二叉搜索树及其C++实现

一棵二叉搜索树由一棵二叉树来组织，可以用链表数据结构来表示，每个结点除了Key和卫星数据，还包含指针left,right,p，分别指向左子树，右子树和双亲。
二叉树中的key总是满足二叉搜索树性质：

设x是二叉搜索树的一个结点，若y是x左子树中的一个结点，则y.key< x.key；若y是x右子树中的一个结点，则y.key>=x.key。（相等时，放在左子树还是右子树看个人习惯，此文是放在右子树中）

#include<iostream>using namespace std;//template<class A>struct BSTNode{    //A value;//卫星数据    int key;//排序关键字    BSTNode *lchild = nullptr;//指向左孩子    BSTNode *rchild = nullptr;//指向右孩子    BSTNode *p = nullptr;//指向双亲};struct Tree{    BSTNode *root = nullptr;};//中序遍历，先序遍历，后序遍历,O(n)void inorder_tree_walk(BSTNode *x){    if(x != nullptr){        inorder_tree_walk(x->lchild);        cout << x->key<<" ";        inorder_tree_walk(x->rchild);    }}void preorder_tree_walk(BSTNode *x){    if(x != nullptr){        cout << x->key <<" ";        preorder_tree_walk(x->lchild);        preorder_tree_walk(x->rchild);    }}void postorder_tree_walk(const BSTNode *x){    if(x != nullptr){        postorder_tree_walk(x->lchild);        postorder_tree_walk(x->rchild);        cout << x->key <<" ";    }}//迭代查找BSTNode* iterative_tree_search(BSTNode *x,int v){    while(x !=nullptr && x->key != v){        if(v < x->key)            x = x->lchild;        else            x = x->rchild;    }    return x;}//递归查找BSTNode* tree_search(BSTNode *x,int v){    if(x == nullptr || x->key == v)        return x;    if(v < x->key)        return tree_search(x->lchild,v);    else        return tree_search(x->rchild,v);}//最小关键字元素BSTNode* tree_minimum(BSTNode *x){    while(x->lchild != nullptr)        x = x->lchild;    return x;}//最大关键字元素BSTNode* tree_maximum(BSTNode *x){    while(x->rchild != nullptr)        x = x->rchild;    return x;}//后继,前驱,O(h)BSTNode* tree_successor(BSTNode *x){    if(x->rchild != nullptr)        return tree_minimum(x->rchild);    BSTNode *y = x->p;    while(y != nullptr && x == y->rchild){        x = y;        y = y->p;    }    return y;}BSTNode* tree_predecessor(BSTNode *x){    if(x->lchild != nullptr)        return tree_minimum(x->rchild);    BSTNode *y = x->p;    while(y != nullptr && x == y->lchild){        x = y;        y = y->p;    }    return y;}//插入void tree_insert(Tree &T,BSTNode *z){    BSTNode *y = nullptr;    BSTNode *x = T.root;    while(x != nullptr){        y = x;        if(z->key < x->key)            x = x->lchild;        else            x = x->rchild;    }    z->p = y;    if(y == nullptr)        T.root = z;    else if(z->key < y->key)        y->lchild = z;    else        y->rchild = z;}/*删除*///将v的双亲换成u的双亲void transplant(Tree &T,BSTNode *u,BSTNode *v){    if(u->p == nullptr)        T.root = v;    else if(u == u->p->lchild)        u->p->lchild = v;    else        u->p->rchild = v;    if(v != nullptr)        v->p = u->p;}void tree_delete(Tree &T,BSTNode *z){    if(z->lchild == nullptr)        transplant(T,z,z->rchild);    else if(z->rchild == nullptr)        transplant(T,z,z->lchild);    else{        BSTNode *y = tree_minimum(z->rchild);        if(y->p != z){            transplant(T,y,y->rchild);            y->rchild = z->rchild;            y->rchild->p = y;        }        transplant(T,z,y);        y->lchild = z->lchild;        y->lchild->p = y;    }}//测试代码int main(){    Tree T;    int k,n;    cout<<"个数：";    cin>>n;    while(n--){//输入#结束        cin>>k;        BSTNode *a = new BSTNode();        a->key = k;        tree_insert(T,a);    }    cout<<"中序输出：";    inorder_tree_walk(T.root);//输出    BSTNode *median;    cout<<"\n输入要删除的节点：";    int v;    cin>>v;    median = iterative_tree_search(T.root,v);//查找key==8的节点    cout<<v<<"的后继"<<tree_successor(median)->key<<endl;    cout<<v<<"的前驱"<<tree_predecessor(median)->key<<endl;    cout<<"删除"<<v<<"得到:";    tree_delete(T,median);//，然后删除该节点    inorder_tree_walk(T.root);//输出    median = tree_minimum(T.root);    cout<<"\nmininum:"<<median->key<<endl;    cout<<"删除最小值得到：";    tree_delete(T,median);    inorder_tree_walk(T.root);//输出    median = tree_maximum(T.root);    cout<<"\nmaxinum:"<<median->key<<endl;    cout<<"删除最大值得到：";    tree_delete(T,median);    inorder_tree_walk(T.root);//输出    cout<<endl;}