# Inorder Tree Traversal: A Fundamental Algorithm for Binary Trees

## Inorder Tree Traversal: Understanding the Concept and Algorithm

When it comes to binary trees, one of the most fundamental operations is traversal. Traversal refers to visiting each node of the tree exactly once.

In general, there are three types of traversal: inorder, preorder, and postorder. In this article, we’ll focus on inorder traversal.

## Concept of Inorder Traversal

Inorder traversal is a depth-first traversal method where each node is visited in a left-root-right order. In other words, we start at the node to the extreme left, visit its parent, then go to the right subtree of the parent and repeat the process.

This continues until we visit all the nodes in the tree. Inorder traversal is called so because it visits the nodes in the same order they would appear if the tree were written in an infix notation.

An infix notation is one where the operator is between the operands, as seen in an arithmetic expression.

## Algorithm for Inorder Traversal

The algorithm for inorder traversal is easy to understand and implement. Here it is:

1. Traverse the left subtree.
2. Visit the root node.
3. Traverse the right subtree.

Let’s look at a simple Python implementation of the algorithm:

``````class TreeNode:
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def inorder_traversal(root):
if root:
inorder_traversal(root.left)
print(root.value, end=' ')
inorder_traversal(root.right)
root = TreeNode(8)
root.left = TreeNode(5)
root.right = TreeNode(10)
root.left.left = TreeNode(3)
root.left.right = TreeNode(6)
root.right.right = TreeNode(15)
inorder_traversal(root) # Output: 3 5 6 8 10 15``````

In the code above, we first define a “TreeNode” class that represents a node in the binary tree.

Each node has a value, a left child, and a right child. Then we define the “inorder_traversal” function that takes the root of the tree as an argument.

The function first checks if the root exists (if it’s not None). If the root exists, we first call the “inorder_traversal” function on the left subtree.

This will visit all the left nodes first. Then we print the value of the root node, and finally, we call the “inorder_traversal” function on the right subtree.

## Implementing Inorder Traversal in Python

Now that we’ve discussed the concept and algorithm of inorder traversal, let’s look at a complete implementation in Python.

### Creation of Binary Search Tree

To implement inorder traversal in Python, we need a binary tree. In this example, we’ll create a binary search tree.

A binary search tree is a binary tree in which every node has a value greater than all the nodes in its left subtree and less than all the nodes in its right subtree. Here’s the Python code to create the binary search tree:

``````class BSTNode:
def __init__(self, data):
self.left = None
self.right = None
self.val = data
class BinarySearchTree:
def __init__(self):
self.root = None
def insert(self, data):
newNode = BSTNode(data)
if self.root is None:
self.root = newNode
return
current = self.root
while True:
if data < current.val:
if current.left is None:
current.left = newNode
break
else:
current = current.left
else:
if current.right is None:
current.right = newNode
break
else:
current = current.right``````

In the code above, we define two classes: BSTNode and BinarySearchTree.

The BSTNode class represents a node in the binary search tree. We define a BinarySearchTree class that has a “root” attribute that represents the root of the tree.

We also define an “insert” method that inserts a node into the tree and maintains the binary search tree property. Now that we have the binary search tree implementation, we can traverse the tree using inorder traversal.

### Implementation of Inorder Traversal in Python

Here’s the code to implement inorder traversal in Python using the binary search tree we created:

``````class BSTNode:
def __init__(self, data):
self.left = None
self.right = None
self.val = data
class BinarySearchTree:
def __init__(self):
self.root = None
def insert(self, data):
newNode = BSTNode(data)
if self.root is None:
self.root = newNode
return
current = self.root
while True:
if data < current.val:
if current.left is None:
current.left = newNode
break
else:
current = current.left
else:
if current.right is None:
current.right = newNode
break
else:
current = current.right
def inorder_traversal(self, node):
if node is not None:
self.inorder_traversal(node.left)
print(node.val, end=" ")
self.inorder_traversal(node.right)``````

In the code above, we added an “inorder_traversal” method to the BinarySearchTree class. This method takes a node as an argument and recursively traverses the left subtree, prints the node value, and then traverses the right subtree.

To use inorder traversal, we first create the BinarySearchTree object, insert some nodes, and then call the “inorder_traversal” method:

``````bst = BinarySearchTree()
bst.insert(10)
bst.insert(5)
bst.insert(20)
bst.insert(8)
bst.insert(3)
bst.inorder_traversal(bst.root) # Output: 3 5 8 10 20``````

In the code above, we create a BinarySearchTree object, insert some nodes, and then call the “inorder_traversal” method with the root of the tree as an argument.

