关于普通二叉树的创建、递归遍历、利用栈遍历、队列的层次遍历、节点、叶子个数,深度综合训练

这篇博客详细介绍了如何创建二叉树,并通过递归和栈、队列实现二叉树的先序、中序、后序遍历。同时,提供了计算节点数量、叶子节点个数以及树的深度的方法。此外,还展示了使用栈实现的二叉树遍历以及层次遍历的方法。

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//.h
#ifndef _BINARYTREE_
#define _BINARYTREE_
#include"stdio.h"
#include"malloc.h"
typedef char datatype;
const int Maxsize = 1000;
typedef struct node
{
	datatype data;
	struct node* left;
	struct node* right;

}Node, *pTree;
typedef pTree ElementType;
pTree create()
{
	pTree t;
	datatype ch;
	//printf("Enter:  ");
	ch = getchar();
	if (ch == '?')
	{
		t = NULL;
		return t;
	}
	else
	{
		t = (pTree)malloc(sizeof(Node));
		t->data = ch;
		//t->left = NULL;
		//t->right = NULL;
		t->left = create();

		t->right = create();
	}
	return t;
}
void preorder(pTree t)
{
	if (t)
	{
		printf("%c", t->data);
		preorder(t->left);
		preorder(t->right);
	}
	//printf("\n");

}
void inorder(pTree t)
{
	if (t)
	{
		inorder(t->left);
		printf("%c", t->data);
		inorder(t->right);
	}
	//printf("\n");

}
void postorder(pTree t)
{
	if (t)
	{
		postorder(t->left);
		postorder(t->right);
		printf("%c", t->data);

	}
	//printf("\n");

}

static int jcount = 0;
static int ycount = 0;
static int dcount = 0;
int NodeCount(pTree t)
{

	if (t)
	{
		jcount++;
		if (!t->left && !t->right)
			ycount++;
		NodeCount(t->left);
		NodeCount(t->right);
	}
	return ycount;


}
int depth(pTree t)
{
	int deep = 0;
	if (t)
	{
		int ldepth = depth(t->left);
		int rdepth = depth(t->right);
		deep = (ldepth >= rdepth ? ldepth + 1 : rdepth + 1);
	}
	return deep;

}

//------------------------------------创建栈-----------------------
//typedef pTree ElementType
typedef struct
{
	ElementType Data[Maxsize];
	int top;
}stack,*pStack;
stack* creat_stack()
{
	stack* s = (stack*)malloc(sizeof(stack));
	s->top = -1;
	return s;
}
//进栈
void Push(stack* pTrs, ElementType item)
{
	if (pTrs->top == Maxsize - 1)//判断栈是否满
	{
		printf("堆栈满");
		//return;

	}
	else
	{
		pTrs->Data[++(pTrs->top)] = item;
		//return;

	}

}
//出栈
//typedef pTree ElementType
ElementType Pop(stack* pTrs)
{
	//出栈的时候如果栈为空,返回nullptr
	if (pTrs->top == -1)
	{
		//printf("\n堆栈空\n");
		//pTree p = NULL;
		return NULL;

	}
	else
	{

		return (pTrs->Data[(pTrs->top)--]);

	}
}
//判断栈是否为空
bool Empty_stack(pStack s)
{
	return (s->top == -1);
}

//------------------------用栈实现二叉树的三种遍历--------------------------------
void sPreOrder(pTree t)//先序
{
	/*
	先序遍历
  ->1.打印左节点
	2.节点入栈
	3.访问下一个左节点,存在入栈
	4.如果左节点下一个节点为空,使栈最上面的节点出栈并访问右节点
	5.->1
	*/
	pStack s;
	pTree p = t;
	s = creat_stack();
	while (p || !Empty_stack(s))
	{
		if (p)
		{
			printf("%c", p->data);
			Push(s, p);
			p = p->left;
		}
		else
		{
			p = Pop(s);
			p = p->right;

		}
	}

}
void sInOrder(pTree t)
{
	/*
	中序遍历
  ->1.节点入栈,如果节点地左节点不为空 循环执行 step 1
	2.左节点为空,使栈最上面节点出栈并访问当前节点的右节点
	3.->1
	*/
	pStack s;
	pTree p = t;
	s = creat_stack();
	while (p || !Empty_stack(s))
	{
		if (p)
		{
			//printf("%c", p->data);
			Push(s, p);
			p = p->left;
		}
		else
		{
			p = Pop(s);
			printf("%c", p->data);
			p = p->right;

