#include <stdio.h>
#include <stdlib.h>
struct Node {
int data;
struct Node* left;
struct Node* right;
};
// Function to create a new node
struct Node* createNode(int key) {
struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
newNode->data = key;
newNode->left = newNode->right = NULL;
return newNode;
}
// Function to insert a key into the BST
struct Node* insert(struct Node* root, int key) {
if (root == NULL) {
return createNode(key);
}
if (key < root->data) {
root->left = insert(root->left, key);
} else if (key > root->data) {
root->right = insert(root->right, key);
}
return root;
}
// Function to find the minimum key in the BST
struct Node* findMinimum(struct Node* root) {
if (root == NULL) {
return NULL;
}
while (root->left != NULL) {
root = root->left;
}
return root;
}
// Function to find the maximum key in the BST
struct Node* findMaximum(struct Node* root) {
if (root == NULL) {
return NULL;
}
while (root->right != NULL) {
root = root->right;
}
return root;
}
// Function to find the second minimum key in the BST
struct Node* findSecondMinimum(struct Node* root) {
if (root == NULL || (root->left == NULL && root->right == NULL)) {
return NULL;
}
if (root->left != NULL) {
return findMinimum(root->left);
}
return findMinimum(root->right);
}
// Function to delete a node with zero children
struct Node* deleteNode(struct Node* root, int key) {
if (root == NULL) {
return root;
}
if (key < root->data) {
root->left = deleteNode(root->left, key);
} else if (key > root->data) {
root->right = deleteNode(root->right, key);
} else {
if (root->left == NULL) {
struct Node* temp = root->right;
free(root);
return temp;
} else if (root->right == NULL) {
struct Node* temp = root->left;
free(root);
return temp;
}
struct Node* temp = findMinimum(root->right);
root->data = temp->data;
root->right = deleteNode(root->right, temp->data);
}
return root;
}
// Function to perform an in-order traversal
void inorder(struct Node* root) {
if (root == NULL) {
return;
}
inorder(root->left);
printf("%d ", root->data);
inorder(root->right);
}
// Function to perform a pre-order traversal
void preorder(struct Node* root) {
if (root == NULL) {
return;
}
printf("%d ", root->data);
preorder(root->left);
preorder(root->right);
}
// Function to perform a post-order traversal
void postorder(struct Node* root) {
if (root == NULL) {
return;
}
postorder(root->left);
postorder(root->right);
printf("%d ", root->data);
}
int main() {
struct Node* root = NULL;
// Inserting elements into the BST
root = insert(root, 6);
root = insert(root, 2);
root = insert(root, 9);
root = insert(root, 4);
root = insert(root, 13);
root = insert(root, 7);
root = insert(root, 1);
printf("In-order traversal: ");
inorder(root);
printf("\n");
printf("Pre-order traversal: ");
preorder(root);
printf("\n");
printf("Post-order traversal: ");
postorder(root);
printf("\n");
struct Node* minNode = findMinimum(root);
printf("Minimum: %d\n", minNode->data);
struct Node* maxNode = findMaximum(root);
printf("Maximum: %d\n", maxNode->data);
struct Node* secondMinNode = findSecondMinimum(root);
printf("Second Minimum: %d\n", secondMinNode->data);
// Deleting nodes
root = deleteNode(root, 1); // Delete a node with 0 children
root = deleteNode(root, 9); // Delete a node with 1 child
printf("In-order traversal after deletion: ");
inorder(root);
printf("\n");
return 0;
}