二叉排序树

声明：图片及内容基于https://www.bilibili.com/video/BV15f4y197v1?from=articleDetail

二叉排序树概念

 

 

二叉树的定义

类的定义 

class BiSortTree{
    private:
        BiNode *root;
    public:
        BiSortTree(DataType array[],int arrayLength);
        ~BiSortTree(){ release(root);}
        BiNode* searchBST(int key){ searchBST(root,key);}
        bool deleteBST(int key){ return deleteBST(root,key);}
        void inOrder(){ inOrder(root);}
    private:
        void insertBST(BiNode* &bt, DataType key);  //插入 
        void release(BiNode *bt);                   //二叉树销毁 
        void inOrder(BiNode *bt);                   //中序遍历 
        bool deleteBST(BiNode* &bt,DataType key);   //删除 
        void deleteNode(BiNode* &bt);               //删除节点 
        BiNode *searchBST(BiNode *bt,DataType key); //查找 
};

二叉树的插入 

 

 

 

 

void BiSortTree::insertBST(BiNode* &bt,DataType key){
    if(bt==NULL){                //二叉树为空时直接创建节点 
        bt=new BiNode;
        bt->data=key;
        bt->lchild=NULL;
        bt->rchild=NULL;
    }
    else{
        if(key<bt->data)         //左小右大 
            insertBST(bt->lchild,key);
        if(key>bt->data)
            insertBST(bt->rchild,key);
    }
}

 二叉树的构造

 

 

 

 

 

BiSortTree::BiSortTree(DataType array[],int length){ //循环建立二叉排序树 
    root=NULL;
    for(int i=0;i<length;i++){
        insertBST(root,array[i]);
    } 
}

 

 二叉树的查找

 

 

 

 

 

 

BiNode* BiSortTree::searchBST(BiNode *bt,DataType key){
    if(bt==NULL)                    //递归终止条件 
        return NULL;
    else{
        if(key==bt->data)           //找到返回 
            return bt;
        else if(key<bt->data)       //左小 
            return searchBST(bt->lchild,key);
        else                        //右大 
            return searchBST(bt->rchild,key);
    }
}

二叉树的删除

 

 

 

 

 

 

 

 

 

 

 

 

bool BiSortTree::deleteBST(BiNode* &bt,DataType key){
    if(bt==NULL)                   //递归终止条件 
        return false;
    else{
        if(bt->data==key)          //找到删除 
            deleteNode(bt);
        else if(key<bt->data)      //左小 
            return deleteBST(bt->lchild,key);
        else                       //右大 
            return deleteBST(bt->rchild,key);
        return true;
    }
}
void BiSortTree::deleteNode(BiNode* &bt){
    BiNode *p;
    if(bt->lchild==NULL&&bt->rchild==NULL){  //叶子节点 
        p=bt;
        bt=NULL;
        delete p;
    }
    else if(bt->rchild==NULL){               //右子树为空 
        p=bt;
        bt=bt->lchild;
        delete p;
    }
    else if(bt->lchild==NULL){               //左子树为空 
        p=bt;
        bt=bt->rchild;
        delete p;
    }
    else{                                    //左右子树均不为空 
        BiNode *parent=bt;
        BiNode *pre=bt->lchild;
        while(pre->rchild){                  //找到左子树中最大的结点 
            parent=pre;
            pre=pre->rchild;
        }
        bt->data=pre->data;                 //pre指向要删结点的前驱，替换bt数据 
        if(parent!=bt)                      //判断是否执行了上述while循环 
            parent->rchild=pre->lchild;     //执行了while循环，重新接pre右子树 
        else 
            parent->lchild=pre->lchild;        //未执行while循环，重接pre左子树 
        delete pre;
    }
}

完整代码

#include<iostream>
#define DataType int
using namespace std;
struct BiNode{
    DataType data;
    BiNode *lchild;
    BiNode *rchild;
};
class BiSortTree{
    private:
        BiNode *root;
    public:
        BiSortTree(DataType array[],int arrayLength);
        ~BiSortTree(){ release(root);}
        BiNode* searchBST(int key){ searchBST(root,key);}
        bool deleteBST(int key){ return deleteBST(root,key);}
        void inOrder(){ inOrder(root);}
    private:
        void insertBST(BiNode* &bt, DataType key);  //插入 
        void release(BiNode *bt);                   //二叉树销毁 
        void inOrder(BiNode *bt);                   //中序遍历 
        bool deleteBST(BiNode* &bt,DataType key);   //删除 
        void deleteNode(BiNode* &bt);               //删除节点 
        BiNode *searchBST(BiNode *bt,DataType key); //查找 
};
void BiSortTree::inOrder(BiNode* bt){               //中序遍历 
    if(bt==NULL) return;
    else{
        inOrder(bt->lchild);
        cout<<bt->data<<" ";
        inOrder(bt->rchild);
    }
    
