How to Construct a Binary Tree from Inorder and Preorder Traversals

How to Construct a Binary Tree from Inorder and Preorder Traversals

Binary trees are a fundamental data structure in computer science. They are used to represent hierarchical data, such as the file system on a computer or the organization of a company. In this article, we will show you how to construct a binary tree from its inorder and preorder traversals.

Inorder and Preorder Traversals

Before we can discuss how to construct a binary tree from its inorder and preorder traversals, we need to understand what these traversals are.

• Inorder traversal visits the nodes of a binary tree in the order left-root-right.
• Preorder traversal visits the nodes of a binary tree in the order root-left-right.

Constructing a Binary Tree from Inorder and Preorder Traversals

Now that we know what inorder and preorder traversals are, we can discuss how to construct a binary tree from them.

The following steps show how to construct a binary tree from its inorder and preorder traversals:

1. Find the root of the tree in the preorder traversal. The root is the first element in the preorder traversal.
2. Find the left subtree of the root in the inorder traversal. The left subtree of the root is the sublist of the inorder traversal that comes before the root.
3. Find the right subtree of the root in the inorder traversal. The right subtree of the root is the sublist of the inorder traversal that comes after the root.
4. Repeat steps 2 and 3 for the left and right subtrees of the root.

By following these steps, you can construct a binary tree from its inorder and preorder traversals.

In this article, we showed you how to construct a binary tree from its inorder and preorder traversals. This is a fundamental skill in computer science, and it is used in a variety of applications. We hope that you found this article informative and helpful.

“`html

Step	Inorder Traversal	Preorder Traversal
1.	A	A
2.	B C	B A C
3.	D E F	D B E A F C
4.	G H I	G D E B F H I A C

“`

A binary tree is a data structure that consists of nodes arranged in a hierarchical manner. Each node has a value, and two child nodes: a left child and a right child. The left child of a node is always less than the value of the node, and the right child is always greater than the value of the node.

Binary trees can be used to represent a variety of data structures, such as sorted lists, sets, and graphs. They are also used in a variety of algorithms, such as binary search and sorting.

In this tutorial, we will show you how to construct a binary tree from inorder and preorder traversals. We will first discuss the inorder and preorder traversals of a binary tree, and then we will present the algorithm for constructing a binary tree from these traversals.

The Inorder and Preorder traversals of a binary tree

The inorder traversal of a binary tree visits the nodes of the tree in the following order:

1. The left subtree of the root node.
2. The root node.
3. The right subtree of the root node.

The preorder traversal of a binary tree visits the nodes of the tree in the following order:

1. The root node.
2. The left subtree of the root node.
3. The right subtree of the root node.

The following diagram shows the inorder and preorder traversals of a binary tree:


The algorithm for constructing a binary tree from inorder and preorder traversals

The algorithm for constructing a binary tree from inorder and preorder traversals is as follows:

1. Create a new node and store the value of the first element in the preorder traversal in the node. This node will be the root of the binary tree.
2. Recursively construct the left subtree of the root node using the elements of the inorder traversal that are less than the value of the root node.
3. Recursively construct the right subtree of the root node using the elements of the inorder traversal that are greater than the value of the root node.

The following diagram shows the steps involved in constructing a binary tree from inorder and preorder traversals:


In this tutorial, we have shown you how to construct a binary tree from inorder and preorder traversals. We have first discussed the inorder and preorder traversals of a binary tree, and then we have presented the algorithm for constructing a binary tree from these traversals.

We hope that you have found this tutorial helpful. If you have any questions, please feel free to ask in the comments section below.

Bonus: Python Code for Constructing a Binary Tree from Inorder and Preorder Traversals

“`python
def construct_binary_tree(inorder, preorder):
“””Constructs a binary tree from inorder and preorder traversals.

Args:
inorder: A list of the values in the inorder traversal of the binary tree.
preorder: A list of the values in the preorder traversal of the binary tree.

Returns:
A root node of the constructed binary tree.
“””

Create a new node and store the value of the first element in the preorder
traversal in the node. This node will be the root of the binary tree.

root = Node(preorder[0])

Recursively construct the left subtree of the root node using the elements of
the inorder traversal that are less than the value of the root node.

left_inorder = [i for i in inorder if i < root.value] root.left = construct_binary_tree(left_inorder, preorder[1:]) Recursively construct the right subtree of the root node using the elements of the inorder traversal that are greater than the value of the root node. right_inorder = [i for i in inorder if i > root.value]
root.right = construct_binary_tree(right_inorder, preorder[1:])

return root

“`

How To Construct Binary Tree From Inorder And Preorder?

Given the inorder and preorder traversals of a binary tree, it is possible to construct the binary tree. The inorder traversal of a binary tree visits the left subtree of a node, then the node itself, and then the right subtree of the node. The preorder traversal of a binary tree visits the node itself, then the left subtree of the node, and then the right subtree of the node.

To construct a binary tree from the inorder and preorder traversals, we can use the following steps:

1. Find the root node in the preorder traversal. The root node is the first element in the preorder traversal.
2. Find the index of the root node in the inorder traversal. The index of the root node in the inorder traversal is the position of the root node in the preorder traversal.
3. Initialize the root node to the first element in the preorder traversal.
4. Recursively construct the left subtree of the root node using the elements in the inorder traversal that come before the root node.
5. Recursively construct the right subtree of the root node using the elements in the inorder traversal that come after the root node.

The following is an example of how to construct a binary tree from the inorder and preorder traversals.

In this example, the inorder traversal is `[‘D’, ‘B’, ‘E’, ‘A’, ‘F’, ‘C’]`, and the preorder traversal is `[‘A’, ‘B’, ‘D’, ‘E’, ‘C’, ‘F’]`.

The root node is `A`. The index of `A` in the inorder traversal is 3.

The left subtree of `A` is constructed using the elements in the inorder traversal that come before `A`, which are `[‘D’, ‘B’, ‘E’]`.

The right subtree of `A` is constructed using the elements in the inorder traversal that come after `A`, which are `[‘C’, ‘F’]`.

The following is the resulting binary tree:

Example

Let’s look at an example of how to construct a binary tree from the inorder and preorder traversals.

The inorder traversal is `[‘D’, ‘B’, ‘E’, ‘A’, ‘F’, ‘C’]`, and the preorder traversal is `[‘A’, ‘B’, ‘D’, ‘E’, ‘C’, ‘F’]`.

The root node is `A`. The index of `A` in the inorder traversal is 3.

The left subtree of `A` is constructed using the elements in the inorder traversal that come before `A`, which are `[‘D’, ‘B’, ‘E’]`.

The right subtree of `A` is constructed using the elements in the inorder traversal that come after `A`, which are `[‘C’, ‘F’]`.

The following is the resulting binary tree:

Code

The following is the code to construct a binary tree from the inorder and preorder traversals in Python:

“`python
def construct_binary_tree(inorder, preorder):
“””Constructs a binary tree from the inorder and preorder traversals.

Args:
inorder: A list of the elements in the inorder traversal of the binary tree.
preorder: A list of the elements in the preorder traversal of the binary tree.

Returns:
A binary tree.
“””

Find the root node in the preorder traversal.
root_index = 0
for i in range(len(

Q: What is a binary tree?

A: A binary tree is a data structure that consists of nodes, each of which has a value and two child nodes: a left child and a right child. The left child of a node is always less than the value of the node, and the right child is always greater than the value of the node. Binary trees are often used to represent hierarchical data, such as the file system on a computer.

Q: What is the inorder traversal of a binary tree?

A: The inorder traversal of a binary tree visits the nodes in the following order: left child, node, right child. This traversal results in the nodes being visited in ascending order by value.

Q: What is the preorder traversal of a binary tree?

A: The preorder traversal of a binary tree visits the nodes in the following order: node, left child, right child. This traversal results in the nodes being visited in the order in which they were added to the tree.

Q: How can I construct a binary tree from the inorder and preorder traversals?

A: To construct a binary tree from the inorder and preorder traversals, you can use the following algorithm:

1. Start by creating a root node with the value of the first element in the preorder traversal.
2. Recursively create the left subtree of the root node using the elements of the inorder traversal that are less than the value of the root node.
3. Recursively create the right subtree of the root node using the elements of the inorder traversal that are greater than the value of the root node.

The following is an example of how to construct a binary tree from the inorder and preorder traversals:

Inorder traversal: 1, 2, 3, 4, 5

Preorder traversal: 4, 2, 1, 3, 5

The following is the binary tree that is constructed from these traversals:

“`
4
/ \
2 5
/ \ / \
1 3 4 5
“`

In this blog post, we discussed how to construct a binary tree from inorder and preorder traversals. We first introduced the concepts of inorder and preorder traversals, and then showed how to use them to construct a binary tree. We also provided a detailed example to illustrate the process.

We hope that this blog post has been helpful in understanding how to construct a binary tree from inorder and preorder traversals. If you have any questions, please feel free to leave them in the comments below.