二叉树实验报告

重庆交通大学综合性设计性实验报告班级：软件开发专业 2010级一班实验项目名称：二叉树实验项目性质：设计性实验实验所属课程：数据结构实验室(中心)： 6教指导教师：鲁云平实验完成时间： 2012 年 4 月 29 日一、实验目的主要完成以下功能:1. 建立二叉树2. 计算结点所在的层次3 .统计结点数量和叶结点数量4. 计算二叉树的高度5. 计算结点的度6. 找结点的双亲和子女7. 二叉树的遍历8. 二叉树的输出等等二、实验内容及要求1.二叉树的结点结构,二叉树的存储结构由学生自由选择和设定2.实验完成后上交打印的实验报告,报告内容与前面所给定的实验模板相同3.将实验报告电子版和源代码在网络教学平台提交三、实验设备及软件Visual studio 2010四、设计方案㈠题目（老师给定或学生自定）二叉树的简单应用㈡设计的主要思路通过递归原理实现大部分遍历二叉树功能㈢主要功能1. 建立二叉树2. 计算结点所在的层次3 .统计结点数量和叶结点数量4. 计算二叉树的高度5. 计算结点的度6. 找结点的双亲和子女7. 二叉树的遍历8. 二叉树的输出五、主要代码栈头文件：stack.hclass Stack{public:Stack(int sz=100);~Stack(){delete[]elements;}void Push(const T &x);bool Pop(T &x);bool getTop(T &x);bool IsEmpty()const{return(top==-1)?true:false;}bool IsFull()const{return(top==maxSize-1)?true:false;} private:T *elements;int top;int maxSize;void overflowProcess();};template<class T>Stack<T>::Stack(int sz):top(-1),maxSize(sz){elements=new T[maxSize];assert(elements!=NULL);};template<class T>void Stack<T>::overflowProcess(){T*newArray=new T[maxSize+stackIncreament];if(newArray=NULL){cerr<<"存储分配失败！"<<endl;exit(1);} for(int i=0;i<=top;i++)newArray[i]=elements[i];maxSize=maxSize+stackIncreament;delete []elements;elements=newArray;};template<class T>void Stack<T>::Push(const T &x){if(IsFull()==true)overflowProcess();elements[++top]=x;};template<class T>bool Stack<T>::Pop(T &x){if(IsEmpty()==true)return false;x=elements[top--];return true;};template<class T>bool Stack<T>::getTop(T &x){if(IsEmpty()==true)return false;x=elements[top];return true;};二叉树头文件tree.h#include<iostream>#include"stack.h"#include<stdlib.h>#include<fstream>using namespace std;template<class T>struct BinTreeNode{T data;BinTreeNode<T> *leftChild,*rightChild;BinTreeNode():leftChild(NULL),rightChild(NULL){}BinTreeNode(T x,BinTreeNode<T> *l=NULL,BinTreeNode<T> *r=NULL):data(x),leftChild(l),rightChild(r){}};template<class T>class BinaryTree{public:BinTreeNode<T> *root;//二叉树的根指针BinTreeNode<T> *current;T RefValue;//数据输入停止标志BinaryTree():root(NULL){}//构造函数BinaryTree(T value):RefValue(value),root(NULL){}//构造函数BinaryTree(BinaryTree<T>&s);//复制构造函数~BinaryTree(){destroy(root);}//析构函数bool IsEmpty(){return (root==NULL)?true:false;}//判断二叉树空否BinTreeNode<T> *Parent(BinTreeNode<T> *current)//返回父结点{return(root==NULL || root==current)?NULL:Parent(root,current);}BinTreeNode<T> *LeftChild(BinTreeNode<T> *current)//返回左子女{return(current!=NULL)?current->leftChild:NULL;}BinTreeNode<T> *RightChild(BinTreeNode<T> *current)//返回右子女{return(current!