DFS traversal of a Tree

Depth-First Search (DFS) is a method used to explore all the nodes in a tree by going as deep as possible along each branch before moving to the next one. It starts at the root node and visits every node in the tree.

Depth-First Search (DFS) can be classified into three main types based on the order in which the nodes are visited:

• Pre-order Traversal: Visits the root node first, then recursively explores the left and right subtrees.
• In-order Traversal: Explores the left subtree first, then visits the root, and finally the right subtree.
• Post-order Traversal: Explores the left and right subtrees first, then visits the root node.

Different DFS Traversals of a Tree

1. Inorder Traversal

• Traverse the left subtree, i.e., call Inorder(left-subtree)
• Visit the root
• Traverse the right subtree, i.e., call Inorder(right-subtree)

4 2 5 1 3 6 

Time Complexity: O(N)
Auxiliary Space: O(log N)

Uses of Inorder Traversal

In the case of binary search trees (BST), Inorder traversal gives nodes in non-decreasing order. To get nodes of BST in non-increasing order, a variation of Inorder traversal where Inorder traversal is reversed can be used.

• Practice Inorder Traversal

2. Preorder Traversal

• Visit the root
• Traverse the left subtree, i.e., call Preorder(left-subtree)
• Traverse the right subtree, i.e., call Preorder(right-subtree)

1 2 4 5 3 6 

Time Complexity: O(N)
Auxiliary Space: O(log N)

Uses of Preorder Traversal

Preorder traversal is used to create a copy of the tree. Preorder traversal is also used to get prefix expressions of an expression tree.

• Practice Preorder Traversal

3. Postorder Traversal

• Traverse the left subtree, i.e., call Postorder(left-subtree)
• Traverse the right subtree, i.e., call Postorder(right-subtree)
• Visit the root

4 5 2 6 3 1 

Time Complexity: O(N)
Auxiliary Space: O(log N)

Uses of Postorder Traversal:

Postorder traversal is used to delete every node of the tree. Postorder traversal is also useful to get the postfix expression of an expression tree

• Practice Postorder Traversal

Related Article : Breadth First Traversal.