Overview
Tree represents nodes connected by edges. We’ll going to 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 two children at maximum. A binary tree have benefits of both an ordered array and a linked list as search is as quick as in sorted array and insertion or deletion operation are as fast as in linked list.
Terms
Following are important terms with respect to tree.
- Path − Path refers to sequence of nodes along the edges of a tree.
- Root − Node at the top of the tree is called root. There is only one root per tree and one path from root node to any node.
- Parent − Any node except root node has one edge upward to a node called parent.
- Child − Node below a given node connected by its edge downward is called its child node.
- Leaf − Node which does not have any child node is called leaf node.
- Subtree − Subtree represents descendents of a node.
- Visiting − Visiting refers to checking 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 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 exibits a special behaviour. A node’s left child must have value less than its parent’s value and node’s right child must have value greater than it’s parent value.
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Binary Search Tree Representation
We’re going to implement tree using node object and connecting them through references.
Basic Operations
Following are basic primary operations of a tree which are following.
- Search − search an element in a tree.
- Insert − insert an element in a tree.
- Preorder Traversal − traverse a tree in a preorder manner.
- Inorder Traversal − traverse a tree in an inorder manner.
- Postorder Traversal − traverse a tree in a postorder manner.
Node
Define a node having some data, references to its left and right child nodes.
public class Node {
public int data;
public Node leftChild;
public Node rightChild;
public Node(){}
public void display(){
System.out.print("("+data+ ")");
}
}Search Operation
Whenever an element is to be search. Start search from root node then if data is less than key value, search element in left subtree otherwise search element in right subtree. Follow the same algorithm for each node.
public Node search(int data){
Node current = root;
System.out.print("Visiting elements: ");
while(current.data != data){
if(current != null)
System.out.print(current.data + " ");
//go to left tree
if(current.data > data){
current = current.leftChild;
}//else go to right tree
else{
current = current.rightChild;
}
//not found
if(current == null){
return null;
}
}
return current;
}Insert Operation
Whenever an element is to be inserted. First locate its proper location. Start search from root node then if data is less than key value, search empty location in left subtree and insert the data. Otherwise search empty location in right subtree and insert the data.
public void insert(int data){
Node tempNode = new Node();
tempNode.data = data;
//if tree is empty
if(root == null){
root = tempNode;
}else{
Node current = root;
Node parent = null;
while(true){
parent = current;
//go to left of the tree
if(data < parent.data){
current = current.leftChild;
//insert to the left
if(current == null){
parent.leftChild = tempNode;
return;
}
}//go to right of the tree
else{
current = current.rightChild;
//insert to the right
if(current == null){
parent.rightChild = tempNode;
return;
}
}
}
}
} Preorder Traversal
It is a simple three step process.
- visit root node
- traverse left subtree
- traverse right subtree
private void preOrder(Node root){
if(root!=null){
System.out.print(root.data + " ");
preOrder(root.leftChild);
preOrder(root.rightChild);
}
}Inorder Traversal
It is a simple three step process.
- traverse left subtree
- visit root node
- traverse right subtree
private void inOrder(Node root){
if(root!=null){
inOrder(root.leftChild);
System.out.print(root.data + " ");
inOrder(root.rightChild);
}
}Postorder Traversal
It is a simple three step process.