=NULL)?current->rightChild:NULL;}int Height(){return Height(root);}//返回树高度int Size(){return Size(root);}//返回结点数BinTreeNode<T> *getRoot()const{return root;}//取根void preOrder(void( *visit)(BinTreeNode<T> *p))//前序遍历{preOrder(root,visit);}void CreateBinTree_one(ifstream& in,BinTreeNode<T> *& BT);//从文件读入建树void CreateBinTree_two(ifstream& in,BinTreeNode<T> *& subTree);void destroy(BinTreeNode<T> *&subTree);//删除int Height(BinTreeNode<T> *subTree);//返回树高度int Size(BinTreeNode<T> *subTree);//返回结点数void Leaf(BinTreeNode<T> *subTree,int &x);//叶结点数目BinTreeNode<T> *Parent(BinTreeNode<T> *subTree,BinTreeNode<T> *current);//返回父结点void Traverse(BinTreeNode<T> *subTree);//前序遍历输出void degree(BinTreeNode<T> *subTree,char &x);//指定结点的度void level(BinTreeNode<T> *subTree,char &x,int &y);//指定结点的层次void Search(BinTreeNode<T> *subTree,char &x);//前序遍历搜索并查找指定结点的子女结点和父结点void PrintBTree(BinTreeNode<T> *subTree);//以广义表的形式输出void perOrder(BinTreeNode<T>* subTree,void(*visit)(BinTreeNode<T> *p));//前序遍历};template<class T>void BinaryTree<T>::destroy(BinTreeNode<T> *&subTree){if(subTree!=NULL){destroy(subTree->leftChild);destroy(subTree->rightChild);delete subTree;}}template<class T>void BinaryTree<T>::CreateBinTree_one(ifstream& in,BinTreeNode<T> *& BT){Stack<BinTreeNode<char> *>s;BT=NULL;BinTreeNode<char> *p,*t;int k;char ch;in>>ch;while(ch!='#'){switch(ch){case '(':s.Push(p);k=1;break;case ')':s.Pop(t);break;case ',':k=2;break;default: p=new BinTreeNode<T>(ch);if(BT==NULL)BT=p;else if(k==1){s.getTop(t);t->leftChild=p;}else{s.getTop(t);t->rightChild=p;}}in>>ch;}}template<class T>void BinaryTree<T>::CreateBinTree_two(ifstream& in,BinTreeNode<T> *&subTree){subTree=NULL;T item;if(!in.eof()){in>>item;if(item!='#'){subTree=new BinTreeNode<T>(item);if(subTree==NULL){cerr<<"存储分配错！"<<endl;exit(1);}CreateBinTree_two(in,subTree->leftChild);CreateBinTree_two(in,subTree->rightChild);}elsesubTree=NULL;}}template<class T>BinTreeNode<T> *BinaryTree<T>::Parent(BinTreeNode<T> *subTree,BinTreeNode<T> *current){if(subTree==NULL)return NULL;if(subTree->leftChild==current||subTree->rightChild==current)return subTree;BinTreeNode<T> *p;if((p=Parent(subTree->leftChild,current))!=NULL)return p;elsereturn Parent(subTree->rightChild,current);}template<class T>void BinaryTree<T>::Traverse(BinTreeNode<T> *subTree){if(subTree!=NULL){cout<<subTree->data<<" ";Traverse(subTree->leftChild);Traverse(subTree->rightChild);}}template<class T>void BinaryTree<T>::perOrder(BinTreeNode<T> *subTree,void(*visit)(BinTreeNode<T> *p)){if(subTree!=NULL){visit(subTree);PreOrder(subTree->leftChild,visit);PreOrder(subTree->rightChild,visit);}}template<class T>int BinaryTree<T>::Size(BinTreeNode<T> *subTree){if(subTree==NULL)return 0;elsereturn 1+Size(subTree->leftChild)+Size(subTree->rightChild); }template<class T>int BinaryTree<T>::Height(BinTreeNode<T> *subTree){if(subTree==NULL)return 0;else{int i=Height(subTree->leftChild);int j=Height(subTree->rightChild);return (i<j)?j+1:i+1;}}template<class T>void BinaryTree<T>::Leaf(BinTreeNode<T> *subTree,int &x){if(subTree!=NULL){if(subTree->leftChild==NULL&&subTree->rightChild==NULL) x++;Leaf(subTree->leftChild,x);Leaf(subTree->rightChild,x);}}template<class T>void BinaryTree<T>::PrintBTree(BinTreeNode<T> *subTree){if(subTree!