（1）结构体和类定义
struct BTreeNode {T data;BTreeNode* left, * right;BTreeNode() :data(0), left(nullptr), right(nullptr) {}BTreeNode(T val, BTreeNode<T>* leftChild = nullptr, BTreeNode<T>* rightChild = nullptr):data(val), left(leftChild), right(rightChild) {}};template<class T>
class BTree {
public:BTree() :root(nullptr) {} // 构造函数BTree(string str); // 重载void createTree(BTreeNode<T>*& bt, string str); // 创建二次树~BTree(); // 析构函数bool IsEmpty(); // 判二叉树空否？int Size(BTreeNode<T>* cur); // 计算结点个数int getSize(); // 获取结点个数BTreeNode<T>* getData(T& item, BTreeNode<T>* cur); // 取得结点数据bool Find(T& item); // 判断item是否在树中int Height(BTreeNode<T>* bt); // 求树高度int getHeight(); // 获取树高度BTreeNode<T>* getRoot(); // 取根void preOrderTraversal(BTreeNode<T>* cur, vector<int>& vec); // 前序遍历void inOrderTraversal(BTreeNode<T>* cur, vector<int>& vec); // 中序遍历void postOrderTraversal(BTreeNode<T>* cur, vector<int>& vec); // 后序遍历void levelOrderTraversal(BTreeNode<T>* cur, vector<int>& vec); // 层序遍历vector<T> preOrder(); // 调用前序遍历，返回vectorvector<T> inOrder(); // 调用中序遍历，返回vectorvector<T> postOrder(); // 调用后序遍历，返回vectorvector<T> levelOrder(); // 调用层序遍历，返回vectorvoid CopyTree(BTreeNode<T>* root, BTreeNode<T>*& copyRoot); // 二叉树复制void Copy(BTreeNode<T>*& copyRoot); // 调用二叉树复制void destroyCopyTree(BTreeNode<T>*& copyRoot); // 销毁复制二叉树BTreeNode<T>* FindParent(BTreeNode<T>* root, BTreeNode<T>* node); // 寻找双亲BTreeNode<T>* LeftChild(BTreeNode<T>* node) { //求结点 node 的左孩子return (node != nullptr) ? node->left : nullptr;}BTreeNode<T>* RightChild(BTreeNode<T>* node) { //求结点 node 的右孩子return (node != nullptr) ? node->right : nullptr;}protected:BTreeNode<T>* root;void destroyTree(BTreeNode<T>* node); // 销毁二叉树
};
（2）创建二叉树
template<class T>
BTree<T>::BTree(string str) {createTree(root, str);cout << "报告：创建一颗二叉树，完成！！！" << endl;
}template<class T>
void BTree<T>::createTree(BTreeNode<T>*& bt, string str) {static int i = 0;char ch = ' ';ch = str[i++];if (ch == '#') bt = nullptr;else {bt = new BTreeNode<T>(ch);createTree(bt->left, str);createTree(bt->right, str);}
};
（3）前中后序遍历和层序遍历
// 前序遍历
template<class T>
void BTree<T>::preOrderTraversal(BTreeNode<T>* cur, vector<int>& vec) {if (cur == nullptr)return;vec.push_back(cur->data); // 中preOrderTraversal(cur->left, vec); // 左preOrderTraversal(cur->right, vec); // 右
}// 调用前序遍历，返回vector
template<class T>
vector<T> BTree<T>::preOrder() {cout << "获取前序遍历数组...." << endl;cout << ">>>>";vector<T> resVec;preOrderTraversal(root, resVec);return resVec;
}// 中序遍历
template<class T>
void BTree<T>::inOrderTraversal(BTreeNode<T>* cur, vector<int>& vec) {if (cur == nullptr)return;inOrderTraversal(cur->left, vec); // 左vec.push_back(cur->data); // 中inOrderTraversal(cur->right, vec); // 右
}// 调用中序遍历，返回vector
template<class T>
vector<T> BTree<T>::inOrder() {cout << "获取中序遍历数组...." << endl;cout << ">>>>";vector<T> resVec;inOrderTraversal(root, resVec);return resVec;
}// 后序遍历
template<class T>
void BTree<T>::postOrderTraversal(BTreeNode<T>* cur, vector<int>& vec) {if (cur == nullptr)return;postOrderTraversal(cur->left, vec); // 左postOrderTraversal(cur->right, vec); // 右vec.push_back(cur->data); // 中
