(C语言)二叉树非递归后序(数据结构十五)

1.数据类型定义

在代码中为了清楚的表示一些错误和函数运行状态，我们预先定义一些变量来表示这些状态。在head.h头文件中有如下定义：

//定义数据结构中要用到的一些变量和类型
#ifndef HEAD_H
#define HEAD_H

#include <stdio.h>
#include <malloc.h>
#include <stdlib.h>
#include <math.h>

#define TRUE  1
#define FALSE 0
#define OK    1
#define ERROR  0
#define INFEASIBLE -1
#define OVERFLOW   -2    //分配内存出错

typedef int  Status;     //函数返回值类型
typedef int  ElemType;   //用户定义的数据类型

#endif

2.非递归过程中需要用到栈

LinkStack.h代码如下:

#ifndef LINKSTACK_H
#define LINKSTACK_H

#include "head.h"


//可用栈类型Stack的相关定义：
typedef struct SElemType {
	pBiNode   root; //二叉树结点的指针类型
	int      tag; // 0..1
}SElemType,*pType;      //栈的元素类型

typedef SElemType Type;

typedef struct Node{
	Type       data;
	struct Node* next;
}Node,*pNode;

typedef struct Stack{
	pNode base;
	pNode top;
	int   length;
}Stack,*pStack;


//初始化栈
Status InitStack(pStack &S){
	S=(pStack)malloc(sizeof(Stack));
	if(!S) return OVERFLOW;
	S->length=0;
	S->base=(pNode)malloc(sizeof(Node));
	if(!S->base) return OVERFLOW;
	S->top=(pNode)malloc(sizeof(Node));
	if(!S->top) return OVERFLOW;
	S->top->next=S->base;
	return OK;
}

Status freeStack(pStack &S){
	free(S);
	S=NULL;
	return OK;
}

//清空栈
Status ClearStack(pStack &S){
	if(S==NULL) return ERROR;
	pNode p=S->top;
	while(p->next!=S->base){
		pNode q=p;
		p=p->next;
		free(q);
		q=NULL;
	}
	S->top=p;
	S->length=0;
	return OK;
}
//销毁栈
Status DestroyStack(pStack S){
	if(S==NULL) return ERROR;
	ClearStack(S);
	free(S->base);
	S->base=NULL;
	free(S->top);
	S->top=NULL;
	freeStack(S);
	S==NULL;
	return OK;
}
//栈是否为空
Status StackEmpty(pStack S){
	return S->length<=0;
}
//栈长度
int StackLength(pStack S){
	return S->length;
}
//得到栈顶数据级e
Status GetTop(pStack S,Type *e){
	*e=S->top->next->data;
	return OK;
}
//入栈
Status Push(pStack &S,Type* e){
	if(S->length==0){
		S->base->data=*e;
	}
	else{
		pNode p=S->top;
		p->data=*e;
		pNode q=(pNode)malloc(sizeof(Node));
		q->next=p;
		S->top=q;
	}
	S->length++;
	return OK;
}
//出栈
Status Pop(pStack S,Type *e){
	if (S->length<=0) return ERROR;
	if(S->length==1){
		*e=S->base->data;
		S->length--;
	}else{
		pNode p=S->top;
		S->top=p->next;
		*e=S->top->data;
		free(p);
		S->length--;
	}
	return OK;
}

Status print(Type e){
	printf("%dn",e);
	return OK;
}

//用vistit遍历栈
Status StackTraverse(pStack S,Status(*visit)(Type)){
	pNode p=S->top;
	do 
	{
		p=p->next;
		(*visit)(p->data);
	} while (p!=S->base);
	return OK;
}
Status printStack(pStack S){
	if (S==NULL ||S->length==0) return ERROR;
	StackTraverse(S,print);
	return OK;
}


#endif

3.二叉树头文件 

BiTree.h代码如下:

#ifndef BITREE_H
#define BITREE_H

#include "head.h"


typedef struct BiNode{
	ElemType data;
	struct BiNode *left,*right;
}BiNode,*pBiNode;


Status InsertRight(pBiNode &root,ElemType e);
Status InsertLeft(pBiNode &root,ElemType e);


Status InitBiTree(pBiNode &tree){
	tree=(pBiNode)malloc(sizeof(BiNode));
	if(!tree) return OVERFLOW;
	tree->data=-999999;
	tree->left=NULL;
	tree->right=NULL;
	return OK;
}
Status BiTreeEmpty(pBiNode root){
	if(root==NULL) return ERROR;
	return root->left==root->right && root->data==-999999;
}

