二叉树

二叉树的遍历方式：

前序，中序，后序，层序

二叉树的储存方式：

链式：动态

数组：静态

二叉树的基本操作：构造，拷贝构造，析构，求深度，叶子节点数，第k层节点，前、中、后序，层序

树的节点结构：

template<class T>struct BinaryTreeNode{BinaryTreeNode<T>* _left;BinaryTreeNode<T>* _right;T _data; BinaryTreeNode(const T& x):_left(NULL), _right(NULL), _data(x){}};

 
构造函数：

BinaryTree( T* a, size_t n, const T& invalid){size_t index = 0;_root = CreatTree(a, n, invalid, index);}Node* CreatTree( T* a, size_t n, const T& invalid, size_t& index){Node* root = NULL;if (index >= n || a[index] == invalid){return NULL;}root = new Node(a[index]);root->_left = CreatTree(a, n, invalid, ++index);root->_right = CreatTree(a, n, invalid, ++index);return root;}

拷贝构造函数：

BinaryTree(const BinaryTree& t){_root = _Copy(t._root);}Node* _Copy(Node* root){if (NULL == root);{return NULL;}Node* newroot = new Node(root->_data);newroot->_left = _Copy(root->_left);newroot->_right = _Copy(root->_right);return newroot;}

赋值运算符重载：

BinaryTree& operator=(const BinaryTree& t){if (this != &t){BinaryTree tmp(t);swap(tmp._root, _root);}return *this;}

析构函数：

析构掉整棵树的时候需要析构他的每个节点，这就要考虑析构节点的先后顺序

前序，中序都不能实现，所以我们选择后序

~BinaryTree(){Destroy(_root);_root = NULL;}void Destroy(Node* root){if (NULL == root){return;}Destroy(root->_left);Destroy(root->_right);delete root;}

前序（递归写法）

void _PrevOrder(Node* root){if (NULL==root){return;}cout << root->_data << " ";_PrevOrder(root->_left);_PrevOrder(root->_right);}

中序

void InOrder(){_InOrder(_root);cout << endl;}void _InOrder(Node* root){if (NULL==root){return;}_InOrder(root->_left);cout << root->_data << " ";_InOrder(root->_right);}

后序

void PostOrder(){_PostOrder(_root);cout << endl;}void _PostOrder(Node* root){if (NULL==root){return;}_PostOrder(root->_left);_PostOrder(root->_right);cout << root->_data << " ";}

层序

层序不能使用递归的写法，但我们可以利用队列。先将根节点插入队列，看队列是否为空，不为空的话就取队列的头，然后将头节点的左右节点插入队列，

最后pop掉这个头节点。这样就可以实现层序了。

void LevelOrder(){queue<Node*> q;if (_root != NULL){q.push(_root);while (!q.empty()){Node* Front = q.front();cout << Front->_data << " ";if (Front->_left != NULL){q.push(Front->_left);}if (Front->_right != NULL){q.push(Front->_right);}q.pop();}}}

求深度

size_t Depth(){return _Depth(_root);}size_t _Depth(Node* root){if (NULL==root){return 0;}size_t LD = _Depth(root->_left);size_t LR = _Depth(root->_right);return LD > LR ? LD + 1 : LR + 1;}

求叶子节点

size_t LeafSize()//叶子节点{return _LeafSize(_root);}size_t _LeafSize(Node* root){if (NULL==root){return 0;}if (root->_left == NULL && root->_right == NULL){return 1;}size_t i = _LeafSize(root->_left);size_t j = _LeafSize(root->_right);return i + j;}

求第k层节点

size_t GetKLevel(size_t k){size_t count = 0;_GetKLevel(_root, k, count);return count;}void _GetKLevel(Node* root, size_t k, size_t& count){if (root == NULL){return ;}if (k == 1){++count;}_GetKLevel(root->_left, k - 1, count);_GetKLevel(root->_right, k - 1, count);}

求节点数：

将整棵树遍历一遍，用一个变量计数即可

size_t Size(){size_t ret = 0;_Size(_root,ret);return ret;}void _Size(Node* root,size_t &ret){if (root == NULL){return ;}ret++;_Size(root->_left);_Size(root->_right);}

