先序扩展序列建立二叉树（后序扩展序列建立二叉树）-优快云博客

本文链接：https://blog.youkuaiyun.com/qq_25837497/article/details/80464035

题目：设计并验证如下算法：按后序序列建立二叉树的二叉链表结构，求其单分支结点数目，双分支结点数目，并交换该二叉树。

后序序列建立二叉树需要借助栈，栈的定义如下stack.h

#include<stdio.h>
#include<stdlib.h>
#include<conio.h>

#define TRUE	1
#define FALSE	0
#define ERROR	0
#define OK		1
#define STACK_INIT_SIZE		100
#define STACKINCREMENT		10

typedef int Status;

typedef struct {
	SElemType *base;
	SElemType *top;
	int stacksize;
}SqStack;

Status InitStack(SqStack *);
Status DestroyStack(SqStack *);
Status StackEmpty(SqStack);
SElemType GetTop(SqStack );
Status Push(SqStack *,SElemType );
SElemType Pop(SqStack *);

Status InitStack(SqStack *S) {
	S->base = (SElemType *)malloc(STACK_INIT_SIZE * sizeof(SElemType));
	S->top = S->base;
	S->stacksize = STACK_INIT_SIZE;
	return OK;
}

Status DestroyStack(SqStack *S) {
	if(S->base) 
		free(S->base);
	S->top = S->base = NULL;
	return OK;
}

Status StackEmpty(SqStack S) {
	if(S.top == S.base) 
		return TRUE;
	else
		return FALSE;
}

SElemType GetTop(SqStack S) {
	SElemType e;
	if(S.top == S.base)
		return ERROR;
	e = *(S.top-1);
	return e;
}

Status Push(SqStack *S,SElemType e) {
	if(S->top - S->base >= S->stacksize) {
		S->base = (SElemType *)realloc(S->base, (S->stacksize + STACKINCREMENT) * sizeof(SElemType));
		S->top = S->base + S->stacksize;
		S->stacksize += STACKINCREMENT;
	}
	*S->top++ = e;
	return OK;
}

SElemType Pop(SqStack *S) {
	SElemType e;
	if(S->top == S->base)
		return ERROR;
	e = *(--S->top);
	return e;
}

程序代码如下：

/*
 *FileName    ：PostCreatTree
 *CopyRight    ：Dengguang
*/

#include<stdio.h>
#include<stdlib.h>
#include<conio.h>
#include<string.h>

#define OK		1
#define ERROR	0

typedef int Status;
typedef char TElemType;
typedef struct BiTNode {
	TElemType data;
	struct BiTNode *lchild, *rchild;
}BiTNode, *BiTree;

typedef char SElemType;

#include"stack.h"
SqStack S; 

Status InitBiTree(BiTree *);
BiTree PreCreateBiTree(BiTree *);		//先序扩展序列递归建树 
BiTree PostCreateBiTree(BiTree *);		//后序扩展序列建树准备工作 
BiTree PostCreateBiTree2(BiTree *);		//后序扩展序列递归建树
Status PreOrder(BiTree );
Status InOrder(BiTree );
Status PostOrder(BiTree );
Status Exchange(BiTree );				//交换该树 
int SingleNodesNumber(BiTree );			//单分支结点 
int DoubleNodesNumber(BiTree );			//双分支结点 

int main() {
	BiTree BT;
	TElemType ch;
	int flag = 1, select = 0;
	InitStack(&S);
	InitBiTree(&BT);
	
	printf("\t*\tPlease select:                             *\n");
	printf("\t*\t1.PreOrder Create with '#'                 *\n");
	printf("\t*\t2.PostOrder Create with '#'                *\n");
	while(1) {
		scanf("%d", &select);
		printf(" Please input:");
		if(select == 1) {
			BT = PreCreateBiTree(&BT);break;
		}
		else if(select == 2) {	
			BT = PostCreateBiTree(&BT);break;
		}
	}
	printf("Create BiTree successfully!\n\n");

	while(flag) {
		printf("\t*\tPlease select:                             *\n");
		printf("\t*\t1.PreOrder Traversal                       *\n");
		printf("\t*\t2.InOrder Traversal                        *\n");
		printf("\t*\t3.PostOrder Traversal                      *\n");
		printf("\t*\t4.Single Nodes Number                      *\n");
		printf("\t*\t5.Double Nodes Number                      *\n");
		printf("\t*\t6.Exchange the left and right nodes        *\n");
		printf("\t*\t7.Exit                                     *\n");
		
		scanf("%d", &select);
		switch(select) {
			case 1:printf("\n The PreOrder Traversal of Binary Tree is: ");
					PreOrder(BT); break;
			case 2:printf("\n The InOrder Traversal of Binary Tree is: ");
					InOrder(BT); break;
			case 3:printf("\n The PostOrder Traversal of Binary Tree is: ");
					PostOrder(BT); break;
			case 4:printf("\n The Number of Single Nodes is %d", SingleNodesNumber(BT));
					break;
			case 5:printf("\n The Number of Double Nodes is %d", DoubleNodesNumber(BT));
					break;
			case 6:Exchange(BT);printf("\n Exchange over!");
					break;
			default:flag = 0;
					printf("Press any key to exit!\n");
					getch();
		}
		printf("\n"); 
	}
	return 0;
} 

