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Chapter 20: Problem 11

The three common types of traversal with a binary tree are __________, __________, and __________.

Short Answer

Expert verified
Answer: The three common types of traversal with binary trees are inorder, preorder, and postorder. In inorder traversal, the sequence is left subtree, root, and right subtree. The steps are: 1. Traverse the left subtree by recursively applying inorder traversal. 2. Visit the root node. 3. Traverse the right subtree by recursively applying inorder traversal. In preorder traversal, the sequence is root, left subtree, and right subtree. The steps are: 1. Visit the root node. 2. Traverse the left subtree by recursively applying preorder traversal. 3. Traverse the right subtree by recursively applying preorder traversal. In postorder traversal, the sequence is left subtree, right subtree, and root. The steps are: 1. Traverse the left subtree by recursively applying postorder traversal. 2. Traverse the right subtree by recursively applying postorder traversal. 3. Visit the root node.

Step by step solution

01

Identify the traversals

There are three common types of traversal with a binary tree: inorder, preorder, and postorder.
02

Explain Inorder Traversal

In inorder traversal, we visit the nodes in a particular sequence: left subtree, root, and then the right subtree. To perform inorder traversal, follow these steps: 1. Traverse the left subtree by recursively applying inorder traversal. 2. Visit the root node. 3. Traverse the right subtree by recursively applying inorder traversal.
03

Explain Preorder Traversal

In preorder traversal, we visit the nodes in a different sequence: root, left subtree, and then the right subtree. To perform preorder traversal, follow these steps: 1. Visit the root node. 2. Traverse the left subtree by recursively applying preorder traversal. 3. Traverse the right subtree by recursively applying preorder traversal.
04

Explain Postorder Traversal

In postorder traversal, we visit the nodes in yet another sequence: left subtree, right subtree, and finally the root. To perform postorder traversal, follow these steps: 1. Traverse the left subtree by recursively applying postorder traversal. 2. Traverse the right subtree by recursively applying postorder traversal. 3. Visit the root node.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Inorder Traversal
Understanding inorder traversal is essential for students diving into the world of binary trees. In simple terms, this method involves visiting the nodes of a binary tree in a specific order - the left subtree first, followed by the root, and finally the right subtree.

To visualize this, imagine navigating a family tree where you pay homage to the left branch of your ancestry, acknowledge your own position, and then proceed to explore the right branch. When applying inorder traversal:
  • Start with the leftmost node and explore its entire subtree.
  • Visit the node you are currently at - which could be seen as acknowledging 'your' place within the family tree.
  • Move on to traverse the right subtree, ensuring you cover every node.

This logical sequencing helps in sorting the data in a binary search tree and is widely used in applications that require sorted data output.
Preorder Traversal
Preorder traversal offers a different approach, prioritizing the root before its descendants. Think of it like writing an autobiography where you introduce yourself before detailing your lineage.

The steps are direct and forward-moving:
  • Kick off the process at the root node - this is the 'introduction' in our analogy.
  • Explore the left subtree as if you were recounting your ancestors from your mother’s side.
  • Complete the traversal by moving to the right subtree, similar to telling the story of your ancestors from your father's side.

This approach is beneficial when you need a copy of the tree, as it replicates the original structure right away. Preorder traversal is also used in creating expression trees and syntax trees in compilers due to its root-first logic.
Postorder Traversal
The postorder traversal is akin to a grand finale at the end of a performance. In this method, the nodes are visited in the order of the left subtree, the right subtree, and the root at the very end.

Imagine you are at a family reunion, and you decide to meet all your extended family members before you finally catch up with your closest ones:
  • Begin by spending time with the left subtree family members.
  • Once complete, move to the right subtree, ensuring you acknowledge all relatives on that side.
  • Finish the reunion by visiting your immediate family, represented by the root node.

This method is particularly useful for deleting trees, as you're able to safely remove child nodes before the parent, ensuring no references are left dangling, and it's also instrumental in mathematical expressions where operations are performed based on the last operands.

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Most popular questions from this chapter

What is a leaf node?

Each node in a binary tree may point to how many other nodes?

T F When a node is inserted into a tree, it must be inserted as a leaf node.

How many predecessors may each node other than the root node have?

What are the three methods of traversing a binary tree? What is the difference between these methods?
See all solutions

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