Binary Search Tree

BST.h

//
// Created by godbmw.com on 2018/9/27.
//

#ifndef BINARYSEARCH_BST_H
#define BINARYSEARCH_BST_H

#include <iostream>
#include <queue>

using namespace std;

template <typename Key, typename Value>
class BST {
private:
    struct Node {
        Key key;
        Value value;
        Node  *left;
        Node *right;

        Node(Key key, Value value) {
            this->key = key;
            this->value = value;
            this->left = NULL;
            this->right = NULL;
        }

        Node(Node* node) {
            this->key = node->key;
            this->value = node->value;
            this->left = node->left;
            this->right = node->right;
        }
    };

    Node *root;
    int count;

private:
    Node* insert(Node* node, Key key, Value value) {
        if(node == NULL) {
            count++;
            return new Node(key, value);
        }

        if(key == node->key) {
            node->value = value;
        } else if( key < node->key) {
            node->left = insert(node->left, key, value);
        } else {
            node->right = insert(node->right, key, value);
        }
        return node;
    }

    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);
        }
    }

    Value* search(Node* node, Key key) {
        if(node == NULL) {
            return NULL;
        }
        if(key == node->key) {
            return &(node->value);
        } else if (key < node->key) {
            return search(node->left, key);
        } else {
            return search(node->right, key);
        }
    }

    void pre_order(Node* node) {
        if(node != NULL) {
            cout<<node->key<<endl;
            pre_order(node->left);
            pre_order(node->right);
        }
    }

    void in_order(Node* node) {
        if(node != NULL) {
            in_order(node->left);
            cout<<node->key<<endl;
            in_order(node->right);
        }
    }

    void post_order(Node *node) {
        if(node != NULL) {
            post_order(node->left);
            post_order(node->right);
            cout<<node->key<<endl;
        }
    }

//    和后序遍历相似：先destroy左右节点，再释放节点自身
    void destroy(Node *node) {
        if(node != NULL) {
            destroy(node->left);
            destroy(node->right);
            delete node;
//            别忘记count变动
            this->count--;
        }
    }

//    层序遍历
    void level_order(Node* node) {
        if(node == NULL) {
            return;
        }
        queue<Node*> q;
        q.push(node);
        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);
            }
        }
    }

//    寻找最小键值
    Node* minimum(Node* node) {
        if(node->left == NULL) {
            return node;
        }
        return minimum(node->left);
    }

    Node* maximum(Node* node) {
        if(node->right == NULL) {
            return node;
        }
        return maximum(node->right);
    }

    Node* remove_min(Node* node) {
        if(node->left == NULL) {
            Node* right = node->right;
            delete node;
            count--;
            return right;
        }
        node->left = remove_min(node->left);
        return node;
    }

    Node* remove_max(Node* node) {
        if(node->right == NULL) {
            Node* left = node->left;
            delete node;
            count--;
            return left;
        }
        node->right = remove_max(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
//    时间复杂度: O(logN)
    Node* remove(Node* node, Key key) {
        if(node == NULL) {
            return NULL;
        }
        if(key < node->key) {
            node->left = remove(node->left, key);
        } else if(key > node->key){
            node->right = remove(node->right, key);
        } else {
//            key == node->key
            if(node->left == NULL) {
                Node* right = node->right;
                delete node;
                count--;
                return right;
            }
            if(node->right == NULL) {
                Node *left = node->left;
                delete node;
                count--;
                return left;
            }
//            node->right != NULL && node->left != NULL
            Node* successor = new Node(minimum(node->right));
            count++;
//            "count --" in "function remove_min(node->right)"
            successor->right = remove_min(node->right);
            successor->left = node->left;
            delete node;
            count--;
            return successor;
        }
        return node;
    }

    Node* floor(Node* node, Key key) {
        if(node == NULL) {
            return NULL;
        }

//        key等于node->key：floor的结果就是node本身
        if(node->key == key) {
            return node;
        }

//        key小于node—>key：floor的结果肯定在node节点的左子树
        if(node->key > key) {
            return floor(node->left, key);
        }

//        key大于node->key：右子树可能存在比node->key大，但是比key小的节点
//        如果存在上述情况，返回这个被选出来的节点
//        否则，函数最后返回node本身
        Node* tmp = floor(node->right, key);
        if(tmp != NULL) {
            return tmp;
        }

        return node;
    }

    Node* ceil(Node* node, Key key) {
        if(node == NULL) {
            return NULL;
        }
        if(node->key == key) {
            return node;
        }

        if(node->key < key) {
            return ceil(node->right, key);
        }

        Node* tmp = ceil(node->left, key);
        if(tmp != NULL) {
            return tmp;
        }

        return node;
    }


public:
    BST() {
        this->root = NULL;
        this->count = 0;
    }
    ~BST() {
        this->destroy(this->root);
    }
    int size() {
        return this->count;
    }
    bool isEmpty() {
        return this->root == NULL;
    }

    void insert(Key key, Value value) {
        this->root = this->insert(this->root, key, value);
    }

    bool contain(Key key) {
        return this->contain(this->root, key);
    }

//    注意返回值类型
    Value* search(Key key) {
        return this->search(this->root, key);
    }

    void pre_order() {
        this->pre_order(this->root);
    }

    void in_order() {
        this->in_order(this->root);
    }

    void post_order() {
        this->post_order(this->root);
    }

    void level_order() {
        this->level_order(this->root);
    }

//    寻找最小键值
    Key* minimum() {
        if(this->count == 0) return NULL;
        Node* min_node = this->minimum(this->root);
        return &(min_node->key);
    }

//    寻找最大键值
    Key* maximum() {
        if(this->count == 0) return NULL;
        Node* max_node = this->maximum(this->root);
        return &(max_node->key);
    }

    void remove_min() {
        if(this->root == NULL) {
            return;
        }
        this->root = this->remove_min(this->root);
    }

    void remove_max() {
        if(this->root == NULL) {
            return;
        }
        this->root = this->remove_max(this->root);
    }

    void remove(Key key) {
        this->root = remove(this->root, key);
    }

    Key* floor(Key key) {
        Key* min_key = this->minimum();
        if(this->isEmpty() || key < *min_key) {
            return NULL;
        }
//        floor node
        Node *node = floor(this->root, key);
        return &(node->key);
    }

    Key* ceil(Key key) {
        Key* max_key = this->maximum();
        if(this->isEmpty() || key > *max_key) {
            return NULL;
        }
//        ceil node
        Node* node = ceil(this->root, key);
        return &(node->key);
    }
};

#endif //BINARYSEARCH_BST_H