数据结构——树和二叉树的性质与存储结构

案例分析：

写出下面二叉树的先、中、后序遍历输出的结果：
注：先自己推算，然后用程序验算。

先序遍历的结果：A F H D C B J G E I K
中序遍历的结果：D H C F J B G A I E K
后序遍历的结果：D C H J G B F I K E A

代码如下：

#include "pch.h"
#include <iostream>
using namespace std;

int top = -1;
typedef struct Bitnode
{
	char data;
	Bitnode *lchild, *rchild;
}Bitnode,*bittree;

//创建一个二叉树
void Createbittree(bittree *t)
{
	*t =(Bitnode *) malloc(sizeof(Bitnode));
	(*t)->data = 'A';
	(*t)->lchild= (Bitnode *)malloc(sizeof(Bitnode));
	(*t)->rchild =(Bitnode *)malloc(sizeof(Bitnode));
	(*t)->lchild->data = 'F';
	(*t)->rchild->data = 'E';
	(*t)->lchild->lchild = (Bitnode *)malloc(sizeof(Bitnode));
	(*t)->lchild->rchild = (Bitnode *)malloc(sizeof(Bitnode));
	(*t)->rchild->lchild = (Bitnode *)malloc(sizeof(Bitnode));
	(*t)->rchild->rchild = (Bitnode *)malloc(sizeof(Bitnode));
	(*t)->lchild->lchild->data = 'H';
	(*t)->lchild->rchild->data = 'B';
	(*t)->rchild->lchild->data = 'I';
	(*t)->rchild->rchild->data = 'K';
	(*t)->rchild->lchild->lchild= NULL;
	(*t)->rchild->lchild->rchild= NULL;
	(*t)->rchild->rchild->lchild = NULL;
	(*t)->rchild->rchild->rchild = NULL;
	(*t)->lchild->lchild->lchild = (Bitnode *)malloc(sizeof(Bitnode));
	(*t)->lchild->lchild->lchild->lchild = NULL;
	(*t)->lchild->lchild->lchild->rchild = NULL;
	(*t)->lchild->lchild->rchild = (Bitnode *)malloc(sizeof(Bitnode));
	(*t)->lchild->lchild->rchild->lchild = NULL;
	(*t)->lchild->lchild->rchild->rchild = NULL;
	(*t)->lchild->rchild->lchild = (Bitnode *)malloc(sizeof(Bitnode));
	(*t)->lchild->rchild->lchild->lchild = NULL;
	(*t)->lchild->rchild->lchild->rchild = NULL;
	(*t)->lchild->rchild->rchild = (Bitnode *)malloc(sizeof(Bitnode));
	(*t)->lchild->rchild->rchild->lchild = NULL;
	(*t)->lchild->rchild->rchild->rchild = NULL;
	(*t)->lchild->lchild->lchild->data = 'D';
	(*t)->lchild->lchild->rchild->data = 'C';
	(*t)->lchild->rchild->lchild->data = 'J';
	(*t)->lchild->rchild->rchild->data = 'G';
}
//先序遍历入栈
void Push(Bitnode **a,Bitnode *elem)
{
	a[++top] = elem;
}
//先序遍历出栈
void Pop()
{
	if (top==-1)
	{
		return;
	}
	top--;
}
//获取栈顶元素
Bitnode *Get_top(Bitnode**a)
{
	return a[top];
}
//输出节点数据
void Printelem(Bitnode *elem)
{
	cout << elem->data << "  ";
}
//实现先序遍历算法
void preorder(Bitnode*tree)
{
	Bitnode *a[30];
	Bitnode *p;
	Push(a, tree);
	while (top!=-1)
	{
		p = Get_top(a);
		Pop();
		while (p)
		 {
			Printelem(p);
			if (p->rchild)
			{
				Push(a,p->rchild);
			}
			p = p->lchild;
		}
	}
}
//中序遍历二叉树
void inorder(bittree tree)
{
	Bitnode *a[30];	//定义一个顺序栈
	Bitnode *p;		//临时指针
	Push(a, tree);	//根节点入栈
	while (top != -1)	//top！=-1来判定栈是否为空
	{
		while ((p=Get_top(a))&&p)//获取栈顶元素不为空
		{
			//左子树节点入栈，如果没有，null入栈
			Push(a, p->lchild);
		}
		Pop();//跳出循环，栈顶元素是空，
		if (top!=-1)
		{
			p = Get_top(a);//获取栈顶元素
			Pop();
			Printelem(p);
			Push(a,p->rchild);//右子树节点入栈
		}
	}
}



//二叉树后序遍历（非递归法）
struct Snode
{
	bittree p;
	int tag;
};
//后序遍历的入栈函数
void PostPush(Snode*a, Snode sdata)
{
	a[++top] = sdata;
}
//后序遍历
void PostOrder(bittree tree)
{
	Snode a[20];
	Bitnode*p;		//节点指针
	int tag;
	Snode sdata;
	p = tree;
	while (p||top!=-1)//用的或，这两种都行
	{
		while (p)
		{
			sdata.p = p;
			sdata.tag = 0;//遍历左子树，设置标记位为0
			PostPush(a, sdata);//入栈
			p = p->lchild;//以该节点为根节点，遍历左子树
		}
		sdata=a[top];
		Pop();
		p = sdata.p;
		tag = sdata.tag;

		if (tag==0)//条件为真，左子树遍历完成，该节点需要遍历右子树
		{
			sdata.p = p;
			sdata.tag = 1;
			PostPush(a, sdata);//更改节点标志位，重新入栈
			p = p->rchild;//将该节点的右子树设置为根节点，重新循环

		}
		else
		{
			Printelem(p);
			p = NULL;
		}
	}
}
int main()
{
	bittree tree;
	Createbittree(&tree);
	cout << "先序遍历的结果为：";
	preorder(tree);
	cout << endl;
	cout << "中序遍历的结果为：";
	inorder(tree);
	cout << endl;
	cout << "后序遍历的结果为：";
	PostOrder(tree);
	cout << endl;
	return 0;
}

结果为：