AVL Trees

AVL Trees are a type of self-balancing binary search tree that maintain the balance factor property. The balance factor of a node is the height of its left subtree minus the height of its right subtree. AVL Trees ensure that the balance factor of every node is either -1, 0, or 1. If the balance factor of a node is not in the range of -1 to 1, rotations are performed to restore balance.

These rotations maintain the height of the tree at O(log n), ensuring efficient search and insertion operations.

AVL Trees are similar to other self-balancing binary search trees like Red-Black Trees but with stricter balance conditions. While Red-Black Trees require a balance factor between -2 and 2, AVL Trees maintain a strict balance factor range of -1, 0, or 1.

The C++ code snippet below demonstrates the structure of an AVL Tree and explains the balance factor concept:

1// Function to explain AVL Trees
2void explainAVLTrees() {
3  cout << "AVL Trees are a type of self-balancing binary search tree that maintain the balance factor property." << endl;
4  cout << "The balance factor of a node is the height of its left subtree minus the height of its right subtree." << endl;
5  cout << "AVL Trees ensure that the balance factor of every node is either -1, 0, or 1." << endl;
6  cout << "If the balance factor of a node is not in the range of -1 to 1, rotations are performed to restore balance." << endl;
7  cout << "These rotations maintain the height of the tree at O(log n), ensuring efficient search and insertion operations." << endl;
8}
9
10int main() {
11  explainAVLTrees();
12  return 0;
13}

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#include <iostream>

using namespace std;

​

// Function to explain AVL Trees

void explainAVLTrees() {

  cout << "AVL Trees are a type of self-balancing binary search tree that maintain the balance factor property." << endl;

  cout << "The balance factor of a node is the height of its left subtree minus the height of its right subtree." << endl;

  cout << "AVL Trees ensure that the balance factor of every node is either -1, 0, or 1." << endl;

  cout << "If the balance factor of a node is not in the range of -1 to 1, rotations are performed to restore balance." << endl;

  cout << "These rotations maintain the height of the tree at O(log n), ensuring efficient search and insertion operations." << endl;

}

​

int main() {

  explainAVLTrees();

  return 0;

}