Status HasNoNode(pBiNode root){
	if(root==NULL) return ERROR;
	return root->left==root->right ;
}

Status CreatTreeNode(pBiNode &node,ElemType e){
	node=(pBiNode)malloc(sizeof(BiNode));
	if(!node) return OVERFLOW;
	node->data=e;
	node->left=NULL;
	node->right=NULL;
	return OK;
}
Status InsertRight(pBiNode &root,ElemType e){
	if(root->right==NULL){
		if(e>root->data){
			pBiNode p;
			CreatTreeNode(p,e);
			root->right=p;
			return OK;
		}else{
			pBiNode p;
			CreatTreeNode(p,e);
			root->left=p;
			return OK;
		}

	}else{
		e>root->data? InsertRight(root->right,e):InsertLeft(root,e);
	}

}
Status InsertLeft(pBiNode &root,ElemType e){
	if(root->left==NULL){
		if(e>root->data){
			pBiNode p;
			CreatTreeNode(p,e);
			root->right=p;
			return OK;
		}else{
			pBiNode p;
			CreatTreeNode(p,e);
			root->left=p;
			return OK;
		}

	}else{
		e<=root->data?InsertLeft(root->left,e):InsertRight(root,e);
	}

}


Status InsertTree(pBiNode &root,ElemType e){
	if(BiTreeEmpty(root)){
		root->data=e;
		return true;
	}
	if(e>root->data){
		InsertRight(root,e);
	}else{
		InsertLeft(root,e);
	}
}


Status CreateBiTree(pBiNode &root,ElemType *a,int n){
	for (int i=0;i<n;i++)
	{
		InsertTree(root,a[i]);
	}
	return true;
}
 Status print(ElemType e ){
 	printf("%d ",e);
 	return true;
 }

Status PreOrderTraverse(pBiNode root,Status(*p)(int)){
	if(root){
		(*p)(root->data);
		PreOrderTraverse(root->left,p);
		PreOrderTraverse(root->right,p);
	}
	return OK;
}

Status MiddleOrderTraverse(pBiNode root,Status(*p)(int)){
	if(root){
		MiddleOrderTraverse(root->left,p);
		(*p)(root->data);
		MiddleOrderTraverse(root->right,p);
	}
	return OK;
}

Status AfterOrderTraverse(pBiNode root,Status(*p)(int)){
	if(root){
		AfterOrderTraverse(root->left,p);
		AfterOrderTraverse(root->right,p);
		(*p)(root->data);
	}
	return OK;
}

Status ClearBiTree(pBiNode &root){
	if(root){
		ClearBiTree(root->left);
		ClearBiTree(root->right);
		free(root);
		root==NULL;
	}
	return OK;
}


#endif

4.测试代码

#include "BiTree.h"
#include "LinkStack.h"

//非北递归后序
void PostOrder(pBiNode root){
	pStack s;
	InitStack(s);
	pType p,t;
	p=(pType)malloc(sizeof(SElemType));
	t=(pType)malloc(sizeof(SElemType));
	p->root=root;        
	while(p->root ||!StackEmpty(s))
	{                
		while(p->root)
		{
			p->tag= 0;
			Push(s,p);
			//printf("%d ",p->root->data);
			p->root=p->root->left;            
		}
		GetTop(s,t);
		while(t->tag && !StackEmpty(s))
		{
			Pop(s,p);
			printf("%d ",p->root->data);
			GetTop(s,t);
		}
		if(!StackEmpty(s)){
			GetTop(s,t);
			t->tag=1;
			Pop(s,p);
			Push(s,t);
			GetTop(s,p);
			p->root=p->root->right;
		}else{
			break;
		}
	}           
}



void main(){
	ElemType a[14]={100,50,200,40,30,45,60,55,61,200,150,300,250,400};
	pBiNode root;
	InitBiTree(root);
	CreateBiTree(root,a,14);
	
	printf("前序：");
	PreOrderTraverse(root,print);
	
	printf("n中序：");
	MiddleOrderTraverse(root,print);
	
	printf("n后序：");
	AfterOrderTraverse(root,print);
	
	printf("n非递归后序：");
	PostOrder(root);
	
	printf("n");
	ClearBiTree(root);
	
}

插入的二叉树为:

5.运行结果: