Crafting Efficient AVL Trees in C++
Discover our in-depth guide on implementing AVL trees in C++, tailored to provide assistance with writing your C++ assignment. Uncover the process of crafting self-balancing binary search trees, ensuring effectiveness in search, insertion, and deletion tasks. With our expert insights, you'll gain proficiency in AVL trees and be ready to excel when you're tasked with writing your C++ assignment.
Prerequisites
Before you begin, it's essential to have a basic understanding of C++ programming and binary search trees. If you're not familiar with these concepts, take a moment to review them before proceeding.
Understanding AVL Trees
AVL trees are binary search trees with an added feature: they're height-balanced. Our AVL tree implementation guarantees that the height difference between a node's left and right subtrees is at most one. This balance ensures a logarithmic time complexity for common operations.
Implementation Steps
Node Structure
Begin by defining the structure of a node in our AVL tree:
```cpp
struct Node {
int data;
Node* left;
Node* right;
int height;
};
``````cpp
int getHeight(Node* node) {
if (node == nullptr)
return -1;
return node->height;
}
int getBalance(Node* node) {
if (node == nullptr)
return 0;
return getHeight(node->left) - getHeight(node->right);
}
```
```cpp
Node* rightRotate(Node* y) {
// Perform right rotation
// Update heights
return x;
}
Node* leftRotate(Node* x) {
// Perform left rotation
// Update heights
return y;
}
```
```cpp
Node* insert(Node* root, int data) {
// Perform standard BST insertion
// Update height of the current node
// Get balance factor
// Perform rotations if necessary
return root;
}
```
Inorder Traversal
```cpp
void inorderTraversal(Node* root) {
if (root != nullptr) {
inorderTraversal(root->left);
// Print node data
inorderTraversal(root->right);
}
}
```
Putting It All Together
```cpp
int main() {
Node* root = nullptr;
// Values to insert
int values[] = {30, 20, 40, 10, 25, 5};
for (int value : values) {
root = insert(root, value);
}
// Print inorder traversal
inorderTraversal(root);
return 0;
}
```