Balanced Trees

In the context of trees, a balanced tree refers to a tree in which the heights of the left and right subtrees of any node differ by at most one.

Balanced trees are important because they provide efficient operations for searching, inserting, and deleting elements in a tree. When a tree is balanced, these operations have a time complexity of O(log n), where n is the number of elements in the tree.

One commonly used balanced tree is the AVL tree, named after its inventors, Adelson-Velsky and Landis. An AVL tree maintains its balance by performing rotations to ensure that the heights of its subtrees remain balanced.

In Java, you can implement a balanced tree using the TreeSet class from the java.util package. Here's an example:

1import java.util.TreeSet;
2
3public class Main {
4  public static void main(String[] args) {
5    // Create a balanced tree
6    TreeSet<Integer> tree = new TreeSet<>();
7
8    // Add elements to the tree
9    tree.add(5);
10    tree.add(3);
11    tree.add(8);
12
13    // Print the elements in the tree
14    for (Integer value : tree) {
15      System.out.println(value);
16    }
17  }
18}

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class Main {

  public static void main(String[] args) {

    // Replace with your Java logic here

  }

}