}// 调用后序遍历，返回vector
template<class T>
vector<T> BTree<T>::postOrder() {cout << "获取后序遍历数组...." << endl;cout << ">>>>";vector<T> resVec;postOrderTraversal(root, resVec);return resVec;
}// 层序遍历
template<class T>
void BTree<T>::levelOrderTraversal(BTreeNode<T>* cur, vector<int>& vec) {if (cur == nullptr) return;queue<BTreeNode<T>*> Queue;BTreeNode<T>* p;Queue.push(cur); // 根结点入队列while (!Queue.empty()) {p = Queue.front();//cout << p->data << " ";//输出出队结点的数据vec.push_back(p->data);Queue.pop();if (p->left != nullptr) {Queue.push(p->left);}if (p->right != nullptr) {Queue.push(p->right);}}
}// 调用层序遍历，返回vector
template<class T>
vector<T> BTree<T>::levelOrder() {cout << "获取层序遍历数组...." << endl;cout << ">>>>";vector<T> resVec;levelOrderTraversal(root, resVec);return resVec;
}
（4）复制二叉树
template<class T>
void BTree<T>::CopyTree(BTreeNode<T>* root, BTreeNode<T>*& copyRoot) {if (!root) {copyRoot = nullptr;}else {copyRoot = new BTreeNode<T>;copyRoot->data = root->data; //复制根节点CopyTree(root->left, copyRoot->left); //递归复制左子树CopyTree(root->right, copyRoot->right);//递归复制左子树}
}template<class T>
void BTree<T>::Copy(BTreeNode<T>*& copyRoot) {CopyTree(root, copyRoot);
}
（5）销毁二叉树
template<class T>
void BTree<T>::destroyCopyTree(BTreeNode<T>*& copyRoot) {destroyTree(copyRoot);cout << "报告，复制二叉树已销毁完毕!!!" << endl;
}// 销毁二叉树
template<class T>
void BTree<T>::destroyTree(BTreeNode<T>* bt) {// 后序遍历删除根为subTree的子树；if (bt != nullptr) {destroyTree(bt->left); //删除左子树destroyTree(bt->right); //删除右子树delete bt; //删除根结点}
}
（6）析构函数
// 析构函数
template<class T>
BTree<T>::~BTree<T>() {//cout << "调用析构函数" << endl;destroyTree(root);cout << "报告，这棵树已经销毁完毕!!!" << endl;
}
（7）求树的高度
// 求树高度
template<class T>
int BTree<T>::Height(BTreeNode<T>* bt) {if (bt == nullptr) return 0;else {int leftH = Height(bt->left);int rightH = Height(bt->right);return (leftH > rightH) ? leftH + 1 : rightH + 1;}
}// 获取树高度
template<class T>
int BTree<T>::getHeight() {return Height(root);
}
（8）获取结点，判断其是否在二叉树中
// 取得结点数据
template<class T>
BTreeNode<T>* BTree<T>::getData(T& item, BTreeNode<T>* cur) {if (cur == nullptr) return nullptr;if (cur->data == item) return cur;return getData(item, cur->left) != nullptr ? getData(item, cur->left) : getData(item, cur->right);
}// 判断item是否在树中
template<class T>
bool BTree<T>::Find(T& item) {if (this->getData(item, root) == nullptr) return false;else return true;
（9）计算结点个数和获取结点个数
// 计算结点个数
template<class T>
int BTree<T>::Size(BTreeNode<T>* cur) {if (cur == nullptr)return 0;elsereturn 1 + Size(cur->left) + Size(cur->right);
}// 获取结点个数
template<class T>
int BTree<T>::getSize() {return Size(root);
}
（10）二叉树判空
// 判二叉树空否？
template<class T>
bool BTree<T>::IsEmpty() {return (root == nullptr) ? true : false;
}
（11）获取根结点
// 获取根
template<class T>
BTreeNode<T>* BTree<T>::getRoot() {if (!root) return nullptr;else {return this->root;}
}
源代码：
btree.h
#pragma once
#include <iostream>
#include <vector>
#include <queue>
using namespace std;template<class T>
struct BTreeNode {T data;BTreeNode* left, * right;BTreeNode() :data(0), left(nullptr), right(nullptr) {}BTreeNode(T val, BTreeNode<T>* leftChild = nullptr, BTreeNode<T>* rightChild = nullptr):data(val), left(leftChild), right(rightChild) {}};template<class T>
