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Chapter 19: Problem 5

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

Short Answer

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Answer: The three common types of binary tree traversal are inorder, preorder, and postorder. 1. Inorder traversal visits nodes in the following order: left subtree, root, and right subtree. 2. Preorder traversal visits nodes in this order: root, left subtree, and right subtree. 3. Postorder traversal visits nodes in this order: left subtree, right subtree, and root.

Step by step solution

01

Introduction to Binary Tree Traversal

Binary tree traversal is a process of visiting each node in the tree exactly once in a specific order. There are three common traversal methods: inorder, preorder, and postorder. Each method visits the nodes in a different order, and they serve various purposes depending on the requirement.
02

Inorder Traversal

In inorder traversal, each node is visited in the following order: left subtree, root, and right subtree. In other words, first visit the left subtree nodes, then the root node, followed by the nodes in the right subtree. This type of traversal is usually used for obtaining a sorted output from the tree. For example, considering the binary tree: 4 / \ 2 6 / \ / \ 1 3 5 7 The inorder traversal will give: 1, 2, 3, 4, 5, 6, 7
03

Preorder Traversal

In preorder traversal, each node is visited in this order: root, left subtree, and right subtree. Traverse the root first, then recursively traverse the left subtree and then the right subtree. Using the same example binary tree: 4 / \ 2 6 / \ / \ 1 3 5 7 The preorder traversal will give: 4, 2, 1, 3, 6, 5, 7
04

Postorder Traversal

In postorder traversal, each node is visited in this order: left subtree, right subtree, and finally the root. Traverse the left subtree and the right subtree first, and visit the root node at the end of the traversal. Again, using the same example binary tree: 4 / \ 2 6 / \ / \ 1 3 5 7 The postorder traversal will give: 1, 3, 2, 5, 7, 6, 4 Now you have learned about the three common types of traversal with a binary tree: Inorder, Preorder, and Postorder.

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Most popular questions from this chapter

Assume that data is stored in a binary tree, but that unlike in the case of binary search tree, no attempt is made to maintain any sort of order in the data stored. Give an algorithm for a function search that searches a binary tree for a particular value num and returns true or false according to whether the value num is found in the tree.

A ternary tree is like a binary tree, except each node in a ternary tree may have three children: a left child, a middle child, and a right child. Write an analogue of the TreeNode declaration that can be used to represent the nodes of a ternary tree.

The first node in a binary tree is called the __________.

Propose a definition of a preorder traversal for ternary trees, and give pseudocode for accomplishing such a traversal.

What problems do you encounter when you try to define the concept of an inorder traversal for ternary trees?
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