Tree

Tree represents the nodes connected by edges. We will discuss binary tree or binary search tree specifically.
Binary Tree is a special datastructure used for data storage purposes. A binary tree has a special condition that each node can have a maximum of two children. A binary tree has the benefits of both an ordered array and a linked list as search is as quick as in a sorted array and insertion or deletion operation are as fast as in linked list.

Important Terms

Following are the important terms with respect to tree.

• Path − Path refers to the sequence of nodes along the edges of a tree.
• Root − The node at the top of the tree is called root. There is only one root per tree and one path from the root node to any node.
• Parent − Any node except the root node has one edge upward to a node called parent.
• Child − The node below a given node connected by its edge downward is called its child node.
• Leaf − The node which does not have any child node is called the leaf node.
• Subtree − Subtree represents the descendants of a node.
• Visiting − Visiting refers to checking the value of a node when control is on the node.
• Traversing − Traversing means passing through nodes in a specific order.
• Levels − Level of a node represents the generation of a node. If the root node is at level 0, then its next child node is at level 1, its grandchild is at level 2, and so on.
• keys − Key represents a value of a node based on which a search operation is to be carried out for a node.

Binary Search Tree Representation

Binary Search tree exhibits a special behavior. A node's left child must have a value less than its parent's value and the node's right child must have a value greater than its parent value.
We're going to implement tree using node object and connecting them through references.

Tree Node

The code to write a tree node would be similar to what is given below. It has a data part and references to its left and right child nodes.

struct node {
   int data;   
   struct node *leftChild;
   struct node *rightChild;
};

In a tree, all nodes share common construct.

BST Basic Operations

The basic operations that can be performed on a binary search tree data structure, are the following −

• Insert − Inserts an element in a tree/create a tree.
• Search − Searches an element in a tree.
• Preorder Traversal   −      Root-Left-Right
• Inorder Traversal     −      Left-Root-Right
• Postorder Traversal  −     Left-Right-Root