二叉树的构造_遍历_求数高和求节点数

//手工构造一颗二叉树 ，并给出递归和非递归2类7种遍历方法，树高,节点数求法和逆时针90度显示二叉树 
//注意本文中2个 typename的使用层次 
//递归遍历容易溢栈 
#include <cstdlib>
#include <iostream>
#include <queue> //用到队列时需要包含此文件 
#include <stack> //用到栈时需要包含此文件 

using namespace std;


template <typename T>//模板类需要template和struct2个语句!!!!!!!! 
struct Btnode{
       Btnode *lc_,*rc_;T value_;
       Btnode(T const& v=T(),Btnode*lc=0,Btnode*rc=0)
       :lc_(lc),rc_(rc),value_(v){}
       bool haslc(void) const{return lc_!=0;}
       bool hasrc(void) const{return rc_!=0;} 
       };

template<typename NT>
//中序遍历 
void inorder(NT* root,void(*visit)(NT*)){//注意第二个参数的函数传递方法 
     if(root!=0){
       inorder(root->lc_,visit);
       visit(root);
       inorder(root->rc_,visit);          
                 } 
     }
template<typename NT>
//中序遍历 
void inorder2(NT* root,void(*visit)(NT*)){   
  if(root==0) return;
   stack<NT* > s; s.push(root);
   while(true){
    root=s.top();
    while(root->haslc()) s.push(root=root->lc_);
    do{visit(root=s.top());s.pop();}while(!root->hasrc()&&!s.empty());
    if(root->hasrc()) s.push(root->rc_);
    else return;           
              }    
     } 
     
//后序遍历 
template<typename NT>    
void postorder(NT* root,void(*visit)(NT*)){
     if(root!=0){
     postorder(root->lc_,visit);
     postorder(root->rc_,visit);
     visit(root);            
                 }
     }  
     
template<typename NT>    
void postorder2(NT* root,void(*visit)(NT*)){    
     if(root==0) return;
     stack<NT*> s; s.push(root);
     while(true){
     root=s.top();
     while(root->haslc()) s.push(root=root->lc_);
     if(root->hasrc()) s.push(root->rc_);
     else{
          do{
             visit(root=s.top());s.pop();
             if(s.empty()) return;         
                       }while((root==s.top()->rc_)||!(s.top()->hasrc()));
                       s.push(s.top()->rc_);
        }
     }
     }
     
         
//先序遍历
template<typename NT>//发现该语句必须紧紧在preorder前面才可以 
void preorder(NT* root,void(*visit)(NT*)){
     if(root!=0){
     visit(root); 
     preorder(root->lc_,visit);
     preorder(root->rc_,visit);              
                 }
     }     
template<typename NT>
 void preorder2(NT*root,void(*visit)(NT*)){
      if(root==0) return;
      stack<NT*> s;
      while(true){
      visit(root);
      if(root->hasrc()) s.push(root->rc_);
      if(root->haslc()) root=root->lc_;
      else if(s.empty()) return;
      else{root=s.top();s.pop();}
                  }
      }    
     
     
  // 按层遍历 
  template<typename NT>   
   void levelorder(NT* root,void(*visit)(NT*)){
     if(root==0) return;
     queue<NT*> q; q.push(root);
     while(!q.empty()){
       NT* t=q.front();q.pop();
       if(t->haslc()) q.push(t->lc_);
       if(t->hasrc()) q.push(t->rc_);    
       visit(t);           
                       } 
     }     
     
 template<typename NT>   
 int height(NT const* root){
    if(root==0) return 0;
    int ld=height(root->lc_);
    int rd=height(root->rc_);
    return 1+std::max(ld,rd); 
   }    
     
  template<typename NT> 
  int size(NT const* root){
      if(root==0) return 0;
      return 1+size(root->lc_)+size(root->rc_);
      }   
 template<typename NT>
 void display(NT* root,int col=0){
      if(root==0) return;
      display(root->rc_,col+1);
      for(int i=0;i<col;++i) std::cout<<"|";
      std::cout<<"|"<<root->value_<<std::endl;
      display(root->lc_,col+1);
      
      }
     
typedef Btnode<char> NT;//该语句必须在print函数前，以防 NT不能找到 
void print(NT*p){std::cout<<p->value_<<"";}


int main(int argc, char *argv[])
{  
   
    //定义二叉树 
    NT i('I',0,0);NT h('H',0,0);  NT f('F',&h,&i);
    NT g('G',0,0);NT e('E',&g,0); NT d('D',0,0);
    NT c('C',0,&f);NT b('B',&d,&e);NT a('A',&b,&c);
    NT* root=&a;
    inorder(root,&print);cout<<endl;
    inorder2(root,&print);cout<<endl;
    preorder(root,&print);cout<<endl;
    preorder2(root,&print);cout<<endl;
    postorder(root,&print);cout<<endl;
    postorder2(root,&print);cout<<endl;
    levelorder(root,&print);cout<<endl;
    cout<<"height="<<height(root)<<endl;
    cout<<"number of nodes="<<size(root)<<endl;
    display(root,0); 
    system("PAUSE");
    return EXIT_SUCCESS;
}