【工程】二叉树已知前序/中序的顺序，构造树的递归等实现

文章中的二叉树原型为 《Data Structures, Algorithms, & Applications in C++》, 1nd Edition中的树类。

要求在源文件的基础上 实现以下三个操作：

【1】给出前序遍历和中序遍历结果，构造树。

【2】给出计算叶子节点数目的函数。

【3】交换树中的左右所有节点。

需要用到的主要函数（异常抛出\链表队列之类与主题没啥关系的请查书）：

遍历查找函数:

BinaryTree<char> MakeTree2(string InOrder, string PreOrder)
	{
		BinaryTree<char> tree;
	if(InOrder.empty()){
		tree.root = 0;
		return tree;
	}
	char RootValue;
	RootValue = PreOrder[0];//根结点的值
	//计算左右子树中结点数
	size_t pos,LeftChildSize, RightChildSize;
	pos = InOrder.find(RootValue);
	LeftChildSize = pos;
	RightChildSize = InOrder.size() - pos - 1;
	string LeftInOrder, LeftPreOrder, RightInOrder, RightPreOrder;
	//原函数不变

	LeftInOrder = InOrder.substr(0, LeftChildSize);
	RightInOrder = InOrder.substr(pos + 1, RightChildSize);

	LeftPreOrder = PreOrder.substr(1,LeftChildSize+1);
	RightPreOrder =PreOrder.substr(LeftChildSize+1,RightChildSize+1);
	                                               
	
	BinaryTree<char> left,right;
	left = MakeTree2(LeftInOrder,LeftPreOrder);
	right = MakeTree2(RightInOrder,RightPreOrder);
	
	tree.root = new BinaryTreeNode<char>(RootValue);
	
    tree.root->LeftChild = left.root;
    tree.root->RightChild = right.root;
    left.root = right.root = 0;
		
	return tree;
		
	}

BinaryTree.h

#include<iostream>
#include "LinkedQueue.h"
#include "binaryTreeNode.h"
#include "myexception.h"
#include <string>
#ifndef _BinaryTree
#define _BinaryTree

int _count;

template<class T>
class BinaryTree {
   public:
      BinaryTree() {root = 0;};
      ~BinaryTree(){}; 
      bool IsEmpty() const
        {return ((root) ? false : true);}
      bool Root(T& x) const;
      void MakeTree(const T& element,
           BinaryTree<T>& left, BinaryTree<T>& right);
      void BreakTree(T& element, BinaryTree<T>& left,
                    BinaryTree<T>& right);
      void PreOrder(void(*Visit)(BinaryTreeNode<T> *u))
           {PreOrder(Visit, root);}
      void InOrder(void(*Visit)(BinaryTreeNode<T> *u))
           {InOrder(Visit, root);}
      void PostOrder(void(*Visit)(BinaryTreeNode<T> *u))
           {PostOrder(Visit, root);}
	  void LevelOrder(void(*Visit)(BinaryTreeNode<T> *u));

	  void ExChange(BinaryTreeNode<T> *u);
      void PreOutput() {PreOrder(Output, root); cout << endl;}
      void InOutput() {InOrder(Output, root); cout << endl;}
      void PostOutput() {PostOrder(Output, root); cout << endl;}
      void LevelOutput() {LevelOrder(Output); cout << endl;}
      void Delete() {PostOrder(Free, root); root = 0;}
      int Height() const {return Height(root);}
      int Size()
         {_count = 0; PreOrder(Add1, root); return _count-1;}
	  //修改 叶子节点个数
	  int SizeLeaf(BinaryTreeNode<T> *root)
      {
		  if(root==NULL)
				return 0;
		  else if(root->LeftChild==NULL && root->RightChild==NULL)
				return 1;
		  else
			  return SizeLeaf(root->LeftChild)+SizeLeaf(root->RightChild);
	  }
	  
	  //自己添加的函数，P31--1
	  bool Compare(BinaryTreeNode<T> *X,BinaryTreeNode<T> *Y)
	  {
		  if(!Y && !X)
			return true;
		  if((!(!Y && !X)) &&((!Y)||(!X)) || Y->data != X->data)
			  return false;
		  if(Compare(X->LeftChild, Y->LeftChild) && Compare(X->RightChild, Y->RightChild))
			  return true;
		  else
			  return false;
		
	  }

	  
	   BinaryTreeNode<T> *root; 

