"Data structure" algorithm design problem: Assuming that the binary tree adopts a binary chain storage structure, the design algorithm outputs the inverse sequence of the path from the root node to each leaf node.
The path from the leaf node to the root node of the binary tree is required to use methods such as preorder traversal, postorder traversal, and hierarchical traversal. This algorithm uses post-order traversal non-recursive and pre-order traversal recursive methods. Write the basic operations of the binary tree used by the program into the file btree.h to achieve the following functions.
- CreateBtree(BTNode *&b, char *str): Use the binary tree bracket string to create a binary chain storage structure b. Bracket notation form: root (left subtree, right subtree)
- DispBTree(BTNode *b): output binary tree in bracket notation
- DestroyBTree(BTNode *&b): Destroy the binary tree.
//文件名：btree.h
#include<stdio.h>
#include<malloc.h>
#define MaxSize 100
typedef char ElemType;
typedef struct node
{
ElemType data; //数据元素
struct node *lchild; //指向左孩子
struct node *rchild; //指向右孩子
} BTNode;
void CreateBTree(BTNode *&b,char *str)
{
BTNode *St[MaxSize],*p=NULL;
int top=-1,k,j=0;
char ch;
b=NULL; //建立的二叉树初始时为空
ch=str[j];
while (ch!='\0') //str未扫描完时循环
{
switch(ch)
{
case '(':St[++top]=p;k=1; break; //为左节点
case ')':--top;break;
case ',':k=2; break; //为右节点
default:p=(BTNode *)malloc(sizeof(BTNode));
p->data=ch;p->lchild=p->rchild=NULL;
if (b==NULL) //p指向二叉树的根节点
b=p;
else //已建立二叉树根节点
{
switch(k)
{
case 1:St[top]->lchild=p;break;
case 2:St[top]->rchild=p;break;
}
}
}
ch=str[++j];
}
}
void DestroyBTree(BTNode *&b)
{ if(b!=NULL)
{ DestroyBTree(b->lchild);
DestroyBTree(b->rchild);
free(b);
}
}
void DispBTree(BTNode *b) //以括号表示法输出二叉树
{
if(b!=NULL)
{
printf("%c", b->data);
if(b->lchild!=NULL || b->rchild!=NULL)
{
printf("(");
DispBTree(b->lchild);
if(b->rchild!=NULL)
printf(",");
DispBTree(b->rchild);
printf(")");
}
}
}
#include "btree.h" //包含二叉树的基本运算算法
void PostOrder(BTNode *b) //后序遍历的递归算法
{
if (b!=NULL)
{
PostOrder(b->lchild); //递归访问左子树
PostOrder(b->rchild); //递归访问右子树
printf("%c ",b->data); //访问根节点
}
}
void PostOrder1(BTNode *b)
{ //后序遍历非递归算法
BTNode *St[MaxSize];
int top=-1; //栈指针置初值
BTNode *p=b;
BTNode *r=NULL;
while (p||top>-1)
{
if(p){
St[++top]=p;
p=p->lchild;
}
else
{
p=St[top]; //取出当前的栈顶元素
if (p->rchild &&p->rchild!=r) //右子树不存在或已被访问,访问之
{ p=p->rchild;
St[++top]=p;
p=p->lchild;
}
else //弹出节点并访问
{ printf("%c ",St[top]->data);
top--;
r=p; //r指向则被访问的节点
p=NULL;
}
}
}
}
void AllPath1(BTNode *b)
{ //后序遍历非递归算法输出每个叶子结点到根结点的路径序列
BTNode *St[MaxSize];
int top=-1; //栈指针置初值
BTNode *p=b;
BTNode *r=NULL;
while (p||top>-1)
{
if(p) //扫描结点p的所有左下结点并进栈
{ St[++top]=p; //结点p进栈
p=p->lchild; //移动到左孩子
}
else
{
p=St[top]; //取出当前的栈顶元素
if (p->rchild &&p->rchild!=r) //右子树不存在或已被访问,访问之
{ p=p->rchild;
St[++top]=p;
p=p->lchild;
}
else //弹出节点并访问
{ if (p->lchild==NULL && p->rchild==NULL) //若为叶子
{ //输出栈中所有结点值
for (int i=top;i>0;i--)
printf("%c->",St[i]->data);
printf("%c\n",St[0]->data);
}
top--;
r=p; //r指向则被访问的节点
p=NULL;
}
}
}
}
void Allpath2(BTNode *b,ElemType path[],int pathlen)
{ //先序遍历方法输出每个叶子结点到根结点的路径序列
if(b!=NULL)
{ if (b->lchild==NULL && b->rchild==NULL) //b为叶子
{ //输出栈中所有结点值
printf("%c->",b->data);
for (int i=pathlen-1;i>0;i--)
printf("%c->",path[i]);
printf("%c\n",path[0]);
}
else
{ path[pathlen++]=b->data;
Allpath2(b->lchild, path, pathlen);
Allpath2(b->rchild, path, pathlen);
}
}
}
void MaxPath(BTNode *b,ElemType path[],int pathlen,ElemType maxpath[],int &maxpathlen)
{ //先序遍历方法输出一条最长路径
if(b==NULL)//pathlen和maxpathlen的初值均为0
{ if(pathlen>maxpathlen) //通过比较求最长路径
{ for(int i=pathlen-1;i>=0;i--)
maxpath[i]=path[i];
maxpathlen=pathlen;
}
}
else
{ path[pathlen]=b->data; //将当前节点放入路径中
pathlen++; //路径长度增1
MaxPath(b->lchild,path,pathlen,maxpath,maxpathlen);
//递归扫描左子树
MaxPath(b->rchild,path,pathlen,maxpath,maxpathlen);
//递归扫描右子树
}
}
int main()
{
BTNode *b;
CreateBTree(b,"A(B(D,E(H(J,K(L,M(,N))))),C(F,G(,I)))");
printf("二叉树b:");DispBTree(b);printf("\n");
printf("后序遍历序列:\n");
printf(" 递归算法:");PostOrder(b);printf("\n");
printf(" 非递归算法:");PostOrder1(b);printf("\n");
printf("Allpath1:\n");AllPath1(b);printf("\n");
ElemType path[MaxSize],maxpath[MaxSize];
int maxpathlen =0;
printf("Allpath2:\n"); Allpath2(b,path,0);
printf("Maxpath:\n");
MaxPath(b,path,0,maxpath,maxpathlen);
for(int i=0;i<maxpathlen-1;i++)
printf("%c->",maxpath[i]);
printf("%c\n",maxpath[maxpathlen-1]);
DestroyBTree(b);
}
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