=NULL){cout<<subTree->data;if(subTree->leftChild!=NULL||subTree->rightChild!=NULL){cout<<'(';PrintBTree(subTree->leftChild);cout<<',';if(subTree->rightChild!=NULL)PrintBTree(subTree->rightChild);cout<<')';}}}template<class T>void BinaryTree<T>::Search(BinTreeNode<T> *subTree,char &x){if(subTree==NULL)return;if(subTree->data==x){cout<<"此字符没有父结点！"<<endl;if(subTree->leftChild!=NULL)cout<<"此字符的左子女为："<<subTree->leftChild->data<<" ";elsecout<<"此字符没有左子女！"<<" ";if(subTree->rightChild!=NULL)cout<<"此字符的右子女为："<<subTree->rightChild->data<<endl;elsecout<<"此字符没有右子女！"<<endl;return;}if(subTree->leftChild!=NULL){if(subTree->leftChild->data==x){if(subTree!=NULL)cout<<"此字符的父结点为："<<subTree->data<<endl;if(subTree->leftChild->leftChild!=NULL)cout<<"此字符的左子女结点为："<<subTree->leftChild->leftChild->data<<" ";elsecout<<"此字符没有左子女结点！"<<" ";if(subTree->leftChild->rightChild!=NULL)cout<<"此字符的右子女结点为："<<subTree->leftChild->rightChild->data<<endl;elsecout<<"此字符没有右子女结点！"<<endl;return;}}if(subTree->rightChild!=NULL){if(subTree->rightChild->data==x){if(subTree!=NULL)cout<<"此字符的父结点为："<<subTree->data<<endl;if(subTree->rightChild->leftChild!=NULL)cout<<"此字符的左子女结点为："<<subTree->rightChild->leftChild->data<<" ";elsecout<<"此字符没有左子女结点！"<<" ";if(subTree->rightChild->rightChild!=NULL)cout<<"此字符的右子女结点为："<<subTree->rightChild->rightChild->data<<endl;elsecout<<"此字符没有右子女结点！"<<endl;return;}}if(subTree!=NULL){Search(subTree->leftChild,x);Search(subTree->rightChild,x);}}template<class T>void BinaryTree<T>::degree(BinTreeNode<T> *subTree,char &x){if(subTree==NULL)return;if(subTree->data==x){if(subTree->leftChild!=NULL&&subTree->rightChild!=NULL) cout<<"此结点的度为：2"<<endl;else if(subTree->leftChild!=NULL||subTree->rightChild!=NULL) cout<<"此结点的度为：1"<<endl;elsecout<<"此结点的度为：0"<<endl;return;}if(subTree!=NULL){degree(subTree->leftChild,x);degree(subTree->rightChild,x);}}template<class T>void BinaryTree<T>::level(BinTreeNode<T> *subTree,char &x,int &y) {if(subTree!=NULL){if(subTree->data==x)cout<<"此结点的层次为："<<y+1<<endl;if(subTree->data!=x){y++;level(subTree->leftChild,x,y);}if(subTree->data!=x){level(subTree->rightChild,x,y);y--;}}}主函数#include<iostream>#include<stdlib.h>#include<assert.h>#include<fstream>#include"tree.h"using namespace std;class tree{private:BinaryTree<char>Tree;public:void menu();void creat();};void tree::menu(){tree Tr;char p;cout<<"_____________________________________________"<<endl;cout<<"| 是否建立一个二叉树? |"<<endl;cout<<"| 点Y 确认建立，点N 退出|"<<endl;cout<<"---------------------------------------------"<<endl;first:cin>>p;switch(p){case 'y':Tr.creat();break;case 'Y':Tr.creat();break;case 'N':return;break;case 'n':return;break;default:{cout<<"输入无效符号请重新输入:"<<endl; goto first;}break;}}void tree::creat(){tree CJ;int Q;ifstream in;zero:cout<<"___________________"<<endl;cout<<"| 请输入建立方式: |"<<endl;cout<<"| 1.用广义表输入|"<<endl;cout<<"| 2.用遍历输入|"<<endl;cout<<"| 3.