Tree Traversal | Binary Tree Traversal

Binary Tree-

 

Before you go through this article, make sure that you gone through the previous article on 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-

  1. Preorder Traversal
  2. Inorder Traversal
  3. Postorder Traversal

 

1. Preorder Traversal-

 

Algorithm-

 

  1. Visit the root
  2. Traverse the left sub tree i.e. call Preorder (left sub tree)
  3. Traverse the right sub tree i.e. call Preorder (right sub tree)

 

Root  Left  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-

 

  1. Traverse the left sub tree i.e. call Inorder (left sub tree)
  2. Visit the root
  3. Traverse the right sub tree i.e. call Inorder (right sub tree)

 

Left  Root  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-

 

  1. Traverse the left sub tree i.e. call Postorder (left sub tree)
  2. Traverse the right sub tree i.e. call Postorder (right sub tree)
  3. Visit the root

 

Left  Right  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,

Watch this Video Lecture

 

Also Read- Binary Tree Properties

 

PRACTICE PROBLEMS BASED ON TREE TRAVERSAL-

 

Problem-01:

 

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-

 

 

Problem-02:

 

Which of the following sequences denotes the postorder traversal sequence of the tree shown in figure?

 

 

  1. FEGCBDBA
  2. GCBDAFE
  3. GCDBFEA
  4. FDEGCBA

 

Solution-

 

Perform the postorder traversal by plucking all the leftmost leaf nodes one by one.

Then,

Postorder Traversal :  G , C , D , B , F , E , A

 

Thus, Option (C) is correct.

 

Problem-03:

 

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?

  1. LASTIN = LASTPOST
  2. LASTIN = LASTPRE
  3. LASTPRE = LASTPOST
  4. None of these

 

Solution-

 

Consider the following complete binary tree-

 

 

Preorder Traversal  : B , A , E

Inorder Traversal     : B , A , E

Postorder Traversal : B , E , A

 

Clearly, LASTIN = LASTPRE.

Thus, Option (B) is correct.

 

Problem-04:

 

Which of the following binary trees has its inorder and preorder traversals as BCAD and ABCD respectively-

 

 

Solution-

 

Option (D) is correct.

 

To watch video solutions and practice more problems,

Watch this Video Lecture

 

Download Handwritten Notes Here-

 

 

Next Article- Binary Search Trees

 

Get more notes and other study material of Data Structures.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Summary
Tree Traversal | Binary Tree Traversal
Article Name
Tree Traversal | Binary Tree Traversal
Description
Tree Traversal is the process of visiting each node exactly once. Binary Tree Traversal Techniques- Preorder Traversal, Inorder Traversal, Postorder Traversal, Level Order Traversal.
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Gate Vidyalay
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