Status InitBiTree(BiTree *BT) {
	*BT = NULL;
}

//先序扩展序列递归建树 
BiTree PreCreateBiTree(BiTree *BT) {
	TElemType ch;
	scanf("%c", &ch);
	
	if(ch == '#') {
		*BT = NULL;
		return *BT;
	}
	else {
		*BT = (BiTNode *)malloc(sizeof(BiTNode));
		(*BT)->data = ch;
		(*BT)->lchild = PreCreateBiTree(&((*BT)->lchild));
		(*BT)->rchild = PreCreateBiTree(&((*BT)->rchild));
	}
	
	return *BT;
}

//后序扩展序列建树准备工作，接收字符入栈 
BiTree PostCreateBiTree(BiTree *BT) {
	TElemType ch;
	scanf("%c", &ch);
	Push(&S, ch); 
	
	while(1) {
		scanf("%c", &ch);
		if(ch == '\n')
			break;
		
		Push(&S, ch); 
	}
	*BT = PostCreateBiTree2(&(*BT));
	return *BT;
}

//后序扩展序列递归建树
BiTree PostCreateBiTree2(BiTree *BT) {
	TElemType ch;
	ch = Pop(&S); 
	if(ch == '#') {
		*BT = NULL;
		return *BT;
	}
	else {
		*BT = (BiTNode *)malloc(sizeof(BiTNode));
		(*BT)->data = ch;	
		(*BT)->rchild = PostCreateBiTree2(&((*BT)->rchild));
		(*BT)->lchild = PostCreateBiTree2(&((*BT)->lchild));
	}
	
	return *BT;
}

Status PreOrder(BiTree BT) {
	if(BT) {
		if(!(BT->data))
			return ERROR;
		printf("%c ", BT->data);
		PreOrder(BT->lchild);
		PreOrder(BT->rchild);
		return OK; 
	}
}

Status InOrder(BiTree BT) {
	if(BT) {
		if(!(BT->data))
			return ERROR;
		InOrder(BT->lchild);
		printf("%c ", BT->data);
		InOrder(BT->rchild);
		return OK; 
	}
}

Status PostOrder(BiTree BT) {
	if(BT) {
		if(!(BT->data))
			return ERROR;
		PostOrder(BT->lchild);
		PostOrder(BT->rchild);
		printf("%c ", BT->data);
		return OK; 
	}
}

//交换该树 
Status Exchange(BiTree BT) {
	if(BT) {
		BiTree temp;
		temp = BT->lchild;
		BT->lchild = BT->rchild;
		BT->rchild = temp;
		Exchange(BT->lchild);
		Exchange(BT->rchild);
	}
}

//单分支结点
int SingleNodesNumber(BiTree BT) {
	if(!BT)
		return 0;
	else {
		int s1=0, s2=0;
		s1 = SingleNodesNumber(BT->lchild);
		s2 = SingleNodesNumber(BT->rchild);
		if((BT->lchild && !BT->rchild) || (BT->rchild && !BT->lchild)) {
		 	printf("%c\t", BT->data); 
			return s1 + s2 + 1;
		} 
		else
			return s1 + s2;
	}
}

//双分支结点
int DoubleNodesNumber(BiTree BT) {
	if(!BT)
		return 0;
	else {
		int n = 0;
		if(BT->lchild && BT->rchild)
			n = 1;
		
		int d1 = DoubleNodesNumber(BT->lchild);
		int d2 = DoubleNodesNumber(BT->rchild);
		if(n == 1) {
			printf("%c\t", BT->data); 
			return d1 + d2 + 1;
		}
		else
			return d1 + d2;
	}
}

测试结果：

        *       Please select:                             *
        *       1.PreOrder Create with '#'                 *
        *       2.PostOrder Create with '#'                *
2
 Please input:###12###3##4567##89
Create BiTree successfully!

        *       Please select:                             *
        *       1.PreOrder Traversal                       *
        *       2.InOrder Traversal                        *
        *       3.PostOrder Traversal                      *
        *       4.Single Nodes Number                      *
        *       5.Double Nodes Number                      *
        *       6.Exchange the left and right nodes        *
        *       7.Exit                                     *
1
 The PreOrder Traversal of Binary Tree is: 9 7 2 1 6 5 3 4 8

2
 The InOrder Traversal of Binary Tree is: 2 1 7 6 3 5 4 9 8

3
 The PostOrder Traversal of Binary Tree is: 1 2 3 4 5 6 7 8 9

4
2       6
 The Number of Single Nodes is 2

5
5       7       9
 The Number of Double Nodes is 3