返回|"<<endl;cout<<"-------------------"<<endl;first:int i;cin>>i;switch(i){case 1:{in.open("10060116(广义).txt",ios::in);if(!in){cout<<"文件打开失败！！"<<endl;exit(1);}Tree.CreateBinTree_one(in,Tree.root);in.close();cout<<"成功从“100600116(广义).txt”里读取广义表示的二叉树："<<endl;Fanhui1:cout<<"_________________________________"<<endl;cout<<"| 请输入操作：|"<<endl;cout<<"| 1.计算二叉树的结点个数|"<<endl;cout<<"| 2.计算二叉树的高度|"<<endl;cout<<"| 3.计算二叉树的叶节点数量|"<<endl;cout<<"| 4.遍历输出|"<<endl;cout<<"| 5.二叉树的广义表输出|"<<endl;cout<<"| 6.寻找指定结点的父结点及子女|"<<endl;cout<<"| 7.计算指定结点的层次和度|"<<endl;cout<<"| 8.返回创建页面|"<<endl;cout<<"---------------------------------"<<endl;cin>>Q;switch(Q){case 1:{cout<<"此二叉树的结点个数为：";cout<<Tree.Size(Tree.root);cout<<'\n'<<endl;goto Fanhui1;}break;case 2:{cout<<"此二叉树的高度为：";cout<<Tree.Height(Tree.root);cout<<'\n'<<endl;goto Fanhui1;}break;case 3:{int x=0;cout<<"此二叉树的叶结点数量为：";Tree.Leaf(Tree.root,x);cout<<x<<'\n'<<endl;goto Fanhui1;}break;case 4:{cout<<"此二叉树的遍历输出为：";Tree.Traverse(Tree.root);cout<<'\n'<<endl;goto Fanhui1;}break;case 5:{cout<<"此二叉树的广义表输出为：";Tree.PrintBTree(Tree.root);cout<<'\n'<<endl;goto Fanhui1;}break;case 6:{char x;cout<<"请输入要查找的字符："<<endl;cin>>x;Tree.Search(Tree.root,x);goto Fanhui1;}break;case 7:{char x;int y=0;cout<<"请输入要查找的字符："<<endl;cin>>x;Tree.degree(Tree.root,x);Tree.level(Tree.root,x,y);gotoFanhui1;}break;case 8:goto zero;break;default:{cout<<"输入无效字符，请重新输入"<<endl;goto Fanhui1;}break;}}break;case 2:{in.open("10060116(遍历).txt",ios::in);if(!in){cout<<"文件打开失败！！"<<endl;exit(1);}Tree.CreateBinTree_two(in,Tree.root);in.close();cout<<"成功从“100600116(遍历).txt”里读取前序序列遍历表示的二叉树："<<endl;Fanhui2:cout<<"_________________________________"<<endl;cout<<"| 请输入操作：|"<<endl;cout<<"| 1.计算二叉树的结点个数|"<<endl;cout<<"| 2.计算二叉树的高度|"<<endl;cout<<"| 3.计算二叉树的叶节点数量|"<<endl;cout<<"| 4.遍历输出|"<<endl;cout<<"| 6.寻找指定结点的父结点及子女|"<<endl;cout<<"| 7.计算指定结点的层次和度|"<<endl;cout<<"| 8.返回创建页面|"<<endl;cout<<"---------------------------------"<<endl;cin>>Q;switch(Q){case 1:{cout<<"此二叉树的结点个数为：";cout<<Tree.Size(Tree.root);cout<<'\n'<<endl;goto Fanhui2;}break;case 2:{cout<<"此二叉树的高度为：";cout<<Tree.Height(Tree.root);cout<<'\n'<<endl;goto Fanhui2;}break;case 3:{int x=0;cout<<"此二叉树的叶结点数量为：";Tree.Leaf(Tree.root,x);cout<<x<<'\n'<<endl;goto Fanhui2;}break;case 4:{cout<<"此二叉树的遍历输出为：";Tree.Traverse(Tree.root);cout<<'\n'<<endl;goto Fanhui2;}break;case 5:{cout<<"此二叉树的广义表输出为：";Tree.PrintBTree(Tree.root);cout<<'\n'<<endl;goto Fanhui2;}break;case 6:{char x;cout<<"请输入要查找的字符："<<endl;cin>>x;Tree.Search(Tree.root,x);goto Fanhui2;}break;case 7:{char x;int y=0;cout<<"请输入要查找的字符："<<endl;cin>>x;Tree.degree(Tree.root,x);Tree.level(Tree.root,x,y);goto Fanhui2;}break;case 8:goto zero;break;default:{cout<<"输入无效字符，请重新输入"<<endl;goto Fanhui2;}break;}}break;case 3:CJ.menu();break;default:{cout<<"输入无效选项，请重新输入"<<'\n'<<endl;goto first;} }}void main(){tree Tr;Tr.menu();}六、测试结果及说明测试成功，可运行。