Binary Tree
Before you go through this article, make sure that you gone through the previous article onÂ Binary Trees.
We have discussed
 Binary tree is a special tree data structure.
 In a binary tree, each node can have at most 2 children.
In this article, we will discuss about Binary Tree Traversal.
Tree Traversal
Tree Traversal refers to the process of visiting each node in a tree data structure exactly once. 
Various tree traversal techniques are
Depth First Traversal
Following three traversal techniques fall under Depth First Traversal
 Preorder Traversal
 Inorder Traversal
 Postorder Traversal
1. Preorder Traversal
Algorithm
 Visit the root
 Traverse the left sub tree i.e. call Preorder (left sub tree)
 Traverse the right sub tree i.e. call Preorder (right sub tree)
RootÂ â†’ LeftÂ â†’ Right
Example
Consider the following example
Preorder Traversal Shortcut
Traverse the entire tree starting from the root node keeping yourself to the left.

Applications
 Preorder traversal is used to get prefix expression of an expression tree.
 Preorder traversal is used to create a copy of the tree.
2. Inorder Traversal
Algorithm
 Traverse the left sub tree i.e. call Inorder (left sub tree)
 Visit the root
 Traverse the right sub tree i.e. call Inorder (right sub tree)
LeftÂ â†’Â RootÂ â†’ Right
Example
Consider the following example
Inorder Traversal Shortcut
Keep a plane mirror horizontally at the bottom of the tree and take the projection of all the nodes.

Application
 Inorder traversal is used to get infix expression of an expression tree.
3. Postorder Traversal
Algorithm
 Traverse the left sub tree i.e. call Postorder (left sub tree)
 Traverse the right sub tree i.e. call Postorder (right sub tree)
 Visit the root
LeftÂ â†’Â RightÂ â†’ Root
Example
Consider the following example
Postorder Traversal Shortcut
Pluck all the leftmost leaf nodes one by one.

Applications
 Postorder traversal is used to get postfix expression of an expression tree.
 Postorder traversal is used to delete the tree.
 This is because it deletes the children first and then it deletes the parent.
Breadth First Traversal
 Breadth First Traversal of a tree prints all the nodes of a tree level by level.
 Breadth First Traversal is also called as Level Order Traversal.
Example
Application
 Level order traversal is used to print the data in the same order as stored in the array representation of a complete binary tree.
To gain better understanding about Tree Traversal,
Also Read Binary Tree Properties
PRACTICE PROBLEMS BASED ON TREE TRAVERSAL
Problem01:
If the binary tree in figure is traversed in inorder, then the order in which the nodes will be visited is ____?
Solution
The inorder traversal will be performed as
Problem02:
Which of the following sequences denotes the postorder traversal sequence of the tree shown in figure?
 FEGCBDBA
 GCBDAFE
 GCDBFEA
 FDEGCBA
Solution
Perform the postorder traversal by plucking all the leftmost leaf nodes one by one.
Then,
Postorder Traversal :Â G , C , D , B , F , E , A
Thus, Option (C) is correct.
Problem03:
Let LASTPOST, LASTIN, LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal respectively of a complete binary tree. Which of the following is always true?
 LASTIN = LASTPOST
 LASTIN = LASTPRE
 LASTPRE = LASTPOST
 None of these
Solution
Consider the following complete binary tree
Preorder TraversalÂ : B , A , E
Inorder TraversalÂ Â Â : B , A , E
Postorder Traversal : B , E , A
Clearly, LASTIN = LASTPRE.
Thus, Option (B) is correct.
Problem04:
Which of the following binary trees has its inorder and preorder traversals as BCAD and ABCD respectively
Solution
Option (D) is correct.
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