Binary Tree Traversal

Binary trees are fundamental data structures in computer science and understanding their traversal is crucial for various applications. Traversing a binary tree means visiting all the nodes in a specific order. There are several traversal methods, each with its unique applications and benefits. This article will explore the main types of binary tree traversal: in-order, pre-order, post-order, and level-order.

Types of Binary Tree Traversal

1. In-Order Binary Tree Traversal

In in-order traversal, the left child is visited first, followed by the node itself, and then the right child. This can be visualized as Left - Root - Right.

In-Order Traversal: 4 1 5 2 3 

Time Complexity: O(N)
Auxiliary Space: If we don’t consider the size of the stack for function calls then O(1) otherwise O(h) where h is the height of the tree.

Below are some important concepts in In-order Traversal:

• Inorder Tree Traversal without Recursion
• Inorder Tree Traversal without recursion and without stack!
• Find all possible binary trees with given Inorder Traversal
• Replace each node in binary tree with the sum of its inorder predecessor and successor
• Populate Inorder Successor for all nodes
• Inorder Successor of a node in Binary Tree
• Find n-th node of inorder traversal

2. Pre-Order Binary Tree Traversal

In pre-order traversal, the node is visited first, followed by its left child and then its right child. This can be visualized as Root - Left - Right.

Pre-Order Traversal: 1 2 4 5 3 

Time Complexity: O(N)
Auxiliary Space: If we don’t consider the size of the stack for function calls then O(1) otherwise O(h) where h is the height of the tree.

Below are some important concepts in Pre-Order Traversal:

• Morris traversal for Preorder
• Iterative Preorder Traversal
• Calculate depth of a full Binary tree from Preorder
• Number of Binary Trees for given Preorder Sequence length
• Modify a binary tree to get Preorder traversal using right pointers only

3. Post-Order Binary Tree Traversal

In post-order traversal, the left child is visited first, then the right child, and finally the node itself. This can be visualized as Left - Right - Root.

Post-Order Traversal: 4 5 2 3 1 

Below are some important concepts in Post-Order Traversal:

• Print Postorder traversal from given Inorder and Preorder traversals
• Iterative Postorder Traversal | Set 1 (Using Two Stacks)
• Iterative Postorder Traversal | Set 2 (Using One Stack)
• Postorder traversal of Binary Tree without recursion and without stack

4. Level-Order Binary Tree Traversal

In level-order traversal, the nodes are visited level by level, starting from the root node and then moving to the next level. This can be visualized as Level 1 - Level 2 - Level 3 - ....

Level-Order Traversal: 1 2 3 4 5 

Below are some important concepts in Level-Order Traversal:

• Level Order Tree Traversal
• Level order traversal in spiral form
• Level order traversal line by line
• Level order traversal with direction change after every two levels
• Reverse Level Order Traversal
• Perfect Binary Tree Specific Level Order Traversal
• Perfect Binary Tree Specific Level Order Traversal | Set 2

Special Binary Tree Traversals

• Reverse tree path
• Reverse alternate levels of a perfect binary tree
• Diagonal Traversal of Binary Tree
• Iterative diagonal traversal of binary tree
• Boundary Traversal of binary tree
• Density of Binary Tree in One Traversal

All articles on Binary Tree !

Quick Links :

• 'Practice Problems' on Trees
• 'Quizzes' on Binary Trees