class BTree {
public:BTree() :root(nullptr) {} // 构造函数BTree(string str); // 重载void createTree(BTreeNode<T>*& bt, string str); // 创建二次树~BTree(); // 析构函数bool IsEmpty(); // 判二叉树空否？int Size(BTreeNode<T>* cur); // 计算结点个数int getSize(); // 获取结点个数BTreeNode<T>* getData(T& item, BTreeNode<T>* cur); // 取得结点数据bool Find(T& item); // 判断item是否在树中int Height(BTreeNode<T>* bt); // 求树高度int getHeight(); // 获取树高度BTreeNode<T>* getRoot(); // 取根void preOrderTraversal(BTreeNode<T>* cur, vector<int>& vec); // 前序遍历void inOrderTraversal(BTreeNode<T>* cur, vector<int>& vec); // 中序遍历void postOrderTraversal(BTreeNode<T>* cur, vector<int>& vec); // 后序遍历void levelOrderTraversal(BTreeNode<T>* cur, vector<int>& vec); // 层序遍历vector<T> preOrder(); // 调用前序遍历，返回vectorvector<T> inOrder(); // 调用中序遍历，返回vectorvector<T> postOrder(); // 调用后序遍历，返回vectorvector<T> levelOrder(); // 调用层序遍历，返回vectorvoid CopyTree(BTreeNode<T>* root, BTreeNode<T>*& copyRoot); // 二叉树复制void Copy(BTreeNode<T>*& copyRoot); // 调用二叉树复制void destroyCopyTree(BTreeNode<T>*& copyRoot); // 销毁复制二叉树BTreeNode<T>* FindParent(BTreeNode<T>* root, BTreeNode<T>* node); // 寻找双亲BTreeNode<T>* LeftChild(BTreeNode<T>* node) { //求结点 node 的左孩子return (node != nullptr) ? node->left : nullptr;}BTreeNode<T>* RightChild(BTreeNode<T>* node) { //求结点 node 的右孩子return (node != nullptr) ? node->right : nullptr;}protected:BTreeNode<T>* root;void destroyTree(BTreeNode<T>* node); // 销毁二叉树
};
btree.cpp
// 每次写递归，都按照这三要素来写，可以保证大家写出正确的递归算法！
// 1.确定递归函数的参数的返回值
// 2.确定终止条件
// 3.确定单层递归的逻辑#include "btree.h"template<class T>
BTree<T>::BTree(string str) {createTree(root, str);cout << "报告：创建一颗二叉树，完成！！！" << endl;
}template<class T>
void BTree<T>::createTree(BTreeNode<T>*& bt, string str) {static int i = 0;char ch = ' ';ch = str[i++];if (ch == '#') bt = nullptr;else {bt = new BTreeNode<T>(ch);createTree(bt->left, str);createTree(bt->right, str);}
};// 判二叉树空否？
template<class T>
bool BTree<T>::IsEmpty() {return (root == nullptr) ? true : false;
}// 计算结点个数
template<class T>
int BTree<T>::Size(BTreeNode<T>* cur) {if (cur == nullptr)return 0;elsereturn 1 + Size(cur->left) + Size(cur->right);
}// 获取结点个数
template<class T>
int BTree<T>::getSize() {return Size(root);
}// 取得结点数据
template<class T>
BTreeNode<T>* BTree<T>::getData(T& item, BTreeNode<T>* cur) {if (cur == nullptr) return nullptr;if (cur->data == item) return cur;return getData(item, cur->left) != nullptr ? getData(item, cur->left) : getData(item, cur->right);
}// 判断item是否在树中
template<class T>
bool BTree<T>::Find(T& item) {if (this->getData(item, root) == nullptr) return false;else return true;
}// 求树高度
template<class T>
int BTree<T>::Height(BTreeNode<T>* bt) {if (bt == nullptr) return 0;else {int leftH = Height(bt->left);int rightH = Height(bt->right);return (leftH > rightH) ? leftH + 1 : rightH + 1;}
}// 获取树高度
template<class T>
int BTree<T>::getHeight() {return Height(root);
}// 获取根
template<class T>
BTreeNode<T>* BTree<T>::getRoot() {if (!root) return nullptr;else {return this->root;}
}// 析构函数
template<class T>