		}
	}

}
void sPostOrder(pTree t)
{
	/*
	后序遍历
	1.建立两个栈
	由于后序遍历先访问左节点再访问右节点,所以入栈地时候先入右节点再入左节点
    2.节点入栈,如果节点地右节点不为空 循环执行 step 1
	3.右节点为空,使栈最上面节点出栈并访问当前节点的左节点
	4.->1
	*/
	pStack s1;
	pStack s2;
	pTree p = t;
	s1 = creat_stack();
	s2 = creat_stack();
	while (p || !Empty_stack(s2)) //树为空且栈为空,退出函数.
	{
		if (p)
		{
			//printf("%c", p->data);
			Push(s1, p);
			Push(s2, p);
			p = p->right;
		}
		else
		{
			p = Pop(s2);
			//printf("%c", p->data);
			p = p->left;

		}
	}
	while (!Empty_stack(s1))
	{
		p = Pop(s1);
		printf("%c", p->data);
	}

}
//-------------------------创建队列-------------------------
typedef struct
{
	ElementType data[Maxsize];
	int front, rear;

}SeqQueue, *pSeqQueue;
pSeqQueue creat_queue()
{
	pSeqQueue Q = (pSeqQueue)malloc(sizeof(SeqQueue));
	if (Q)
	{
		Q->front = -1;
		Q->rear = -1;
	}
	return Q;
}
//判断队列是否为空
bool Empty_Queue(pSeqQueue q)
{
	return (q->front == ((q->rear + 1) % Maxsize));
}
//入队列
void Qpush(pSeqQueue q, ElementType n)
{
	if ((q->rear + 1) % Maxsize == q->front)
	{
		printf("队列满");
		//return -1;
	}
	else
	{
		q->rear = (q->rear + 1) % Maxsize;
		q->data[q->rear] = n;
		//return 1;
	}

}
//出队列
ElementType Qpop(pSeqQueue q)
{
	if (q && q->front == q->rear)
	{
		//printf("队列空");
		//return 1;
		//exit(0);
		return nullptr;

	}
	else
	{
		q->front = (q->front + 1) % Maxsize;
		return q->data[q->front];
	}
}
//层次遍历
void Printlevel(pTree t)
{
	pTree temp = t;
	pSeqQueue q;
	q = creat_queue();
	if (t == NULL)
	{
		printf("根节点为空");      //根节点为空,返回-1
	}
	else
	{
		Qpush(q, temp);           //根节点(非指针)入队
	}
	while (!Empty_Queue(q))                   //队列不为空
	{
		temp = Qpop(q);   //指针出队//输出出队元素
		if (temp)
		printf("%c", temp->data);
		else
		break;
		
		if (temp->left)             //左子树不为空
		{
			Qpush(q, temp->left);//左子树入队
		}
		if (temp->right)             //右子树不为空
		{
			Qpush(q, temp->right);//右子树入队
		}
	}
}

#endif

//.cpp
#include"BinaryTree.h"
#include"stdio.h"
int main()
{
	pTree t;
	t = create();
	NodeCount(t);
	int deep = depth(t);
	printf("结点个数: %d 叶子结点个数: %d 深度: %d \n", jcount, ycount, deep);
	int i = 1;
	printf("1 for preorder | 2 for inorder | 3 for postorder | 4 for levelorder\n");
	while (i)
	{
		scanf_s("%d", &i);
		//int count2 = NodeCount(t);

		switch (i)
		{
		case 1:
			//preorder(t);
			printf("Pre-Order: ");
			sPreOrder(t);
			printf("\n");
			break;
		case 2:
			//inorder(t);
			printf("In-Order: ");
			sInOrder(t);
			printf("\n");
			break;
		case 3:
			//postorder(t);
			printf("Post-Order: ");
			sPostOrder(t);
			printf("\n");
			break;
		case 4:
			printf("Level-Order: ");
			Printlevel(t);
			printf("\n");
			break;
		}
	}
	return 0;
}

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