【数据结构】二叉树的定义，递归遍历，非递归遍历，层次遍历，深度等

#include<iostream>
using namespace std;
typedef char Elemtype;
struct BiNode{
	Elemtype date;
	BiNode *lchild,*rchild;
};
typedef BiNode *Bitree;
//树的初始化 
void Inittree(Bitree &bt)
{
	bt=NULL;
}
//树的先序创建
void Create(Bitree &bt)
{
	//abc##d##ef##g##
	Elemtype d;
	cin>>d;
	if(d=='#') bt=NULL;
	else
	{
		bt=new BiNode;
		bt->date=d;
		Create(bt->lchild);
		Create(bt->rchild);
	}
} 
//递归 
//树的先序遍历
void preOrder(Bitree &bt)
{
	if(bt)
	{
		cout<<bt->date<<" ";
		preOrder(bt->lchild);
		preOrder(bt->rchild);
	}
} 
//树的中序遍历 
void inOrder(Bitree &bt)
{
	if(bt)
	{
		inOrder(bt->lchild);
		cout<<bt->date<<" ";
		inOrder(bt->rchild);
	}
}
//树的后序遍历 
 void postOrder(Bitree &bt)
{
	if(bt)
	{
		postOrder(bt->lchild);
		postOrder(bt->rchild);		
		cout<<bt->date<<" ";
	}
} 
//非递归 
//非递归先序遍历
void preIterOrder(Bitree &bt)
{
	BiNode* s[100]; //栈s
	int top=-1;  //空栈
	BiNode *p=bt;
	while(p||top!=-1)
	{
		while(p)
		{
			s[++top]=p; //入栈
			cout<<p->date<<" ";
			p=p->lchild; 
		}
		p=s[top--]; //出栈 
		p=p->rchild;
	} 
} 
//非递归中序遍历
void inIterOrder(Bitree &bt)
{
	BiNode* s[100]; //栈s
	int top=-1;  //空栈
	BiNode *p=bt;
	while(p||top!=-1)
	{
		while(p)
		{
			s[++top]=p; //入栈
			
			p=p->lchild; 
		}
		p=s[top--]; //出栈 
		cout<<p->date<<" ";
		p=p->rchild;
	} 
} 
//非递归后序遍历
void postIterOrder(Bitree &bt)
{
	BiNode* s[100]; //栈s
	int top=-1;  //空栈
	BiNode *p=bt; 
	BiNode *q=NULL; //q为当前访问过的节点，初始为空
	while(p||top!=-1)
	{
		while(p)
		{
			s[++top]=p;
			p=p->lchild;
		}
		p=s[top]; //取栈顶
		if(p->rchild==NULL||p->rchild==q)
		{//如果p没有右孩子或者右孩子是q
		//表明以p为根的右子树已经遍历结束，此时可以访问根结点p了
			cout<<p->date<<" ";
			q=p; //q指向刚访问过的结点
			top--; //出栈 
			p=NULL;
		} 
		else p=p->rchild;
	} 
} 
//二叉树的按层遍历算法
void levelOrder(Bitree &bt)
{
	const int N=100; //队列空间大小
	BiNode *q[N];
	int front=0,rear=0;
	if(bt)
	{
		q[rear]=bt;//树根入队
		rear=(rear+1)%N; 
	} 
	BiNode *p;
	while(front!=rear)
	{
		p=q[front];front=(front+1)%N;//出队
		cout<<p->date<<" ";
		if(p->lchild) q[rear++]=p->lchild;//左孩子入队
		if(p->rchild) q[rear++]=p->rchild;//右孩子入队
	}
} 
//输出带括号的中缀表达式
void inOrder2(Bitree &bt)
{
	if(bt)
	{
		if(bt->lchild&&bt->lchild->lchild&&bt->lchild->rchild) cout<<"("<<" ";
		inOrder(bt->lchild);
		if(bt->lchild&&bt->lchild->lchild&&bt->lchild->rchild) cout<<")"<<" ";
		cout<<bt->date<<" ";
		if(bt->rchild&&bt->rchild->lchild&&bt->rchild->rchild) cout<<"("<<" ";
		inOrder(bt->rchild);
		if(bt->rchild&&bt->rchild->lchild&&bt->rchild->rchild) cout<<")"<<" ";
	}
}
//求二叉树的深度
int height(const Bitree &bt)
{
	int lh,rh;
	if(bt==NULL) return 0;
	lh=height(bt->lchild);
	rh=height(bt->rchild);
	return (lh>=rh?lh:rh)+1;
} 
//求二叉树叶子个数
int leafs(const Bitree &bt)
{
	if(bt==NULL) return 0;
	if(bt->lchild==NULL&&bt->rchild==NULL) return 1;
	return leafs(bt->lchild)+leafs(bt->rchild);
} 
//打印叶子
void Printleaf(const Bitree &bt)
{
	if(bt==NULL) return;
	if(bt->lchild==NULL&&bt->rchild==NULL) 
	cout<<bt->date<<" ";
	Printleaf(bt->lchild);
	Printleaf(bt->rchild);
	
} 
int main()
{
	Bitree bt;
	Inittree(bt);
	Create(bt);
	cout<<"递归先序遍历二叉树：";
	preOrder(bt);
	cout<<endl;
	cout<<"递归中序遍历二叉树：";
	inOrder(bt);
	cout<<endl;
	cout<<"递归后序遍历二叉树：";
	postOrder(bt);
	cout<<endl;
	cout<<"递非归先序遍历二叉树：";
	preIterOrder(bt); 
	cout<<endl;
	cout<<"非递归中序遍历二叉树：";
	inIterOrder(bt); 
	cout<<endl;
	cout<<"非递归后序遍历二叉树：";
	postIterOrder(bt); 
	cout<<endl;
	cout<<"按层遍历二叉树："; 
	levelOrder(bt);
	cout<<endl;
	cout<<"输出带括号的中缀表达式：";
	inOrder2(bt);
	cout<<endl;
	cout<<"输出二叉树高度：";
	cout<<height(bt);
	cout<<endl;
	cout<<"输出二叉树叶子个数：";
	cout<<leafs(bt);
	cout<<endl;
	cout<<"输出二叉树的叶子：";
	Printleaf(bt);
	cout<<endl;
	return 0;
}