BTree<T>::~BTree<T>() {//cout << "调用析构函数" << endl;destroyTree(root);cout << "报告，这棵树已经销毁完毕!!!" << endl;
}// 销毁二叉树
template<class T>
void BTree<T>::destroyTree(BTreeNode<T>* bt) {// 后序遍历删除根为subTree的子树；if (bt != nullptr) {destroyTree(bt->left); //删除左子树destroyTree(bt->right); //删除右子树delete bt; //删除根结点}
}// 前序遍历
template<class T>
void BTree<T>::preOrderTraversal(BTreeNode<T>* cur, vector<int>& vec) {if (cur == nullptr)return;vec.push_back(cur->data); // 中preOrderTraversal(cur->left, vec); // 左preOrderTraversal(cur->right, vec); // 右
}// 调用前序遍历，返回vector
template<class T>
vector<T> BTree<T>::preOrder() {cout << "获取前序遍历数组...." << endl;cout << ">>>>";vector<T> resVec;preOrderTraversal(root, resVec);return resVec;
}// 中序遍历
template<class T>
void BTree<T>::inOrderTraversal(BTreeNode<T>* cur, vector<int>& vec) {if (cur == nullptr)return;inOrderTraversal(cur->left, vec); // 左vec.push_back(cur->data); // 中inOrderTraversal(cur->right, vec); // 右
}// 调用中序遍历，返回vector
template<class T>
vector<T> BTree<T>::inOrder() {cout << "获取中序遍历数组...." << endl;cout << ">>>>";vector<T> resVec;inOrderTraversal(root, resVec);return resVec;
}// 后序遍历
template<class T>
void BTree<T>::postOrderTraversal(BTreeNode<T>* cur, vector<int>& vec) {if (cur == nullptr)return;postOrderTraversal(cur->left, vec); // 左postOrderTraversal(cur->right, vec); // 右vec.push_back(cur->data); // 中
}// 调用后序遍历，返回vector
template<class T>
vector<T> BTree<T>::postOrder() {cout << "获取后序遍历数组...." << endl;cout << ">>>>";vector<T> resVec;postOrderTraversal(root, resVec);return resVec;
}// 层序遍历
template<class T>
void BTree<T>::levelOrderTraversal(BTreeNode<T>* cur, vector<int>& vec) {if (cur == nullptr) return;queue<BTreeNode<T>*> Queue;BTreeNode<T>* p;Queue.push(cur); // 根结点入队列while (!Queue.empty()) {p = Queue.front();//cout << p->data << " ";//输出出队结点的数据vec.push_back(p->data);Queue.pop();if (p->left != nullptr) {Queue.push(p->left);}if (p->right != nullptr) {Queue.push(p->right);}}
}// 调用层序遍历，返回vector
template<class T>
vector<T> BTree<T>::levelOrder() {cout << "获取层序遍历数组...." << endl;cout << ">>>>";vector<T> resVec;levelOrderTraversal(root, resVec);return resVec;
}template<class T>
void BTree<T>::CopyTree(BTreeNode<T>* root, BTreeNode<T>*& copyRoot) {if (!root) {copyRoot = nullptr;}else {copyRoot = new BTreeNode<T>;copyRoot->data = root->data; //复制根节点CopyTree(root->left, copyRoot->left); //递归复制左子树CopyTree(root->right, copyRoot->right);//递归复制左子树}
}template<class T>
void BTree<T>::Copy(BTreeNode<T>*& copyRoot) {CopyTree(root, copyRoot);
}template<class T>
void BTree<T>::destroyCopyTree(BTreeNode<T>*& copyRoot) {destroyTree(copyRoot);cout << "报告，复制二叉树已销毁完毕!!!" << endl;
}template<class T>
BTreeNode<T>* BTree<T>::FindParent(BTreeNode<T>* root, BTreeNode<T>* node) {if (root == nullptr) return nullptr;if (root->left == node || root->right == node)return root; //找到, 返回父结点地址BTreeNode <T>* p;if ((p = FindParent(root->left, node)) != nullptr)return p; //递归在左子树中搜索else return FindParent(root->right, node);
}
test.cpp
#include "btree.h"
#include "btree.cpp"
//#include <iostream>
//using namespace std;
