二叉排序树的常见操作和算法的设计与实现

二叉排序树的创建

二叉排序树中增加和删除关键字

判别是否是二叉排序树

二叉排序树的最大值和第k大的值

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

typedef struct TreeNode
{
    int data;
    struct TreeNode *left;
    struct TreeNode *right;
} TreeNode;
TreeNode *createNode(int value)
{
    TreeNode *newNode = (TreeNode *)malloc(sizeof(TreeNode));
    newNode->data = value;
    newNode->left = NULL;
    newNode->right = NULL;
    return newNode;
}
TreeNode *insert(TreeNode *root, int value)
{
    if (root == NULL)
    {
        return createNode(value);
    }
    if (value < root->data)
    {
        root->left = insert(root->left, value);
    }
    else if (value > root->data)
    {
        root->right = insert(root->right, value);
    }
    return root;
}
TreeNode *findMin(TreeNode *node)
{
    while (node->left != NULL)
    {
        node = node->left;
    }
    return node;
}

TreeNode *deleteNode(TreeNode *root, int value)
{
    if (root == NULL)
    {
        return root;
    }
    if (value < root->data)
    {
        root->left = deleteNode(root->left, value);
    }
    else if (value > root->data)
    {
        root->right = deleteNode(root->right, value);
    }
    else
    {
        if (root->left == NULL)
        {
            TreeNode *temp = root->right;
            free(root);
            return temp;
        }
        else if (root->right == NULL)
        {
            TreeNode *temp = root->left;
            free(root);
            return temp;
        }
        TreeNode *temp = findMin(root->right);
        root->data = temp->data;
        root->right = deleteNode(root->right, temp->data);
    }
    return root;
}
int isBSTUtil(TreeNode *node, int min, int max)
{
    if (node == NULL)
    {
        return 1;
    }
    if (node->data <= min || node->data >= max)
    {
        return 0;
    }
    return isBSTUtil(node->left, min, node->data) && isBSTUtil(node->right, node->data, max);
}

int isBST(TreeNode *root)
{
    return isBSTUtil(root, INT_MIN, INT_MAX);
}
int findMax(TreeNode *root)
{
    if (root == NULL)
    {
        printf("树为空\n");
        return -1; // 或者抛出异常
    }
    while (root->right != NULL)
    {
        root = root->right;
    }
    return root->data;
}
void inorderTraversal(TreeNode *root, int k, int *count, int *result)
{
    if (root == NULL || *count >= k)
    {
        return;
    }
    inorderTraversal(root->right, k, count, result);
    (*count)++;
    if (*count == k)
    {
        *result = root->data;
        return;
    }
    inorderTraversal(root->left, k, count, result);
}

int findKthLargest(TreeNode *root, int k)
{
    int count = 0;
    int result = -1; // 或者抛出异常
    inorderTraversal(root, k, &count, &result);
    return result;
}