- traverse left subtree
- traverse right subtree
- visit root node
private void postOrder(Node root){
if(root!=null){
postOrder(root.leftChild);
postOrder(root.rightChild);
System.out.print(root.data + " ");
}
}Tree Implementation
Node.java
package com.tutorialspoint.datastructure;
public class Node {
public int data;
public Node leftChild;
public Node rightChild;
public Node(){}
public void display(){
System.out.print("("+data+ ")");
}
}Tree.java
package com.tutorialspoint.datastructure;
public class Tree {
private Node root;
public Tree(){
root = null;
}
public Node search(int data){
Node current = root;
System.out.print("Visiting elements: ");
while(current.data != data){
if(current != null)
System.out.print(current.data + " ");
//go to left tree
if(current.data > data){
current = current.leftChild;
}//else go to right tree
else{
current = current.rightChild;
}
//not found
if(current == null){
return null;
}
}
return current;
}
public void insert(int data){
Node tempNode = new Node();
tempNode.data = data;
//if tree is empty
if(root == null){
root = tempNode;
}else{
Node current = root;
Node parent = null;
while(true){
parent = current;
//go to left of the tree
if(data < parent.data){
current = current.leftChild;
//insert to the left
if(current == null){
parent.leftChild = tempNode;
return;
}
}//go to right of the tree
else{
current = current.rightChild;
//insert to the right
if(current == null){
parent.rightChild = tempNode;
return;
}
}
}
}
}
public void traverse(int traversalType){
switch(traversalType){
case 1:
System.out.print("\nPreorder traversal: ");
preOrder(root);
break;
case 2:
System.out.print("\nInorder traversal: ");
inOrder(root);
break;
case 3:
System.out.print("\nPostorder traversal: ");
postOrder(root);
break;
}
}
private void preOrder(Node root){
if(root!=null){
System.out.print(root.data + " ");
preOrder(root.leftChild);
preOrder(root.rightChild);
}
}
private void inOrder(Node root){
if(root!=null){
inOrder(root.leftChild);
System.out.print(root.data + " ");
inOrder(root.rightChild);
}
}
private void postOrder(Node root){
if(root!=null){
postOrder(root.leftChild);
postOrder(root.rightChild);
System.out.print(root.data + " ");
}
}
}Demo Program
TreeDemo.java
package com.tutorialspoint.datastructure;
public class TreeDemo {
public static void main(String[] args){
Tree tree = new Tree();
/* 11 //Level 0
*/
tree.insert(11);
/* 11 //Level 0
* |
* |---20 //Level 1
*/
tree.insert(20);
/* 11 //Level 0
* |
* 3---|---20 //Level 1
*/
tree.insert(3);
/* 11 //Level 0
* |
* 3---|---20 //Level 1
* |
* |--42 //Level 2
*/
tree.insert(42);
/* 11 //Level 0
* |
* 3---|---20 //Level 1
* |
* |--42 //Level 2
* |
* |--54 //Level 3
*/
tree.insert(54);
/* 11 //Level 0
* |
* 3---|---20 //Level 1
* |
* 16--|--42 //Level 2
* |
* |--54 //Level 3
*/
tree.insert(16);
/* 11 //Level 0
* |
* 3---|---20 //Level 1
* |
* 16--|--42 //Level 2
* |
* 32--|--54 //Level 3
*/
tree.insert(32);
/* 11 //Level 0
* |
* 3---|---20 //Level 1
* | |
* |--9 16--|--42 //Level 2
* |
* 32--|--54 //Level 3
*/
tree.insert(9);
/* 11 //Level 0
* |
* 3---|---20 //Level 1
* | |
* |--9 16--|--42 //Level 2
* | |
* 4--| 32--|--54 //Level 3
*/
tree.insert(4);
/* 11 //Level 0
* |
* 3---|---20 //Level 1
* | |
* |--9 16--|--42 //Level 2
* | |
* 4--|--10 32--|--54 //Level 3
*/
tree.insert(10);
Node node = tree.search(32);
if(node!=null){
System.out.print("Element found.");
node.display();
System.out.println();
}else{
System.out.println("Element not found.");
}
Node node1 = tree.search(2);
if(node1!=null){
System.out.println("Element found.");
node1.display();
System.out.println();
}else{
System.out.println("Element not found.");
}
//pre-order traversal
//root, left ,right
tree.traverse(1);
//in-order traversal
//left, root ,right
tree.traverse(2);
//post order traversal
//left, right, root
tree.traverse(3);
}
}If we compile and run the above program then it would produce following result −
Visiting elements: 11 20 42 Element found.(32)
Visiting elements: 11 3 Element not found.
Preorder traversal: 11 3 9 4 10 20 16 42 32 54
Inorder traversal: 3 4 9 10 11 16 20 32 42 54
Postorder traversal: 4 10 9 3 16 32 54 42 20 11
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