{  
int val;  
cout<<"请输入一个值："<<endl;  
cin>>val;  
BSTree \*node = searchPreMidOrder(root,val);  
if(node==NULL)  
cout<<"不存在此其值为"<<val<<"的节点或其前趋节点"<<endl;  
else  
\{  
cout<<"此节点的值为："<<val<<endl;  
cout<<"其中序前趋节点的值："<<node->data<<endl;  
\}  
\}  
else if(cs==5)  
\{  
int val;  
cout<<"请输入一个值："<<endl;  
cin>>val;  
BSTree \*node = searchPostMidOrder(root,val);  
if(node==NULL)  
cout<<"不存在此其值为"<<val<<"的节点或其后继节点"<<endl;  
else  
\{  
cout<<"此节点的值为："<<val<<endl;  
cout<<"其中序后继节点的值："<<node->data<<endl;  
\}  
\}  
else if(cs==6)  
break;  
else  
\{  
cout<<"输入的指令不对，请重新输入！"<<endl;  
  
  
\}  
cout<<"请问您需要查询哪种信息？"<<endl;  
cin>>cs;  
\}**

**\}  
else if(s=='D'||s=='d')  
\{  
cout<<"请输入您要删除的节点的值："<<endl;  
int value;  
cin>>value;  
cout<<"你确定要删除吗？(Yy/Nn)"<<endl;  
char order;  
cin>>order;  
while(1)  
\{  
if(order=='Y'||order=='y')  
\{  
BSTree \* node;  
node = search(root,value);  
if(node==NULL)  
cout<<"该节点不存在！"<<endl;  
else  
BSTree \*nodeDel = deleteNode(root,node);  
break;  
\}  
else if(order=='N'||order=='n')  
\{  
break;  
\}  
else  
\{  
cout<<"命令不正确，请重新输入！"<<endl;  
cin>>order;  
\}  
\}  
\}  
else if(s=='P'||s=='p')  
\{  
cout<<"其前序输出为："<<endl;  
preOrder(root);  
cout<<endl;  
\}  
else if(s=='M'||s=='m')  
\{  
cout<<"其中序输出为："<<endl;  
inOrder(root);  
cout<<endl;  
\}  
else if(s=='L'||s=='l')  
\{  
cout<<"其后序输出为："<<endl;  
postOrder(root);  
cout<<endl;  
\}  
else  
\{  
cout<<"命令有误，请重新输入！"<<endl;  
\}  
cout<<"请选择您要进行的操作："<<endl;  
cin>>s;  
\}  
\}  
system("pause");  
return 0;  
\}**