Explain what a balanced binary search tree is and why it is used.

A balanced binary search tree (BST) is a data structure in which the following condition holds for each node: all elements in the left subtree are less than the node's value, and those in the right are greater. The tree is balanced, meaning the heights of the left and right subtrees for each node differ insignificantly (for example, no more than 1 in AVL trees). This ensures that search, insert, and delete operations are performed in O(log n) time, where n is the number of elements.

Balanced BSTs are used for efficient storage and quick data retrieval when element order and fast key access are important. Examples include AVL trees or red-black trees.

Example in Java (simplified node):

class Node {
    int key;
    Node left, right;
    int height; // for balancing

    Node(int key) {
        this.key = key;
        height = 1;
    }
}

In real-world tasks, ready-made implementations are used, such as TreeMap in Java, which is based on a red-black tree.