二叉树的一些实现

// binarytree.cpp : 定义控制台应用程序的入口点。//#include "stdafx.h"#include <iostream>#include <string>#include <deque>#include <cassert>using namespace std;/*模拟二叉树的一些操作：作者：wangyang时间：2010年10月29日*//*数的节点类*/template <typename T>class TNode{public:TNode(){}//构造函数TNode(T data, TNode<T> *lptr = NULL, TNode<T> *rptr = NULL){nodeValue = data;left = lptr;right = rptr;}//数据成员T nodeValue;TNode<T> *left;TNode<T> *right;};/*二叉树类*/template <typename T>class BinaryTree{public:TNode<T>* createTree(T arr[],int start, int end);//创建二叉树void inorderOutput(TNode<T>* root, const string& separator = " ");//中序输出树的节点void postorderOutput(TNode<T>* root, const string& separator = " ");//后序输出树的节点void beforeorderOutput(TNode<T>* root, const string& separator = " ");//前序输出树的节点)void levelorderOutput(TNode<T>* root, const string& separator = " ");//层次遍历树的节点void countLeaf(TNode<T> *t, int &count);//计算叶子节点的数目int depth(TNode<T>* root);//计算数的深度private:TNode<T> *root; //树根};/*二叉树的创建：arr为数组，start为起点，end的终点*/template <typename T>TNode<T>* BinaryTree<T>::createTree(T arr[], int start, int end){TNode<T> *p;//树的节点if (start >= end){p = NULL;}else{p = new TNode<T>();assert(p != NULL);p->nodeValue = arr[start];p->left = createTree(arr, 2*start+1, end);p->right = createTree(arr, 2*start+2, end);}return p;}/*中序递归输出二叉树中的元素:*//*参数root为数的根参数separator为两个元素间的间隔符*/template <typename T>void BinaryTree<T>::inorderOutput(TNode<T> *root, const string& separator /* = */){if (root != NULL){inorderOutput(root->left, separator);cout<<root->nodeValue<<separator;inorderOutput(root->right, separator);}}/*后序递归输出二叉树中的元素:*//*参数root为数的根参数separator为两个元素间的间隔符*/template <typename T>void BinaryTree<T>::postorderOutput(TNode<T> *root, const string& separator /* = */){if (root != NULL){postorderOutput(root->left, separator);postorderOutput(root->right, separator);cout<<root->nodeValue<<separator;}}/*前序递归输出二叉树中的元素:*//*参数root为数的根参数separator为两个元素间的间隔符*/template <typename T>void BinaryTree<T>::beforeorderOutput(TNode<T> *root, const string& separator /* = */){if (root != NULL){cout<<root->nodeValue<<separator;beforeorderOutput(root->left, separator);beforeorderOutput(root->right, separator);}}/*层次遍历树的节点：借助队列做存储容器*//*参数root为数的根参数separator为两个元素间的间隔符*/template <typename T>void BinaryTree<T>::levelorderOutput(TNode<T>* root, const string& separator /* = */){deque<TNode<T> *> d;TNode<T> *temp;d.push_back(root);while (!d.empty()){temp = d.front();cout<<temp->nodeValue<<separator;d.pop_front();if (temp->left != NULL){d.push_back(temp->left);}if (temp->right != NULL){d.push_back(temp->right);}}}/*计算叶子节点的数目：通过递归来实现*//*参数root为数的根参数count为引用计数，初值必须为0*/template <typename T>void BinaryTree<T>::countLeaf(TNode<T> *t, int &count){if (t != NULL){//检查t是否为叶子节点，如是count加1if ((t->left != NULL) && (t->right != NULL)){count++;}countLeaf(t->left, count);//计算左子树countLeaf(t->right, count);//计算右子树}}/*计算树的深度：运用递归实现，定义空树的深度为-1,这样叶子节点的深度为0*/template <typename T>int BinaryTree<T>::depth(TNode<T>* root){int leftdepth;//左子树深度int rightdepth;//右子树深度int currentdepth;//当前节点深度if (root == NULL){currentdepth = -1;}else{leftdepth = depth(root->left);rightdepth = depth(root->right);currentdepth = max(leftdepth, rightdepth) + 1;}return currentdepth;}int _tmain(int argc, _TCHAR* argv[]){int arr[10];int size = sizeof(arr) / sizeof(int);cout<<"原数组为：";for (int i=0; i<size; i++){arr[i] = rand()/100 + 10;cout<<arr[i]<<" ";}cout<<endl;BinaryTree<int> bintree;TNode<int> *root;root = bintree.createTree(arr, 0, size);cout<<"中序为 ：";bintree.inorderOutput(root);cout<<endl;cout<<"后序为 ：";bintree.postorderOutput(root);cout<<endl;cout<<"前序为 ：";bintree.beforeorderOutput(root);cout<<endl;cout<<"层次为 ：";bintree.levelorderOutput(root);cout<<endl;int count = 0;bintree.countLeaf(root, count);cout<<"叶子节点的数量:"<<count<<endl;cout<<"当前树的深度为:"<<bintree.depth(root)<<endl;return 0;}