Introduction to Trees

In the world of data structures, a tree is a non-linear data structure that represents a hierarchical structure. It consists of nodes connected by edges, where each node can have zero or more child nodes.

Trees have a root node that is the topmost node in the tree, and each node can have multiple child nodes. Nodes that don't have any children are called leaf nodes. The child nodes of a particular node are called its children, and the node itself is called the parent of its children.

Tree Terminology

To better understand trees, let's get familiar with some common terminology:

• Node: Each element in a tree is called a node. It contains a value and may have references to its children nodes.
• Edge: The connection between two nodes.
• Root: The topmost node in the tree.
• Leaf: A node that doesn't have any children.
• Parent: A node that has child nodes.
• Child: The nodes that are direct descendants of a particular node.

Types of Trees

There are various types of trees that are used to solve different problems. Some common types of trees include:

• Binary Tree: A binary tree is a tree in which each node can have at most two children nodes: a left child and a right child.
• Binary Search Tree: A binary search tree (BST) is a binary tree where the left child of a node contains a value smaller than the node's value, and the right child contains a value greater than the node's value. This property allows for efficient searching, insertion, and deletion operations.
• Balanced Tree: A balanced tree is a tree where the heights of the left and right subtrees of any node differ by at most one. It ensures that the tree remains balanced, which improves the performance of various operations.

Tree Traversal

Tree traversal is the process of visiting each node in a tree exactly once. There are several ways to traverse a tree:

• Preorder Traversal: In a preorder traversal, we visit the root node first, followed by the left subtree, and then the right subtree. Here's an example of a preorder traversal in Java:

1%code%

The output of the above code snippet will be:

1Preorder Traversal:
21 -> 2 -> 4 -> 5 -> 3 -> 

Conclusion

Trees are powerful data structures that allow us to represent hierarchical relationships. They have various applications in computer science and can be used to solve a wide range of problems. Understanding the different types of trees and their traversal methods will help you in solving problems efficiently.

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class Main {

  public static void main(String[] args) {

    // replace with your Java logic here

    TreeNode root = new TreeNode(1);

    TreeNode node2 = new TreeNode(2);

    TreeNode node3 = new TreeNode(3);

    TreeNode node4 = new TreeNode(4);

    TreeNode node5 = new TreeNode(5);

​

    root.left = node2;

    root.right = node3;

    node2.left = node4;

    node2.right = node5;

​

    System.out.println("Preorder Traversal: ");

    preorderTraversal(root);

  }

​

  // Preorder Traversal

  public static void preorderTraversal(TreeNode root) {

    if (root == null) {

      return;

    }

​

    System.out.print(root.val + " -> ");

    preorderTraversal(root.left);

    preorderTraversal(root.right);

  }

}