int main() {cout << "-------------------------Start--------------------------" << endl;cout << "---------------------创建原始二叉树---------------------" << endl;string str = "ABD#G##E##CF###";BTree<int>* T = new BTree<int>(str);BTreeNode<int>* root = T->getRoot();cout << "这棵树有 " << T->getSize() << " 个结点" << endl;int zifu = 'G';if (T->Find(zifu)) {cout << "这棵树有 " << (char)zifu << " 结点" << endl;}else {cout << "这棵树无 " << (char)zifu << " 结点" << endl;}BTreeNode<int>* node = T->getData(zifu, root);if (node) {cout << (char)node->data << endl;BTreeNode<int>* nodeParent = T->FindParent(root, node);if (!nodeParent) {cout << "找不到父亲结点" << endl;}else {cout << "结点 " << (char)zifu << " 的父亲结点是: " << (char)nodeParent->data << " 结点" << endl;if (nodeParent->left) cout << "我的左孩子是: " << (char)nodeParent->left->data << endl;else cout << "我没有左孩子..." << endl;if (nodeParent->right) cout << "我的右孩子是: " << (char)nodeParent->right->data << endl;else cout << "我没有右孩子..." << endl;}}cout << "这棵树的高度为: " << T->getHeight() << endl;vector<int> vec = T->preOrder();for (auto i : vec) {cout << (char)i;}cout << endl;vec.clear();vec = T->inOrder();for (auto i : vec) {cout << (char)i;}cout << endl;vec.clear();vec = T->postOrder();for (auto i : vec) {cout << (char)i;}cout << endl;vec.clear();vec = T->levelOrder();for (auto i : vec) {cout << (char)i;}cout << endl;cout << "-----------------------复制二叉树-----------------------" << endl;// 复制二叉树//vector<int> vec;//BTreeNode<int>* root = T->getRoot();BTreeNode<int>* copyRoot = new BTreeNode<int>;//T->Copy(copyRoot); // 方法一T->CopyTree(root, copyRoot); // 方法二vec.clear();cout << "获取前序遍历数组...." << endl;cout << ">>>>";T->preOrderTraversal(copyRoot, vec);for (auto i : vec) {cout << (char)i;}cout << endl;vec.clear();cout << "获取中序遍历数组...." << endl;cout << ">>>>";T->inOrderTraversal(copyRoot, vec);for (auto i : vec) {cout << (char)i;}cout << endl;vec.clear();cout << "获取后序遍历数组...." << endl;cout << ">>>>";T->postOrderTraversal(copyRoot, vec);for (auto i : vec) {cout << (char)i;}cout << endl;vec.clear();cout << "获取层序遍历数组...." << endl;cout << ">>>>";T->levelOrderTraversal(copyRoot, vec);for (auto i : vec) {cout << (char)i;}cout << endl;cout << "---------------------销毁复制二叉树---------------------" << endl;T->destroyCopyTree(copyRoot);cout << "---------------------销毁原始二叉树---------------------" << endl;T->~BTree();cout << "--------------------------End---------------------------" << endl;return 0;
}
>>测试结果
-------------------------Start--------------------------
---------------------创建原始二叉树---------------------
报告：创建一颗二叉树，完成！！！
这棵树有 7 个结点
这棵树有 G 结点
G
结点 G 的父亲结点是: D 结点
我没有左孩子...
我的右孩子是: G
这棵树的高度为: 4
获取前序遍历数组....
>>>>ABDGECF
获取中序遍历数组....
>>>>DGBEAFC
获取后序遍历数组....
>>>>GDEBFCA
获取层序遍历数组....
>>>>ABCDEFG
-----------------------复制二叉树-----------------------
获取前序遍历数组....
>>>>ABDGECF
获取中序遍历数组....
>>>>DGBEAFC
获取后序遍历数组....
>>>>GDEBFCA
获取层序遍历数组....
>>>>ABCDEFG
---------------------销毁复制二叉树---------------------
报告，复制二叉树已销毁完毕!!!
---------------------销毁原始二叉树---------------------
报告，这棵树已经销毁完毕!!!
--------------------------End---------------------------
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