## Conclusion

In conclusion, we’ve discussed the concept and algorithm of inorder traversal of a binary tree. We also looked at a complete implementation of inorder traversal in Python using a binary search tree.

If you’re interested in learning more about binary trees, try implementing preorder and postorder traversals.

## Example of Inorder Traversal

Now that we’ve discussed the concept and implementation of inorder traversal using a binary search tree, let’s take a look at an example to see how it all comes together.

### Creation of Binary Search Tree for Example

For this example, we’ll create a binary search tree with the following values: 8, 3, 10, 1, 6, and 14. Here’s the Python code to create the binary search tree:

``````class TreeNode:
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def insert(root, value):
if root is None:
return TreeNode(value)
else:
if root.value < value:
root.right = insert(root.right, value)
else:
root.left = insert(root.left, value)
return root
root = None
root = insert(root, 8)
root = insert(root, 3)
root = insert(root, 10)
root = insert(root, 1)
root = insert(root, 6)
root = insert(root, 14)``````

In the code above, we define a “TreeNode” class that represents a node in the binary tree.

Each node has a value, a left child, and a right child. Then we define the “insert” function that inserts a new node into the binary search tree.

It takes the root of the tree and the value to be inserted as arguments. If the root is None, we return a new node with the given value.

If the value is less than the root value, we insert it into the left subtree. Otherwise, we insert it into the right subtree.

Finally, we create an empty root node and insert the values 8, 3, 10, 1, 6, and 14 into the tree.

### Inorder Traversal Output for Example

Now that we have the binary search tree, let’s use inorder traversal to visit all the nodes in the tree in a left-root-right order. Here’s the code to implement inorder traversal using the binary tree we created:

``````def inorder_traversal(root):
if root:
inorder_traversal(root.left)
print(root.value, end=' ')
inorder_traversal(root.right)
inorder_traversal(root) # Output: 1 3 6 8 10 14``````

In the code above, we define the “inorder_traversal” function that takes the root of the tree as an argument.

The function first checks if the root exists (if it’s not None). If the root exists, we recursively call the “inorder_traversal” function on the left subtree.

This will visit all the left nodes first. Then we print the value of the root node, and finally, we call the “inorder_traversal” function on the right subtree.

When we call the “inorder_traversal” function with the root of the tree as an argument, it prints the values 1, 3, 6, 8, 10, and 14 in a left-root-right order.

## Recap of Inorder Tree Traversal

Inorder traversal is a fundamental traversal method in binary trees where each node is visited in a left-root-right order. It visits the nodes in the same order they would appear if the tree were written in an infix notation.

The algorithm for inorder traversal is simple and easy to implement. We recursively perform inorder traversal on the left subtree, print the root node value, and then perform inorder traversal on the right subtree.

In Python, we can implement inorder traversal using a binary search tree. A binary search tree is a binary tree in which every node has a value greater than all the nodes in its left subtree and less than all the nodes in its right subtree.

## Importance and Future Learning

Understanding and implementing inorder traversal is essential for anyone working with binary trees, as it is the basis for other traversal methods such as preorder and postorder traversal. It is a useful tool for searching and sorting data efficiently.

If you’re interested in learning more about binary trees and traversal methods, there are many resources available online, including tutorials, articles, and videos. With enough practice, you can become proficient in implementing complex algorithms using Python and other programming languages.

In conclusion, understanding and implementing inorder traversal is an essential skill for anyone working with binary trees. It is a fundamental traversal method that visits nodes in a left-root-right order, in the same order they would appear in infix notation.

The algorithm for inorder traversal is easy to implement, and it forms the basis for other traversal methods such as preorder and postorder traversal. By creating a binary search tree and implementing inorder traversal, we can search and sort data efficiently.

Continual practice and exploration of binary tree concepts can increase our proficiency in implementing complex algorithms using Python and other programming languages.