Introduction to Trees

Trees are an important data structure in computer science that are used to represent hierarchical relationships between elements. Just like a real tree in nature, a tree data structure consists of a collection of nodes, where each node has a value and can have zero or more child nodes.

In a tree, there is a special node called the root node, which is the topmost node and has no parent. The root node serves as the starting point for accessing the other nodes in the tree.

Nodes in a tree are connected by edges, which represent the relationships between the nodes. Each node, except for the root, has exactly one parent node, and each node can have multiple child nodes.

The depth of a node in a tree is the number of edges between the node and the root. The height of a tree is the maximum depth of any node in the tree.

Trees can be classified into different types based on the number of children each node can have. Some common types of trees include binary trees, ternary trees, and n-ary trees.

Binary Trees

A binary tree is a type of tree where each node can have at most two children, referred to as the left child and the right child. These children are unordered, meaning there is no specific order in which they are arranged.

Binary trees are commonly used in various applications such as binary search trees, heaps, and expression trees.

Tree Traversal

Tree traversal is the process of visiting each node in a tree exactly once. There are different methods for tree traversal, including pre-order, in-order, and post-order traversal.

In pre-order traversal, the root node is visited first, followed by the left subtree and then the right subtree. In in-order traversal, the left subtree is visited first, then the root node, and finally the right subtree. In post-order traversal, the left subtree is visited first, then the right subtree, and finally the root node.

Example Usage

Let's consider an example of a binary tree that represents a family tree:

1class Node {
2  String name;
3  Node father;
4  Node mother;
5
6  public Node(String name) {
7    this.name = name;
8    father = null;
9    mother = null;
10  }
11}
12
13Node rootNode = new Node("John");
14Node child1 = new Node("Jane");
15Node child2 = new Node("Joe");
16
17rootNode.father = child1;
18rootNode.mother = child2;