全部实现：

#include<iostream>#include<queue>using namespace std;template<class T>struct BinaryTreeNode{BinaryTreeNode<T>* _left;BinaryTreeNode<T>* _right;T _data; BinaryTreeNode(const T& x):_left(NULL), _right(NULL), _data(x){}};template<class T>class BinaryTree{typedef BinaryTreeNode<T> Node;public:BinaryTree()//构造函数:_root(NULL){}BinaryTree( T* a, size_t n, const T& invalid)//构造树{size_t index = 0;//数组下标_root = CreatTree(a, n, invalid, index);}Node* CreatTree( T* a, size_t n, const T& invalid, size_t& index)//构造二叉树 ，这里的index要用引用，否则上一层递归到里面的++对index没有影响{Node* root = NULL;if (index >= n || a[index] == invalid){return NULL;}root = new Node(a[index]);root->_left = CreatTree(a, n, invalid, ++index);root->_right = CreatTree(a, n, invalid, ++index);return root;}BinaryTree(const BinaryTree& t)//拷贝构造{_root = _Copy(t._root);}Node* _Copy(Node* root){if (NULL == root){return NULL;}Node* newroot = new Node(root->_data);newroot->_left = _Copy(root->_left);newroot->_right = _Copy(root->_right);return newroot;}BinaryTree& operator=(const BinaryTree& t){if (this != &t){BinaryTree tmp(t);swap(tmp._root, _root);}return *this;}void PrevOrder(){_PrevOrder(_root);cout << endl;}void _PrevOrder(Node* root){if (NULL==root){return;}cout << root->_data << " ";_PrevOrder(root->_left);_PrevOrder(root->_right);}void InOrder(){_InOrder(_root);cout << endl;}void _InOrder(Node* root){if (root == NULL){return;}_InOrder(root->_left);cout << root->_data << " ";_InOrder(root->_right);}void PostOrder(){_PostOrder(_root);cout << endl;}void _PostOrder(Node* root){if (root == NULL){return;}_PostOrder(root->_left);_PostOrder(root->_right);cout << root->_data << " ";}void LevelOrder(){queue<Node*> q;if (_root != NULL){q.push(_root);while (!q.empty()){Node* Front = q.front();cout << Front->_data << " ";if (Front->_left != NULL){q.push(Front->_left);}if (Front->_right != NULL){q.push(Front->_right);}q.pop();}}cout << endl;}size_t Size(){size_t ret = 0;_Size(_root,ret);return ret;}void _Size(Node* root,size_t &ret){if (root == NULL){return ;}ret++;_Size(root->_left);_Size(root->_right);}size_t Depth(){return _Depth(_root);}size_t _Depth(Node* root){if (NULL==root){return 0;}size_t LD = _Depth(root->_left);size_t LR = _Depth(root->_right);return LD > LR ? LD + 1 : LR + 1;}size_t LeafSize()//叶子节点{return _LeafSize(_root);}size_t _LeafSize(Node* root){if (NULL==root){return 0;}if (root->_left == NULL && root->_right == NULL){return 1;}size_t i = _LeafSize(root->_left);size_t j = _LeafSize(root->_right);return i + j;}/*size_t GetKLevel(size_t k){size_t count = 0;_GetKLevel(_root, 1, k, count);return count;}void _GetKLevel(Node* root, size_t cur, size_t k, size_t& count){if (root == NULL){return;}if (cur == k){count++;}_GetKLevel(root->_left, cur + 1, k, count);_GetKLevel(root->_right, cur + 1, k, count);}*/size_t GetKLevel(size_t k){size_t count = 0;_GetKLevel(_root, k, count);return count;}void _GetKLevel(Node* root, size_t k, size_t& count){if (root == NULL){return ;}if (k == 1){++count;}_GetKLevel(root->_left, k - 1, count);_GetKLevel(root->_right, k - 1, count);}//析构函数即销毁这棵树，几种遍历只有后序可以实现~BinaryTree(){Destroy(_root);_root = NULL;}void Destroy(Node* root){if (NULL == root){return;}Destroy(root->_left);Destroy(root->_right);delete root;}private:Node* _root;};int main(){int arr[10] = { 1, 2, 3, '#', '#', 4, '#', '#', 5, 6 };int arr2[5] = { 1, 2, 3, 4 };BinaryTree<int> t1(arr, sizeof(arr) / sizeof(arr[0]), '#');BinaryTree<int> t2(arr2, sizeof(arr2) / sizeof(arr2[0]), '#');//t1 = t2;t1.PostOrder();t1.InOrder();t1.PrevOrder();t1.LevelOrder();size_t i = t1.Depth();cout << i << endl;size_t k=t1.GetKLevel(2);cout << k << endl;size_t j = t1.LeafSize();cout << j << endl;system("pause");return 0;}