实验题目:
实现二叉树各种遍历算法
实验目的:
领会二叉树的各种遍历过程以及遍历算法设计
实验内容:
设计程序,实现二叉树的先序遍历、中序遍历和后序遍历的
递归和非递归算法,以及层次遍历的算法。
二叉树各种基本运算的代码btree.h
//
// Created by liushihao on 19-4-26.
//
#include "iostream"
#define Maxsize 100
using namespace std;
typedef char ElemType;
typedef struct node
{
ElemType data;
struct node *lchild;
struct node *rchild;
}BTNode;
void CreateBTree(BTNode * &b, char *str) //创造二叉树
{
BTNode *St[Maxsize], *p;
int top=-1,k,j=0;
char ch;
b=NULL;
ch=str[j];
while(ch!='\0')
{
switch (ch)
{
case '(':top++;St[top]=p;k=1;break;
case ')':top--; break;
case ',':k=2; break;
default:
p=(BTNode*)malloc(sizeof(BTNode));
p->data=ch;
p->lchild=p->rchild=NULL;
if(b==NULL)
b=p;
else
{
switch(k)
{
case 1:St[top]->lchild=p;break;
case 2:St[top]->rchild=p;break;
}
}
}
j++;
ch=str[j];
}
}
void DestroyBtree(BTNode *&b) //销毁二叉树
{
if(b!=NULL)
{
DestroyBtree(b->lchild);
DestroyBtree(b->rchild);
free(b);
}
}
BTNode *FindNode(BTNode *b,ElemType x)
{
BTNode *p;
if(b==NULL)
{
return NULL;
}
else if(b->data==x)
{
return b;
}
else
{
p=FindNode(b->lchild, x);
if(p!=NULL)
{
return p;
}
else
{
return FindNode(b->rchild, x);
}
}
}
BTNode *LchildNode(BTNode *p)
{
return p->lchild;
}
BTNode *RchildNode(BTNode *p)
{
return p->rchild;
}
int BTHeight(BTNode *b)
{
int lchildh,rchildh;
if(b==NULL) return 0;
else
{
lchildh=BTHeight(b->lchild);
rchildh=BTHeight(b->rchild);
return (lchildh>rchildh)? (lchildh+1):(rchildh+1);
}
}
void DispBTree(BTNode *b)
{
if(b!=NULL)
{
cout<<b->data;
if(b->lchild!=NULL || b->rchild!=NULL)
{
cout<<"(";
DispBTree(b->lchild);
if(b->rchild!= NULL) cout<<",";
DispBTree(b->rchild);
cout<<")";
}
}
}
以二叉树结点为元素的栈的定义代码stack.h
//
// Created by liushihao on 19-4-26.
//
#include <iostream>
#include "btree.h"
using namespace std;
#define Maxsize 50
typedef struct
{
BTNode *data[Maxsize];
int top;
}SqStack;
void InitStack(SqStack *&s)
{
s=(SqStack*)malloc(sizeof(SqStack));
s->top=-1;
}
void DestroyStack(SqStack *&s)
{
free(s);
}
bool StackEmpty(SqStack *s)
{
return (s->top==-1);
}
bool Push(SqStack *&s,BTNode *e)
{
if(s->top==Maxsize-1){
return false;
}
s->top++;
s->data[s->top]=e;
return true;
}
bool Pop(SqStack *&s,BTNode* &e)
{
if(s->top==-1)
return false;
e=s->data[s->top];
s->top--;
return true;
}
bool GetTop(SqStack *s,BTNode* &e)
{
if(s->top==-1)
return false;
e=s->data[s->top];
return true;
}
exp7-2.cpp
//
// Created by liushihao on 19-4-26.
//
#include "stack.h"
void PreOrder_recursion(BTNode *b) //递归先序遍历
{
if(b!=NULL)
{
cout<<b->data;
PreOrder_recursion(b->lchild);
PreOrder_recursion(b->rchild);
}
}
void PreOrder_not_recursion(BTNode *b) //非递归先序遍历
{
BTNode *p;
SqStack *st;
InitStack(st);
if(b!=NULL)
{
Push(st,b);
while(!StackEmpty(st))
{
Pop(st,p);
cout<<p->data;
if(p->rchild!=NULL)
{
Push(st,p->rchild);
}
if(p->lchild!=NULL)
{
Push(st,p->lchild);
}
}
cout<<endl;
}
DestroyStack(st);
}
void InOrder_recursion(BTNode *b) //递归中序遍历
{
if(b!=NULL)
{
InOrder_recursion(b->lchild);
cout<<b->data;
InOrder_recursion(b->rchild);
}
}
void InOrder_not_recursion(BTNode *b) //非递归中序遍历
{
BTNode *p;
SqStack *st;
InitStack(st);
p=b;
while(!StackEmpty(st) || p!=NULL)
{
while(p!=NULL)
{
Push(st,p);
p=p->lchild;
}
if(!StackEmpty(st))
{
Pop(st,p);
cout<<p->data;
p=p->rchild;
}
}
cout<<endl;
DestroyStack(st);
}
void PostOrder_recursion(BTNode *b) //递归后序遍历
{
if(b!=NULL)
{
PostOrder_recursion(b->lchild);
PostOrder_recursion(b->rchild);
cout<<b->data;
}
}
void PostOrder_not_recursion(BTNode *b) //非递归后序遍历
{
BTNode *p,*r;
bool flag;
SqStack *st;
InitStack(st);
p=b;
do{
while(p!=NULL)
{
Push(st,p);
p=p->lchild;
}
r=NULL;
flag=true;
while(!StackEmpty(st)&&flag)
{
GetTop(st,p);
if(p->rchild==r)
{
cout<<p->data;
Pop(st,p);
r=p;
}
else
{
p=p->rchild;
flag=false;
}
}
}while (!StackEmpty(st));
cout<<endl;
DestroyStack(st);
}
//void LevelOrder(BTNode *b) 层次遍历。。。还在更新
//{
// BTNode *p;
// SqQueue *qu;
// InitQueue(qu);
// enQueue(qu,b);
// while(!QueueEmpty(qu))
// {
// deQueue(qu,p);
// cout<<p->data;
// if(p->lchild!=NULL)
// {
// enQueue(qu,p->lchild);
// }
// if(p->rchild!=NULL)
// {
// enQueue(qu,p->rchild);
// }
// }
//}
int main()
{
BTNode *b;
char str[]="A(B(D,E(H(J,K(L,M(,N))))),C(F,G(,I)))";
CreateBTree(b, str);
cout<<"初始化二叉树为:"<<endl;
DispBTree(b);
cout<<endl;
cout<<"递归先序遍历";PreOrder_recursion(b);
cout<<endl;
cout<<"非递归先序遍历";PreOrder_not_recursion(b);
cout<<"递归中序遍历";InOrder_recursion(b);
cout<<endl;
cout<<"非递归中序遍历";InOrder_not_recursion(b);
cout<<"递归先序遍历";PostOrder_recursion(b);
cout<<endl;
cout<<"非递归先序遍历";PostOrder_not_recursion(b);
// cout<<"层次遍历:";LevelOrder(b);
return 0;
}