数据结构实验--------二叉树(Binary Tree)

来源：互联网发布：恐怖海峡知乎编辑：程序博客网时间：2024/06/01 23:20

使用的教材是电子工业出版社出版的《Data Structures and Algorithm Analysis in C++ 》（《数据结构与算法分析（C++）》（第三版）），作者是【美】Clifford A Shaffer，译者是张铭、刘晓丹等。所以，有些代码与书上给出来的几近相同，如有侵权，请联系本人（741239458@qq.com），我会删除文章的。

实验内容：1、编写递归函数search，传入参数为一棵二叉树和一个值k，如果值k 出现在树中则返回true，否则返回flase。

2、编写递归函数返回二叉树的高度。

3、编写递归函数计算二叉树的叶结点数。

4、按广度优先搜索树。

------------BSTNode.h----------------

//节点的ADTtemplate<typename E>class BinNode{public:    virtual ~BinNode() {}virtual E& element() =0 ;virtual void setElement(const E& ) =0;virtual BinNode* left() const = 0;virtual void setLeft(BinNode* ) =0;virtual BinNode* right() const =0;virtual void setRight(BinNode*) = 0;virtual bool isLeaf() = 0;};template<typename E>class BSTNode:public BinNode<E>{private:    char k;E it;BSTNode* lc;BSTNode* rc;public:    BSTNode(){    lc = rc = NULL;}BSTNode(char temp, E e, BSTNode* l=NULL, BSTNode* r=NULL){    k = temp;it = e;lc = l;rc = r;}~BSTNode()  {}E& element(){    return it;}void setElement(const E& e){    it = e;}char& key() { return k; }void setKey(const char& temp )  {    k = temp;}inline BSTNode* left() const{    return lc;}void setLeft(BinNode<E>* b){    lc = (BSTNode*) b;}inline BSTNode* right() const{    return rc;}void setRight(BinNode<E>* b){    rc = (BSTNode*) b;}bool isLeaf(){    return lc==NULL&&rc==NULL;}};//队列的ADTtemplate<typename E>class Queue{void operator = (const Queue&) {}Queue(const Queue&) {}public:Queue() {}virtual ~Queue() {}virtual void clear() = 0;virtual void enqueue(BSTNode<E>*) = 0;virtual BSTNode<E>* dequeue() = 0;virtual const BSTNode<E>* frontValue() const = 0;virtual  int length() const = 0;};template<typename E>class Knot{public:BSTNode<E>* value;Knot* next;Knot( BSTNode<E>* v = NULL ,Knot* n = NULL){value = v;next = n;}};template<typename E>class Lqueue : public Queue<E>{int size;Knot<E>* front;Knot<E>* rear;public :Lqueue()  { front = rear = new Knot<E>(); size = 0; }~Lqueue() { clear();  delete front; }void clear(){while(front->next != NULL){rear = front->next;delete rear;}rear = front;size = 0;}void enqueue( BSTNode<E>* it){rear->next = new Knot<E>(it,NULL);rear = rear->next;size++;}BSTNode<E>* dequeue(){if(size==0)return NULL;BSTNode<E>* it = front->next->value;Knot<E>* temp = front->next;front->next = temp->next;size--;if(size==0)rear = front;delete temp;temp = NULL;return it;}const BSTNode<E>* frontValue() const{return front->next->value;}int length() const{return size;}};

------------Main.cpp----------

#include<iostream>#include"BSTNode.h"using namespace std;//二叉树进行搜索template<typename E>bool search(BSTNode<E>* root,char temp){    if(root==NULL) return false;if(root->key()==temp)    return true;if(search(root->left(),temp))    return true;return search(root->right(),temp);}//返回树的高度template<typename E>int getHight(BSTNode<E>* root){int h = 0,h1 = 0;if(root == NULL)return h;else{h1 = h = 1;}h += getHight(root->left());h1 += getHight(root->right());return h > h1? h : h1;}//返回叶子数template<typename E>int getNumOfLeaves(BSTNode<E>* root){if(root == NULL)return 1;return getNumOfLeaves(root->left())+getNumOfLeaves(root->right());}//build the tree/*         A(0)     -----/  \----- |            | B(1)         C(2)----/\-----   ----/\----|         |   |       |D(3)     E(4) F(5)    G(6)  */template<typename E>void asign(BSTNode<E>*& root){root = new BSTNode<int>('A',0);root->setLeft(new BSTNode<int>('B',1));root->setRight(new BSTNode<int>('C',2));BSTNode<E>* temp = root->left();temp->setLeft(new BSTNode<int>('D',3));temp->setRight(new BSTNode<int>('E',4));temp = root->right();temp->setLeft(new BSTNode<int>('F',5));temp->setRight(new BSTNode<int>('G',6));}//广度搜索二叉树template<typename E>void breadthFirstSearch(BSTNode<E>*& root){Lqueue<E> lq;lq.enqueue(root);//记录树遍历的层数，用于决定什么时候换行int h = getHight(root);int* level = new int[h];int i = 0;for(;i<h;i++)level[i] = 0;i = 0;level[i]++;while(lq.length()>0){BSTNode<E>* temp = lq.dequeue();level[i]--;if(temp->left()!=NULL){lq.enqueue(temp->left());level[i+1]++;}if(temp->right()!=NULL){lq.enqueue(temp->right());level[i+1]++;}cout<<temp->key()<<"     ";if(level[i]==0){i++;cout<<endl;}}}int main(){BSTNode<int>* root = NULL;asign<int>(root);cout<<"search 'E'  is :";if(search(root, 'E'))cout<<"true"<<endl;elsecout<<"false"<<endl;cout<<"search 'J'  is :";if(search(root, 'J'))cout<<"true"<<endl;elsecout<<"false"<<endl;cout<<"The hight of the tree is :"<<getHight<int>(root)<<endl;cout<<"The count of the leaf is :"<<getNumOfLeaves<int>(root)<<endl;cout<<"Breadth first search tree is:\n";breadthFirstSearch<int>(root);system("PAUSE");}

运行截图：

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