	

   private:
     
      void PreOrder(void(*Visit)
        (BinaryTreeNode<T> *u), BinaryTreeNode<T> *t);
      void InOrder(void(*Visit)
        (BinaryTreeNode<T> *u), BinaryTreeNode<T> *t);
      void PostOrder(void(*Visit)
        (BinaryTreeNode<T> *u), BinaryTreeNode<T> *t);
      static void Free(BinaryTreeNode<T> *t) {delete t;}
      static void Output(BinaryTreeNode<T> *t)
                  {cout << t->data << ' ';}
      static void Add1(BinaryTreeNode<T> *t) {_count++;}
      int Height(BinaryTreeNode<T> *t) const;
};

template<class T>
bool BinaryTree<T>::Root(T& x) const
{
   if (root) {x = root->data;
              return true;}
   else return false; 
}

template<class T>
void BinaryTree<T>::MakeTree(const T& element,
          BinaryTree<T>& left, BinaryTree<T>& right)
{
   root = new BinaryTreeNode<T>
              (element, left.root, right.root);

  
   left.root = right.root = 0;
}

template<class T>
void BinaryTree<T>::BreakTree(T& element,
       BinaryTree<T>& left, BinaryTree<T>& right)
{
   if (!root) throw BadInput(); 
   element = root->data;
   left.root = root->LeftChild;
   right.root = root->RightChild;

   delete root;
   root = 0;
}

//交换树的左右子节点.
template <class T>
 void BinaryTree<T>::ExChange(BinaryTreeNode<T> *u)
{
   BinaryTreeNode<T> *temp;
   temp = root;
   if(u)
   {
	   temp=u->LeftChild;
	   (u)->LeftChild=(u)->RightChild;
	   (u)->RightChild=temp;

	   ExChange((*u).LeftChild);
	   ExChange((*u).RightChild);
   }
}

 template<class T>
 void BinaryTree<T>::PreOrder(
               void(*Visit)(BinaryTreeNode<T> *u),
                         BinaryTreeNode<T> *t)
{
   if (t) 
   {
	   Visit(t);
   	   PreOrder(Visit, t->LeftChild);
   	   PreOrder(Visit, t->RightChild);
   }

}

 template <class T>
 void BinaryTree<T>::InOrder(
            void(*Visit)(BinaryTreeNode<T> *u),
                         BinaryTreeNode<T> *t)

{
   if (t) {
	   InOrder(Visit, t->LeftChild);
   	   Visit(t);
   	   InOrder(Visit, t->RightChild);
          }
}

 template <class T>
 void BinaryTree<T>::PostOrder(
            void(*Visit)(BinaryTreeNode<T> *u),
                         BinaryTreeNode<T> *t)

{
   if (t) {
		   PostOrder(Visit, t->LeftChild);
           PostOrder(Visit, t->RightChild);
           Visit(t);
           }
}

 template <class T>
 void BinaryTree<T>::LevelOrder(
           void(*Visit)(BinaryTreeNode<T> *u))
{
   LinkedQueue<BinaryTreeNode<T>*> Q;
   BinaryTreeNode<T> *t;
   t = root;
   while (t) {
      Visit(t);
      if (t->LeftChild) Q.Add(t->LeftChild);
      if (t->RightChild) Q.Add(t->RightChild);
      try {Q.Delete(t);}
      catch (OutOfBounds) {return;}
      }
}

template <class T>
int BinaryTree<T>::Height(BinaryTreeNode<T> *t) const
{
   if (!t) return 0;              
   int hl = Height(t->LeftChild); 
   int hr = Height(t->RightChild);
   if (hl > hr) return ++hl;
   else return ++hr;
}
#endif

BinaryTreeNode.h,没改。。

#ifndef BinaryNode
#define BinaryNode

template <class T> class BinaryTree;

template <class T>
class BinaryTreeNode {
   friend BinaryTree<T>;

   public:
      BinaryTreeNode() {LeftChild = RightChild = 0;}
      BinaryTreeNode(const T& e)
            {data = e; LeftChild = RightChild = 0;}
      BinaryTreeNode(const T& e, BinaryTreeNode *l,
                     BinaryTreeNode *r)
       {data = e; LeftChild = l; RightChild = r;}
      T data;
      BinaryTreeNode<T> *LeftChild,  
                        *RightChild; 
};

#endif

测试文件:

#include <iostream>
#include <string>
#include "BinaryTree.h"
#include "myexception.h"
#include "BinaryTreeNode.h"
using namespace std;

int count = 0;
BinaryTree<int> a,x,y,z,q,r,s;

int main()
{
	y.MakeTree(3,a,a);
	x.MakeTree(4,a,a);
	z.MakeTree(5,y,x);

	cout<<"交换前:";
	z.PreOutput();
	//交换测试
	z.ExChange(z.root);
	cout<<"交换后:";
	z.PreOutput();

	//个数测试
	cout<<"叶子节点个数:"<<z.SizeLeaf(z.root)<<endl;

	//声明一个变量
	BinaryTree<char> p;

	//qianxu="111",zhongxu="111";
	
	/*string zhongxu="1234";
	string qianxu="4321";*/

	/*string zhongxu="312";
	string qianxu="132";*/

	string zhongxu="32145";
	string qianxu="12345";

	p=MakeTree2(zhongxu,qianxu);

	cout<<"Add之后 前序的结果:";

	p.PreOutput();
	cout<<endl;

   system("pause");
   return 0;
}