Balanced Binary Trees

A balanced binary tree is a binary tree in which the difference in the heights of its left and right subtrees is at most 1.

The importance of balanced trees lies in their efficient search and insertion operations. When a binary tree is balanced, the height of the tree is minimized, ensuring that these operations can be performed in logarithmic time.

There are several common balanced tree algorithms, including:

1. AVL Trees: AVL trees are self-balancing binary search trees in which the heights of the left and right subtrees differ by at most 1.
2. Red-Black Trees: Red-black trees are another type of self-balancing binary search tree that ensure the tree remains balanced by applying certain rules on every insertion and deletion operation.
3. B-Trees: B-trees are multiway search trees that are commonly used in databases and file systems. They are designed to efficiently store and retrieve large amounts of data from disk.

Let's take a look at an example of checking if a binary tree is balanced in C++:

xxxxxxxxxx

}

#include <iostream>

using namespace std;

​

// Function to check if a binary tree is balanced

bool isBalanced(Node* root) {

  // Base case

  if (root == NULL) {

    return true;

  }

​

  // Get the heights of the left and right subtrees

  int leftHeight = getHeight(root->left);

  int rightHeight = getHeight(root->right);

​

  // Check if the absolute difference between the heights is at most 1

  if (abs(leftHeight - rightHeight) <= 1 && isBalanced(root->left) && isBalanced(root->right)) {

    return true;

  }

​

  return false;

}

​

// Function to get the height of a binary tree

int getHeight(Node* root) {

  // Base case

  if (root == NULL) {

    return 0;

  }

​