二叉树的练习-Toy模板网

这篇具有很好参考价值的文章主要介绍了二叉树的练习。希望对大家有所帮助。如果存在错误或未考虑完全的地方，请大家不吝赐教，您也可以点击"举报违法"按钮提交疑问。

单值二叉树

单值二叉树，可以使用等式的传递性来解决，根的值和左右子树的值相比较，看是否相等。再比较左右子树。递归求出是否为单值二叉树。
代码如下：

bool isUnivalTree(struct TreeNode* root){
    if(root == NULL)
    {
        return true;
    }
    if(root->left&&root->left->val!=root->val)
    {
        return false;
    }
    if(root->right&&root->right->val!=root->val)
    {
        return false;
    }
    return isUnivalTree(root->left)&&isUnivalTree(root->right);
}

检查两颗树是否相同

先比比较根，在比较左右子树。

bool isSameTree(struct TreeNode* p, struct TreeNode* q){
    if(p==NULL&&q==NULL)
    {
        return true;
    }
    if(p==NULL||q==NULL)
    {
        return false;
    }
    if(p->val!=q->val)
    {
        return false;
    }
    return isSameTree(p->left,q->left) && isSameTree(p->right,q->right);
}

对称二叉树

先比较根的左右子树的根。在比较左子树的左和右子树的右，左子树的右和右子树的左

bool _isSymmetric(struct TreeNode* RootLeft,struct TreeNode* RootRight)
{
    if(RootLeft == NULL&&RootRight == NULL)
    {
        return true;
    }
    if(RootLeft == NULL ||RootRight == NULL)
    {
        return false;
    }
    if(RootLeft->val != RootRight ->val)
    {
        return false;
    }
    return _isSymmetric(RootLeft->left,RootRight->right) && 
    _isSymmetric(RootLeft->right,RootRight->left);
}
bool isSymmetric(struct TreeNode* root){
    return _isSymmetric(root->left,root->right);
}

二叉树的前序遍历

前序遍历到数组中，注意下标的传值要使用传址调用

int BTreeSize(struct TreeNode* root)
{
  if(root == NULL)
  {
    return 0;
  }
  int lcount = BTreeSize(root->left);
  int rcount = BTreeSize(root-> right);
  return lcount + rcount + 1;
  
}
void _preorderTraversal(struct TreeNode* root,int* a,int* i)
{
  if(root==NULL)
  {
    return;
  }
  a[(*i)++] = root->val;
  _preorderTraversal(root->left,a,i);
  _preorderTraversal(root->right,a,i);
}
int* preorderTraversal(struct TreeNode* root, int* returnSize){
    *returnSize = BTreeSize(root);
    //malloc一个数组
    int* a = (int*)malloc(sizeof(int)*(*returnSize));
    //执行前序遍历
    //下标
    int i  = 0;
    _preorderTraversal(root,a,&i);
    return a;
}

二叉树的中序遍历

调换这几条语句的顺序
a[(*i)++] = root->val; _preorderTraversal(root->left,a,i); _preorderTraversal(root->right,a,i);
函数名要保证和对应的遍历相同

 int BTreeSize(struct TreeNode* root)
{
  if(root == NULL)
  {
    return 0;
  }
  int lcount = BTreeSize(root->left);
  int rcount = BTreeSize(root-> right);
  return lcount + rcount + 1;
  
}
void _inorderTraversal(struct TreeNode* root,int* a,int* i)
{
  if(root==NULL)
  {
    return;
  }
 
  _inorderTraversal(root->left,a,i);
   a[(*i)++] = root->val;
  _inorderTraversal(root->right,a,i);
}
int* inorderTraversal(struct TreeNode* root, int* returnSize){
    *returnSize = BTreeSize(root);
    //malloc一个数组
    int* a = (int*)malloc(sizeof(int)*(*returnSize));
    //执行前序遍历
    //下标
    int i  = 0;
    _inorderTraversal(root,a,&i);
    return a;  
}

二叉树的后序遍历

与上题相同

  int BTreeSize(struct TreeNode* root)
{
  if(root == NULL)
  {
    return 0;
  }
  int lcount = BTreeSize(root->left);
  int rcount = BTreeSize(root-> right);
  return lcount + rcount + 1;
  
}
void _postorderTraversal(struct TreeNode* root,int* a,int* i)
{
  if(root==NULL)
  {
    return;
  }
 
  _postorderTraversal(root->left,a,i);
  _postorderTraversal(root->right,a,i);
   a[(*i)++] = root->val;
}
int* postorderTraversal(struct TreeNode* root, int* returnSize){
     *returnSize = BTreeSize(root);
    //malloc一个数组
    int* a = (int*)malloc(sizeof(int)*(*returnSize));
    //执行前序遍历
    //下标
    int i  = 0;
    _postorderTraversal(root,a,&i);
    return a;  
}

另一颗树的子树

二叉树的练习

bool isSameTree(struct TreeNode* p, struct TreeNode* q){
    if(p==NULL&&q==NULL)
    {
        return true;
    }
    if(p==NULL||q==NULL)
    {
        return false;
    }
    if(p->val!=q->val)
    {
        return false;
    }
    return isSameTree(p->left,q->left) && isSameTree(p->right,q->right);
}
bool isSubtree(struct TreeNode* root, struct TreeNode* subRoot){
    if(root == NULL)
    {
        return false;
    }
    if(isSameTree(root,subRoot))
    {
        return true;
    }
    
    return isSubtree(root->left,subRoot) || isSubtree(root->right,subRoot);
}

通过前序遍历的数组构建二叉树

#include <stdio.h>
#include <stdlib.h>
typedef struct BTNode
{
	char data;
	struct BTNode* left;
	struct BTNode* right;
}BTNode;

BTNode* BuyNode(char x)
{
	BTNode* newnode = (BTNode*)malloc(sizeof(BTNode));
	if (newnode == NULL)
	{
		perror("malloc failed!\n");
		return NULL;
	}
	newnode->data = x;
	newnode->left = NULL;
	newnode->right = NULL;
	return newnode;
}
BTNode* BinaryTreeCreate(char* a,int* pi)
{
    if(a[*pi] == '#')
    {
        (*pi)++;
        return NULL;
    }
	//创建根节点
	BTNode* root = BuyNode(a[*pi]);
	(*pi)++;
	root->left = BinaryTreeCreate(a,pi);
	root->right = BinaryTreeCreate(a,pi);
	return root;
}
void InOrder(BTNode* root)
{
    if(root==NULL)
    {
        return;
    }
    InOrder(root->left);
    printf("%c ",root->data);
    InOrder(root->right);
}
int main() {
    int* a = (int*)malloc(sizeof(int)*100);
	scanf("%s",a);
	int pi = 0;
	BTNode* root = BinaryTreeCreate(a,&pi);
	InOrder(root);
}

判断二叉树是否是完全二叉树

二叉树的练习

//判断是否为完全二叉树
bool BTreeComplete(BT* root)
{
	//新建一个队列
	Que q;
	QueueInit(&q);
	//把root入队列
	QueuePush(&q, root);
	//队列不为空时继续遍历
	while (!QueueEmpty(&q))
	{
		//出队列
		BT* front = QueueFront(&q);
		QueuePop(&q);
		if (front == NULL)
		{
			break;
		}
		//带入左右子树
		QueuePush(&q, front->left);
		QueuePush(&q, front->right);
	}
	while (!QueueEmpty(&q))
	{
		BT* front = QueueFront(&q);
		QueuePop(&q);
		if (front != NULL)   //遇到不为空证明不是完全二叉树
		{
			QueueDestory(&q);
			return false;
		}
	}
	QueueDestory(&q);
	return true;  //程序执行到这一步时，证明为完全二叉树
}

层序遍历

二叉树的练习

//二叉树的层序遍历
void LevelOrder(BT* root)
{
	//新建一个队列
	Que q;
	QueueInit(&q);
	//把root入队列
	QueuePush(&q, root);
	//队列不为空时继续遍历
	while (!QueueEmpty(&q))
	{
		//出队列
		BT* front = QueueFront(&q);
		QueuePop(&q);
		printf("%d ", front->data);
		//带入左右子树
		if (front->left)
		{
			QueuePush(&q, front->left);
		}
		if (front->right)
		{
			QueuePush(&q, front->right);
		}
	}
	QueueDestory(&q);
}

k层节点数

// 二叉树第k层节点个数
int BTreeLevelKSize(BT* root, int k)
{
	assert(k > 0);
	if (root == NULL)
	{
		return 0;
	}
	if (k == 1)
	{
		return 1; 
	}
	int left = BTreeLevelKSize(root->left, k - 1);
	int right = BTreeLevelKSize(root->right, k - 1);
	return left + right;
}

二叉树的销毁

递归展开图
二叉树的练习文章来源地址https://www.toymoban.com/news/detail-514468.html

void BTDestory(BT* root)
{
	if (root == NULL)
	{
		return;
	}
	//先销毁左树，然后销毁右树，然后再销毁根
	BTDestory(root->left);
	BTDestory(root->right);
	free(root);
}

