二分搜索树常见操作(C++版)

来源：互联网发布：小林一茶知乎编辑：程序博客网时间：2024/06/10 01:49
#include <iostream>#include <algorithm>#include <string>#include <ctime>#include <cmath>#include <cassert>#include <queue>using namespace std;template <typename Key,typename Value>class BST{public:    BST(){        root=NULL;        Count=0;    }    ~BST(){        destory(root);    }    int size(){        return Count;    }    bool isEmpty(){        return Count=0;    }    void Insert(Key key,Value value){        root=Insert(root,key,value);    }    Value* Search(Key key){        return Search(root,key);    }    //前序遍历    void preOrder(){        preOrder(root);    }    //中序遍历    void inOrder(){        inOrder(root);    }    //后序遍历    void postOrder(){        postOrder(root);    }    //层序遍历    void levelOrder(){        queue<Node *>q;        q.push(root);        while(!q.empty()){            Node *node=q.front();            q.pop();            cout<<node->key<<endl;            if(node->left)                q.push(node->left);            if(node->right)                q.push(node->right);        }    }    //寻找最小的键值    Key minimum(){        assert(Count!=0);        Node* minNode=minimum(root);        return minNode->key;    }     //寻找最大的键值    Key maximum(){        assert(Count!=0);        Node* maxNode=maximum(root);        return maxNode->key;    }    //从二叉树中删除最小值所在的节点    void removeMin(){        if(root)            root=removeMin(root);    }    //从二叉树中删除最大值所在的节点    void removeMax(){        if(root)            root=removeMax(root);    }    //从二叉树中删除键值为key的节点    void Remove(Key key){        root=Remove(root,key);    }private:    //向以node为根的二分搜索树中，插入节点(key,value)    //返回插入新节点后的二分搜索树的根    Node* Insert(Node *node,Key key,Value value){        if(node==NULL){            Count++;            return new Node(key,value);        }        if(key==node->key)            node->key=key;        else if(key<node->key)            node->left=Insert(node->left,key,value);        else            node->right=Insert(node->right,key,value);        return node;    }    //查找以node为根的二分搜索树中是否包含键值为key的节点    bool contain(Node *node,Key key){        if(node==NULL)            return false;        if(key==node->key)            return true;        else if(key<node->key)            return contain(node->left,key);        else            return contain(node->right,key);    }    //在以node为根的二分搜索树中查找key所对应的value    Value* Search(Node *node,Key key){        if(node==NULL)            return NULL;        if(key==node->value)            return &(node->value);        else if(key<node->key)            return Search(node->left,key);        else            return Search(node->right,key);    }    //对以node为根的二分搜索树进行前序遍历    void preOrder(Node *node){        if(node !=NULL){            cout<<node->key<<endl;            preOrder(node->left);            preOrder(node->right);        }    }    //对以node为根的二分搜索树进行中序遍历    void inOrder(Node *node){        if(node!=NULL){            inOrder(node->left);            cout<<node->key<<endl;            inOrder(node->right);        }    }     //对以node为根的二分搜索树进行后序遍历     void postOrder(Node *node){        if(node!=NULL){            postOrder(node->left);            postOrder(node->right);            cout<<node->key<<endl;        }     }     //用类似后序遍历的方法释放空间     void destory(Node *node){        if(node !=NULL){            destory(node->left);            destory(node->right);            delete(node);            Count--;        }     }     //在以node为根的二分搜索树中，返回最小键值的节点     Node* minimum(Node* node){        if(node->left == NULL)            return node;        return minimum(node->left);     }     //在以node为根的二分搜索树中，返回最大键值的节点     Node* maximum(Node *node){        if(node->right==NULL){            return node;        }        return maximum(node->right);     }     //删除掉以node为根的二分搜索树中的最小节点     //返回删除节点后新的二分搜索树的根     Node* removeMin(Node *node){        if(node->left==NULL){            Node* rightNode=node->right;            delete node;            Count--;            return rightNode;        }        node->left=removeMin(node->left);        return node;     }     //删除掉以node为根的二分搜索树中的最大节点     //返回删除节点后新的二分搜索树的根     Node* removeMax(Node* node){        if(node->right==NULL){            Node* leftNode=node->left;            delete node;            Count--;            return leftNode;        }        node->right=removeMax(node->right);        return node;     }     //删除掉以node为根的二分搜索树中键值为key的节点     //返回删除节点后新的二分搜索树的根O(logn)     Node* Remove(Node* node,Key key){        if(node == NULL)            return NULL;        if(key<node->key){            node->left=Remove(node->left,key);            return node;        }        else if(key>node->key){            node->right=Remove(node->right,key);            return node;        }        else{//key==node->key            if(node->left==NULL){                Node *rightNode=node->right;                delete node;                Count--;                return rightNode;            }            if(node->right==NULL){                Node *leftNode=node->left;                delete node;                Count--;                return leftNode;            }            //node->left!=NULL && node->right!=NULL;            Node *successor=new Node(minimum(node->right));            Count++;            successor->right=removeMin(node->right);            successor->left=node->left;            delete node;            Count--;            return successor;        }     }private:    struct Node{        Key key;        Value value;        Node *left;        Node *right;        Node(Key key,Value value){            this->key=key;            this->value=value;            this->left=this->right=NULL;        }        Node(Node *node){            this->key=node->key;            this->value=node->value;            this->left=node->left;            this->right=node->right;        }    };    Node *root;//根节点    int Count;//记录节点数};
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