}
void BiSortTree::release(BiNode *bt){
    if (bt != NULL)
    {
        release(bt->lchild);       //后序遍历销毁二叉树
        release(bt->rchild);
        delete bt;
        bt = NULL;
    }
}
void BiSortTree::insertBST(BiNode* &bt,DataType key){
    if(bt==NULL){                //二叉树为空时直接创建节点 
        bt=new BiNode;
        bt->data=key;
        bt->lchild=NULL;
        bt->rchild=NULL;
    }
    else{
        if(key<bt->data)         //左小右大 
            insertBST(bt->lchild,key);
        if(key>bt->data)
            insertBST(bt->rchild,key);
    }
}
BiSortTree::BiSortTree(DataType array[],int length){ //循环建立二叉排序树 
    root=NULL;
    for(int i=0;i<length;i++){
        insertBST(root,array[i]);
    } 
}
BiNode* BiSortTree::searchBST(BiNode *bt,DataType key){
    if(bt==NULL)                    //递归终止条件 
        return NULL;
    else{
        if(key==bt->data)           //找到返回 
            return bt;
        else if(key<bt->data)       //左小 
            return searchBST(bt->lchild,key);
        else                        //右大 
            return searchBST(bt->rchild,key);
    }
}
bool BiSortTree::deleteBST(BiNode* &bt,DataType key){
    if(bt==NULL)                   //递归终止条件 
        return false;
    else{
        if(bt->data==key)          //找到删除 
            deleteNode(bt);
        else if(key<bt->data)      //左小 
            return deleteBST(bt->lchild,key);
        else                       //右大 
            return deleteBST(bt->rchild,key);
        return true;
    }
}
void BiSortTree::deleteNode(BiNode* &bt){
    BiNode *p;
    if(bt->lchild==NULL&&bt->rchild==NULL){  //叶子节点 
        p=bt;
        bt=NULL;
        delete p;
    }
    else if(bt->rchild==NULL){               //右子树为空 
        p=bt;
        bt=bt->lchild;
        delete p;
    }
    else if(bt->lchild==NULL){               //左子树为空 
        p=bt;
        bt=bt->rchild;
        delete p;
    }
    else{                                    //左右子树均不为空 
        BiNode *parent=bt;
        BiNode *pre=bt->lchild;
        while(pre->rchild){                  //找到左子树中最大的结点 
            parent=pre;
            pre=pre->rchild;
        }
        bt->data=pre->data;                 //pre指向要删结点的前驱，替换bt数据 
        if(parent!=bt)                      //判断是否执行了上述while循环 
            parent->rchild=pre->lchild;     //执行了while循环，重新接pre右子树 
        else 
            parent->lchild=pre->lchild;        //未执行while循环，重接pre左子树 
        delete pre;
    }
}
int main(){
    int length;
    int *array;
    cout<<"请输入数组长度"<<endl;
    cin>>length;
    cout<<"请输入"<<length<<"个数据"<<endl; 
    array=new int[length];
    for(int i=0;i<length;i++)
        cin>>array[i];
    
    BiSortTree bitree(array,length);
    cout<<"中序遍历结果："<<endl;
    bitree.inOrder();
    cout<<endl;
    cout<<"查找34"<<(bitree.searchBST(34)?"成功":"失败")<<endl;
    cout<<endl;
    cout<<"删除40:"<<(bitree.deleteBST(40)?"成功":"失败")<<endl;
    cout<<"删除34:"<<(bitree.deleteBST(34)?"成功":"失败")<<endl;
    cout<<"删除13:"<<(bitree.deleteBST(13)?"成功":"失败")<<endl;
    cout<<"删除38:"<<(bitree.deleteBST(38)?"成功":"失败")<<endl;
    cout<<"删除12:"<<(bitree.deleteBST(12)?"成功":"失败")<<endl;
    cout<<"删除4:"<<(bitree.deleteBST(4)?"成功":"失败")<<endl;
    return 0;
}

输入：

10
38 12 34 56 13 6 98 17 40 78

输出：

中序遍历结果：
6 12 13 17 34 38 40 56 78 98
查找34成功

删除40:成功
删除34:成功
删除13:成功
删除38:成功
删除12:成功
删除4:失败