[数据结构]二叉树的建立与遍历(递归)

news2024/9/27 23:35:07

一、二叉树的遍历与建立

首先我们拥有如下二叉树:

要了解二叉树遍历,我们得先了解二叉树的三种遍历方式:前序遍历,中序遍历,后序遍历

1.前序遍历

前序遍历:根,左子树,右子树

遍历的结果就是:1 2 4 8 N N 9 N N 5 10 N N 11 N N 3 6 N N 7 N N

2.中序遍历

中序遍历:左子树根右子树

遍历的结果:N 8 N 4 N 9 N 2 N 10 N 5 N 11 N N 6 N 5 N 7 N

3.后序遍历

后续遍历:左子树右子树根

遍历的结果:N N 8 N N 9 4 N N 10 N N 11 5 2 N N 6 N N 7 3 1

注意:N是NULL(即不存在次节点)

4.手撕一棵二叉树

那么我们如何用代码实现这样的遍历并打印,我们先可以写一个二叉树

typedef struct BinTreeNode
{
	struct BinTreeNode* left;
	struct BinTreeNode* right;
	int val;
}BTNode;

然后我们创建相应的节点:

BTNode* BuyBTNode(int val)
{
	BTNode* newnode = (BTNode*)malloc(sizeof(BTNode));
	if (newnode == NULL)
	{
		perror("malloc fail");
		return NULL;
	}
	newnode->val = val;
	newnode->left = NULL;
	newnode->right = NULL;
	return newnode;
}

然后我们手撕一棵二叉树

BTNode* CreateTree()
{
	BTNode* n1 = BuyBTNode(1);
	BTNode* n2 = BuyBTNode(2);
	BTNode* n3 = BuyBTNode(3);
	BTNode* n4 = BuyBTNode(4);
	BTNode* n5 = BuyBTNode(5);
	BTNode* n6 = BuyBTNode(6);

	n1->left = n2;
	n1->right = n4;
	n2->left = n3;
	n4->left = n5;
	n4->right = n6;

	return n1;
}

这样们就创建好一个二叉树了,接下来我们来写如何遍历吧!

5.用函数来完成遍历

1)前序遍历:

void PreOrder(BTNode* root)
{
	if (root == NULL)
	{
		printf("N ");
		return;
	}

	printf("%d ", root->val);
	PreOrder(root->left);
	PreOrder(root->right);
}

按照根左子树右子树打印如果不为空就继续递归打印根数据然后左子树最后右子树如果为空就打印N然后返回

2)中序遍历

按照左子树根右子树大体思路如上

void InOrder(BTNode* root)
{
	if (root == NULL)
	{
		printf("N ");
		return;
	}

	InOrder(root->left);
	printf("%d ", root->val);
	InOrder(root->right);
}

3)后序遍历

按照:左子树右子树根

void PostOrder(BTNode* root);
{
	if (root == NULL)
	{
		printf("N ");
		return;
	}

	PostOrder(root->left);
	PostOrder(root->right);
	printf("%d ", root->val);
}

下面我们来进行一下测试:

首先二叉树如图,我们不然得到

前序遍历:1 2 3 N N N 4 5 N N 6 N N

中序遍历:N 3 N 2 N 1 N 5 N 4 N 6 N

后序遍历:N N 3 N 2 N N 5 N N 6 4 2

我们把上面的代码整合一下

#include<stdio.h>
#include<stdlib.h>
typedef struct BinTreeNode
{
	struct BinTreeNode* left;
	struct BinTreeNode* right;
	int val;
}BTNode;
BTNode* BuyBTNode(int val)
{
	BTNode* newnode = (BTNode*)malloc(sizeof(BTNode));
	if (newnode == NULL)
	{
		perror("malloc fail");
		return NULL;
	}
	newnode->val = val;
	newnode->left = NULL;
	newnode->right = NULL;
	return newnode;
}
BTNode* CreateTree()
{
	BTNode* n1 = BuyBTNode(1);
	BTNode* n2 = BuyBTNode(2);
	BTNode* n3 = BuyBTNode(3);
	BTNode* n4 = BuyBTNode(4);
	BTNode* n5 = BuyBTNode(5);
	BTNode* n6 = BuyBTNode(6);

	n1->left = n2;
	n1->right = n4;
	n2->left = n3;
	n4->left = n5;
	n4->right = n6;

	return n1;
}
void PreOrder(BTNode* root)
{
	if (root == NULL)
	{
		printf("N ");
		return;
	}

	printf("%d ", root->val);
	PreOrder(root->left);
	PreOrder(root->right);
}

void InOrder(BTNode* root)
{
	if (root == NULL)
	{
		printf("N ");
		return;
	}

	InOrder(root->left);
	printf("%d ", root->val);
	InOrder(root->right);
}
void PostOrder(BTNode* root)
{
	if (root == NULL)
	{
		printf("N ");
		return;
	}

	PostOrder(root->left);
	PostOrder(root->right);
	printf("%d ", root->val);
}



int main()
{
	BTNode* root = CreateTree();
	printf("前序遍历:");
	PreOrder(root);
	printf("\n");

	printf("中序遍历:");
	InOrder(root);
	printf("\n");

	printf("后序遍历:");
	PostOrder(root);
	printf("\n");

	return 0;
}

运行结果: