目录
1.二叉树前序遍历,中序遍历和后序的实现
#include<stdio.h>
#include<stdlib.h>
//快速构建一棵二叉树
typedef int DataType;
typedef struct TreeNode
{
struct TreeNode* left;
struct TreeNode* right;
DataType data;
}TreeNode;
//创建节点
TreeNode* BuyNode(DataType x)
{
TreeNode* newnode = (TreeNode*)malloc(sizeof(TreeNode));
if (newnode == NULL)
{
perror("malloc fail");
exit(-1);
}
newnode->data = x;
newnode->left = NULL;
newnode->right = NULL;
return newnode;
}
//快速构建一棵树
TreeNode* CreateBinaryTree()
{
TreeNode* n1 = BuyNode(1);
TreeNode* n2 = BuyNode(2);
TreeNode* n3 = BuyNode(3);
TreeNode* n4 = BuyNode(4);
TreeNode* n5 = BuyNode(5);
TreeNode* n6 = BuyNode(6);
n1->left = n2;
n1->right = n4;
n2->left = n3;
n2->right = NULL;
n3->left = NULL;
n3->right = NULL;
n4->left = n5;
n4->right = n6;
n5->left = NULL;
n5->right = NULL;
n6->left = NULL;
n6->right = NULL;
return n1;
}
//二叉树的前序遍历
TreeNode* PreOrder(TreeNode* root)
{
if (root == NULL)
{
printf("NULL ");
return;
}
printf("%d ", root->data);
PreOrder(root->left);
PreOrder(root->right);
}
int main()
{
TreeNode* root = CreateBinaryTree();
PreOrder(root);
return 0;
}
输出结果如下:
//二叉树的中序遍历
TreeNode* InOrder(TreeNode* root)
{
if (root == NULL)
{
printf("NULL ");
return;
}
InOrder(root->left);
printf("%d ", root->data);
InOrder(root->right);
}
//二叉树的后序遍历
TreeNode* PostOrder(TreeNode* root)
{
if (root == NULL)
{
printf("NULL ");
return;
}
PostOrder(root->left);
PostOrder(root->right);
printf("%d ", root->data);
}
2.层序遍历
// 队列的定义
typedef struct QueueNode
{
TreeNode* data;
struct QueueNode* next;
}QNode;
typedef struct Queue
{
QNode* head;
QNode* tail;
}Queue;
// 层序遍历
void BinaryTreeLevelOrder(TreeNode* root)
{
Queue q;
QueueInit(&q);
//根节点入队
if (root)
{
QueuePush(&q, root);
}
//队列不为空时
while (!QueueEmpty(&q))
{
//访问队头元素并出队
TreeNode* front = QueueFront(&q);
QueuePop(&q);
printf("%d", front->val);
//队头元素的孩子节点入队
if (front->left)
{
QueuePush(&q, front->left);
}
if (front->right)
{
QueuePush(&q, front->right);
}
}
printf("\n");
QueueDestroy(&q);
}
//队列初始化
void QueueInit(Queue* pq)
{
assert(pq);
pq->head = pq->tail = NULL;
}
//判断队列是否为空
bool QueueEmpty(Queue* pq)
{
assert(pq);
return pq->head == NULL && pq->tail == NULL;
}
//队列销毁
void QueueDestroy(Queue* pq)
{
assert(pq);
QNode* cur = pq->head;
while (cur)
{
QNode* del = cur;
cur = cur->next;
free(del);
}
pq->head = pq->tail = NULL;
}
//访问队头数据
TreeNode* QueueFront(Queue* pq)
{
assert(pq);
assert(!QueueEmpty(pq));
return pq->head->data;
}
//数据入队
void QueuePush(Queue* pq, TreeNode* x)
{
assert(pq);
QNode* newnode = (QNode*)malloc(sizeof(QNode));
if (newnode == NULL)
{
perror("malloc fail");
exit(-1);
}
else
{
newnode->data = x;
newnode->next = NULL;
}
//空队列时插入
if (pq->tail == NULL)
{
pq->head = pq->tail = newnode;
}
//非空队列时插入
else
{
pq->tail->next = newnode;//链接新元素
pq->tail = newnode;//更新队尾
}
}
//数据出队
void QueuePop(Queue* pq)
{
assert(pq);
//空队列不能进行出队操作
assert(!QueueEmpty(pq));
//队列中只有一个元素
if (pq->head->next == NULL)
{
free(pq->head);
pq->head = pq->tail = NULL;
}
else
{
QNode* del = pq->head;
pq->head = pq->head->next;
free(del);
del = NULL;
}
}
3.求二叉树中的节点个数
//求二叉树节点个数
int TreeSize(TreeNode* root)
{
int size = 0;
if (root == NULL)
{
return 0;
}
size++;
TreeSize(root->left);
TreeSize(root->right);
return size;
}
//求二叉树节点个数
int TreeSize(TreeNode* root)
{
static int size = 0;
if (root == NULL)
{
return 0;
}
size++;
TreeSize(root->left);
TreeSize(root->right);
return size;
}
正确的定义与调用
#include<stdio.h>
#include<stdlib.h>
int size = 0;
//快速构建一棵二叉树
typedef int DataType;
typedef struct TreeNode
{
struct TreeNode* left;
struct TreeNode* right;
DataType data;
}TreeNode;
//创建节点
TreeNode* BuyNode(DataType x)
{
TreeNode* newnode = (TreeNode*)malloc(sizeof(TreeNode));
if (newnode == NULL)
{
perror("malloc fail");
exit(-1);
}
newnode->data = x;
newnode->left = NULL;
newnode->right = NULL;
return newnode;
}
//快速构建一棵树
TreeNode* CreateBinaryTree()
{
TreeNode* n1 = BuyNode(1);
TreeNode* n2 = BuyNode(2);
TreeNode* n3 = BuyNode(3);
TreeNode* n4 = BuyNode(4);
TreeNode* n5 = BuyNode(5);
TreeNode* n6 = BuyNode(6);
n1->left = n2;
n1->right = n4;
n2->left = n3;
n2->right = NULL;
n3->left = NULL;
n3->right = NULL;
n4->left = n5;
n4->right = n6;
n5->left = NULL;
n5->right = NULL;
n6->left = NULL;
n6->right = NULL;
return n1;
}
//求二叉树节点个数
int TreeSize(TreeNode* root)
{
if (root == NULL)
{
return 0;
}
size++;
TreeSize(root->left);
TreeSize(root->right);
return size;
}
int main()
{
TreeNode* root = CreateBinaryTree();
printf("%d\n", TreeSize(root));
size = 0;//初始化size
printf("%d\n", TreeSize(root));
return 0;
}
int TreeSize(TreeNode* root)
{
return root == NULL ? 0 : TreeSize(root->left) + TreeSize(root->right) + 1;
}
4.求二叉树中的叶子节点个数
//二叉树叶子节点的个数
int TreeLeafSize(TreeNode* root)
{
if (root == NULL)
{
return 0;
}
if (root->left == NULL && root->right == NULL)
{
return 1;
}
return TreeLeafSize(root->left) + TreeLeafSize(root->right);
}
5.求二叉树的高度
//二叉树的高度
int TreeHeight(TreeNode* root)
{
if (root == NULL)
{
return 0;
}
int left = TreeHeight(root->left);
int right = TreeHeight(root->right);
return left > right ? left + 1 : right + 1;
}
6.求二叉树第k层节点个数
//二叉树第k层节点的个数
int TreeKLevel(TreeNode* root, int k)
{
assert(k > 0);
if (root == NULL)
{
return 0;
}
if (k == 1)
{
return 1;
}
k = k - 1;
return TreeKLevel(root->left, k) + TreeKLevel(root->right, k);
}
7.二叉树查找值为x的节点
//二叉树查找值为x的节点
TreeNode* TreeFind(TreeNode* root, int x)
{
if(root == NULL)
{
return NULL;
}
if (root->data == x)
{
return root;
}
//在左子树查找
TreeNode* ret = TreeFind(root->left, x);
if (ret)
{
return ret;
}
//左子树没找到,再在右子树查找
ret = TreeFind(root->right, x);
if (ret)
{
return ret;
}
//整棵树都没找到
return NULL;
}
8.单值二叉树
单值二叉树题目链接:. - 力扣(LeetCode)
bool isUnivalTree(struct TreeNode* root) {
if (root == NULL)
{
return true;
}
//有左右孩子
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);
}
9.二叉树最大深度
二叉树最大深度:. - 力扣(LeetCode)
int maxDepth(struct TreeNode* root) {
if(root == NULL)
{
return 0;
}
int leftmax = maxDepth(root->left);
int rightmax = maxDepth(root->right);
return leftmax > rightmax ? leftmax + 1 : rightmax + 1;
}
10.翻转二叉树
翻转二叉树题目链接:226. 翻转二叉树 - 力扣(LeetCode)
11. 检查两颗树是否相同
检查两颗树是否相同题目链接:. - 力扣(LeetCode)
bool isSameTree(struct TreeNode* p, struct TreeNode* q) {
//都为空树
if (p == NULL && q == NULL)
{
return true;
}
//一个空树一个非空树
if (p == NULL || q == NULL)
{
return false;
}
//两个非空树
if (p->val != q->val)
{
return false;
}
return isSameTree(p->left, q->left) && isSameTree(p->right, q->right);
}
12. 对称二叉树
对称二叉树题目链接:. - 力扣(LeetCode)
//相同的二叉树
bool isSameTree(struct TreeNode* p, struct TreeNode* q) {
//都为空树
if (p == NULL && q == NULL)
{
return true;
}
//一个空树一个非空树
if (p == NULL || q == NULL)
{
return false;
}
//两个非空树
if (p->val != q->val)
{
return false;
}
return isSameTree(p->left, q->left) && isSameTree(p->right, q->right);
}
//翻转二叉树
struct TreeNode* invertTree(struct TreeNode* root) {
if (root == NULL)
{
return root;
}
//交换左右子树
struct TreeNode* tmp = root->left;
root->left = root->right;
root->right = tmp;
invertTree(root->left);
invertTree(root->right);
return root;
}
//对称二叉树
bool isSymmetric(struct TreeNode* root) {
//空树
if (root == NULL)
{
return true;
}
//只有一个节点的树
if (root->left == NULL && root->right == NULL)
{
return true;
}
//有左右孩子,且左右孩子为相同的树
invertTree(root->right);
return isSameTree(root->left,root->right);
}
13. 另一颗树的子树
另一颗树的子树题目链接:572. 另一棵树的子树 - 力扣(LeetCode)
//另一棵树的子树
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);
}
14.二叉树的前序遍历
二叉树的前序遍历题目链接:144. 二叉树的前序遍历 - 力扣(LeetCode)
//求二叉树节点个数
int TreeSize(struct TreeNode* root)
{
return root == NULL ? 0 : TreeSize(root->left) + TreeSize(root->right) + 1;
}
//二叉树的前序遍历
void PreOrder(struct TreeNode* root, int* a, int* pi)
{
if (root == NULL)
{
return;
}
//static int i = 0;
a[*pi] = root->val;
printf("a[%d] = %d\n", pi, a[*pi]);
++(*pi);
PreOrder(root->left, a, pi);
PreOrder(root->right, a, pi);
}
//二叉树的前序遍历,返回序列数组
int* preorderTraversal(struct TreeNode* root, int* returnSize) {
//开辟数组空间
int n = TreeSize(root);
//printf("%d\n",n);
int* a = (int*)malloc(sizeof(int) * n);
int i = 0;
PreOrder(root, a, &i);
*returnSize = n;
return a;
}
15.通过前序遍历的数组构建二叉树
题目链接:二叉树遍历_牛客题霸_牛客网 (nowcoder.com)
#include <stdio.h>
#include<stdlib.h>
typedef char BTDataType;
typedef struct BinaryTreeNode
{
BTDataType data;
struct BinaryTreeNode* left;
struct BinaryTreeNode* right;
}BTNode;
//由前序序列构造二叉树
BTNode* BinaryTreeCreate(BTDataType* a,int* pi)
{
if(a[*pi] == '#')
{
(*pi)++;
return NULL;
}
BTNode* root = (BTNode*)malloc(sizeof(BTNode));
if(root == NULL)
{
perror("malloc fail\n");
return NULL;
}
root->data = a[*pi];
(*pi)++;
root->left = BinaryTreeCreate(a, pi);
root->right = BinaryTreeCreate(a, pi);
return root;
}
//中序遍历
void InOrder(BTNode* root)
{
if(root == NULL)
{
return;
}
InOrder(root->left);
printf("%c ",root->data);
InOrder(root->right);
}
int main() {
char str[100];
scanf("%s", str);
int i = 0;
BTNode* root = BinaryTreeCreate(str, &i);
InOrder(root);
return 0;
}
16.判断二叉树是否是完全二叉树
//判断一棵树是否为完全二叉树
int BinaryTreeComplete(TreeNode* root)
{
Queue q;
QueueInit(&q);
if (root)
{
QueuePush(&q,root);
}
//节点入队
while (!QueueEmpty(&q))
{
TreeNode* front = QueueFront(&q);
QueuePop(&q);
if (front == NULL)
{
break;
}
QueuePush(&q, root->left);
QueuePush(&q, root->right);
}
//判断后续队列中是否有非空节点,有则不是完全二叉树
while (!QueueEmpty(&q))
{
TreeNode* front = QueueFront(&q);
QueuePop(&q);
//存在非空元素
if (front != NULL)
{
QueueDestroy(&q);
return false;
}
}
QueueDestroy(&q);
return true;
}
17.判断二叉树是否是平衡二叉树
平衡二叉树题目链接:110. 平衡二叉树 - 力扣(LeetCode)
//二叉树的最大高度
int maxDepth(struct TreeNode* root) {
if (root == NULL)
{
return 0;
}
int leftmax = maxDepth(root->left);
int rightmax = maxDepth(root->right);
return leftmax > rightmax ? leftmax + 1 : rightmax + 1;
}
//平衡二叉树
bool isBalanced(struct TreeNode* root) {
if (root == NULL)
{
return true;
}
if (root->left == NULL && root->right == NULL)
{
return true;
}
int left_heigh = maxDepth(root->left);
int right_heigh = maxDepth(root->right);
if (left_heigh - right_heigh == -1 || left_heigh - right_heigh == 0
|| left_heigh - right_heigh == 1)
{
if(isBalanced(root->left) && isBalanced(root->right))
return true;
}
return false;
}
18.二叉树销毁
//二叉树的额销毁
void BinaryTreeDestroy(TreeNode* root)
{
if (root == NULL)
{
return;
}
BinaryTreeDestroy(root->left);
BinaryTreeDestroy(root->right);
free(root);
}