二叉树的整体

#include "Tree.h"
#include "Queue.h"
int BTreeLeafSize(BT* root)
{
	if (root == NULL)
	{
		return 0;
	}
	if (root->left == NULL && root->right == NULL)
	{
		return 1;
	}
	return BTreeLeafSize(root->left) + BTreeLeafSize(root->right);
	
}
int BTreeSize(BT* root)
{
	if (root == NULL)
	{
		return 0;
	}
	int lcount = BTreeSize(root->left);
	int rcount = BTreeSize(root->right);
	return lcount + rcount + 1;
}
int BTreeHeight(BT* root)
{
	if (root == NULL)
	{
		return 0;
	}
	int leftheight = BTreeHeight(root->left);
	int rightheight = BTreeHeight(root->right);
	//return leftheight > rightheight ? leftheight + 1: rightheight + 1;0
	return 1 + (leftheight > rightheight ? leftheight : rightheight);
}

BT* BTreeFind(BT* root, BTDataType x)
{
	if (root == NULL)
	{
		return NULL;
	}
	if (root->data == x)
	{
		return root;
	}
	BT* left = BTreeFind(root->left, x);
	if (left)
	{
		return left;
	}
	BT* right = BTreeFind(root->right, x);
	if (right)
	{
		return right;
	}
	return NULL;
}

BT* BuyNode(BTDataType x)
{
	BT* node = (BT*)malloc(sizeof(BT));
	if (node == NULL)
	{
		perror("malloc failed!\n");
		return NULL;
	}
	node->data = x;
	node->left = NULL;
	node->right = NULL;
	return node;
}
BT* BTCreate()
{
	BT* node1 = BuyNode(1);
	BT* node2 = BuyNode(2);
	BT* node3 = BuyNode(3);
	BT* node4= BuyNode(4);
	BT* node5= BuyNode(5);
	BT* node6 = BuyNode(6);
	//BT* node7 = BuyNode(7);


	node1->left = node2;
	node1->right = node4;
	node2->left = node3;
	node4->left = node5;
	node4->right = node6;

	return node1;
}

//二叉树的遍历
//先序遍历
void Prevorder(BT* root)
{
	if (root == NULL)
	{
		printf("N ");
		return;
	}
	printf("%d ", root->data);
	Prevorder(root->left);
	Prevorder(root->right);
}
//中序遍历
void Inorder(BT* root)
{
	if (root == NULL)
	{
		printf("N ");
		return;
	}
	Inorder(root->left);
	printf("%d ", root->data);
	Inorder(root->right);
}
//后序遍历
void Postorder(BT* root)
{
	if (root == NULL)
	{
		printf("N ");
		return;
	}
	Postorder(root->left);
	Postorder(root->right);
	printf("%d ", root->data);
}

// 二叉树第k层节点个数
int BTreeLevelKSize(BT* root, int k)
{
	assert(k > 0);
	if (root == NULL)
	{
		return 0;
	}
	if (k == 1)
	{
		return 1; 
	}
	int left = BTreeLevelKSize(root->left, k - 1);
	int right = BTreeLevelKSize(root->right, k - 1);
	return left + right;
}
//二叉树的层序遍历
void LevelOrder(BT* root)
{
	//新建一个队列
	Que q;
	QueueInit(&q);
	//把root入队列
	QueuePush(&q, root);
	//队列不为空时继续遍历
	while (!QueueEmpty(&q))
	{
		//出队列
		BT* front = QueueFront(&q);
		QueuePop(&q);
		printf("%d ", front->data);
		//带入左右子树
		if (front->left)
		{
			QueuePush(&q, front->left);
		}
		if (front->right)
		{
			QueuePush(&q, front->right);
		}
	}
	QueueDestory(&q);
}

//判断是否为完全二叉树
bool BTreeComplete(BT* root)
{
	//新建一个队列
	Que q;
	QueueInit(&q);
	//把root入队列
	QueuePush(&q, root);
	//队列不为空时继续遍历
	while (!QueueEmpty(&q))
	{
		//出队列
		BT* front = QueueFront(&q);
		QueuePop(&q);
		if (front == NULL)
		{
			break;
		}
		//带入左右子树
		QueuePush(&q, front->left);
		QueuePush(&q, front->right);
	}
	while (!QueueEmpty(&q))
	{
		BT* front = QueueFront(&q);
		QueuePop(&q);
		if (front != NULL)   //遇到不为空证明不是完全二叉树
		{
			QueueDestory(&q);
			return false;
		}
	}
	QueueDestory(&q);
	return true;  //程序执行到这一步时，证明为完全二叉树
}
void BTDestory(BT* root)
{
	if (root == NULL)
	{
		return;
	}
	//先销毁左树，然后销毁右树，然后再销毁根
	BTDestory(root->left);
	BTDestory(root->right);
	free(root);
}