Tree Traversal Inorder Left Root Right in DSA Python - Time & Space Complexity

Time Complexity: Tree Traversal Inorder Left Root Right

O(n)

Understanding Time Complexity

We want to understand how the time needed to visit all nodes in a tree grows as the tree gets bigger.

How does the number of steps change when we do an inorder traversal?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def inorder(root):
    if root is None:
        return
    inorder(root.left)
    print(root.val)
    inorder(root.right)

This code visits each node in a tree in the order: left child, then root, then right child.

Identify Repeating Operations

• Primary operation: Recursive calls to visit each node once.
• How many times: Once per node in the tree.

How Execution Grows With Input

Each node is visited exactly once, so the total steps grow directly with the number of nodes.

Input Size (n)	Approx. Operations
10	About 10 visits
100	About 100 visits
1000	About 1000 visits

Pattern observation: The work grows in a straight line with the number of nodes.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete the traversal grows directly with the number of nodes in the tree.

Common Mistake

[X] Wrong: "Inorder traversal takes more time because it visits nodes multiple times."

[OK] Correct: Each node is visited exactly once, so the time grows linearly, not more.

Interview Connect

Understanding this helps you explain how tree traversals work efficiently and shows you can analyze recursive code clearly.

Self-Check

"What if we changed inorder traversal to preorder traversal? How would the time complexity change?"

Practice

1. What is the order of nodes visited in an inorder traversal of a binary tree?

easy

A. Root, Left subtree, Right subtree

B. Root, Right subtree, Left subtree

C. Right subtree, Root, Left subtree

D. Left subtree, Root, Right subtree

Solution

1. Step 1: Understand inorder traversal definition

   Inorder traversal visits nodes in the order: left subtree first, then root node, then right subtree.

2. Step 2: Apply the order to the tree nodes

   This means we first explore all nodes in the left subtree, then the root, then the right subtree.

3. Final Answer:

   Left subtree, Root, Right subtree -> Option D

4. Quick Check:

   Inorder = Left, Root, Right [OK]

Hint: Remember: Inorder means Left, Root, then Right [OK]

Common Mistakes:

• Confusing inorder with preorder or postorder
• Visiting root before left subtree
• Visiting right subtree before root

2. Which of the following Python function definitions correctly implements inorder traversal of a binary tree node root?

easy

A. def inorder(root):
if root:
inorder(root.left)
print(root.val)
inorder(root.right)

B. def inorder(root):
if root:
print(root.val)
inorder(root.left)
inorder(root.right)

C. def inorder(root):
if root:
inorder(root.right)
print(root.val)
inorder(root.left)

D. def inorder(root):
if root:
inorder(root.right)
inorder(root.left)
print(root.val)

Solution

1. Step 1: Recall inorder traversal order

   Inorder visits left subtree, then root, then right subtree.

2. Step 2: Match code to order

   def inorder(root): if root: inorder(root.left) print(root.val) inorder(root.right) calls inorder on left, prints root value, then calls inorder on right, matching inorder traversal.

3. Final Answer:

   Option A code correctly implements inorder traversal -> Option A

4. Quick Check:

   Left, Root, Right order in code [OK]

Hint: Inorder: recursive left call, print root, recursive right call [OK]

Common Mistakes:

• Printing root before left subtree call
• Swapping left and right subtree calls
• Missing base case check for None

3. Given the binary tree below, what is the output of inorder traversal?

    2
   / \
  1   3

class Node: def __init__(self, val): self.val = val self.left = None self.right = None def inorder(root): if root: inorder(root.left) print(root.val, end=' ') inorder(root.right) root = Node(2) root.left = Node(1) root.right = Node(3) inorder(root)

medium

A. 1 2 3

B. 2 1 3

C. 3 2 1

D. 1 3 2

Solution

1. Step 1: Trace inorder traversal on given tree

   Start at root (2), first visit left subtree (1), print 1, then print root 2, then visit right subtree (3), print 3.

2. Step 2: Write output sequence

   The printed sequence is: 1 2 3.

3. Final Answer:

   1 2 3 -> Option A

4. Quick Check:

   Inorder output = 1 2 3 [OK]

Hint: Inorder prints nodes in ascending order for BST [OK]

Common Mistakes:

• Printing root before left subtree
• Swapping left and right subtree outputs
• Confusing preorder or postorder output

4. The following code is intended to perform inorder traversal but produces no output. What is the error?

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def inorder(root):
    inorder(root.left)
    print(root.val, end=' ')
    inorder(root.right)

root = Node(1)
inorder(root)

medium

A. The root node is never created

B. The print statement is outside the function

C. The base case is missing; should check if root is None first

D. The function calls right subtree before printing root

Solution

1. Step 1: Analyze base case in inorder function

   The function checks root.left and root.right but never checks if root itself is None, which causes errors or no output if root is None.

2. Step 2: Identify missing base case effect

   Without checking if root is None, the function may fail or skip printing when called with None, so adding if root is None: return fixes it.

3. Final Answer:

   The base case is missing; should check if root is None first -> Option C

4. Quick Check:

   Check root None before recursion [OK]

Hint: Always check if node is None before recursion [OK]

Common Mistakes:

• Not checking if root is None before accessing attributes
• Incorrect order of print and recursive calls
• Forgetting to create root node before traversal

5. You have a binary tree where some nodes have only one child. Which inorder traversal output correctly represents the tree below?

      5
     / \
    3   8
     \    \
      4    9

Options: A) 3 5 4 8 9 B) 4 3 5 9 8 C) 3 4 5 8 9 D) 5 3 4 8 9

hard

A. 3 5 4 8 9

B. 3 4 5 8 9

C. 4 3 5 9 8

D. 5 3 4 8 9

Solution

1. Step 1: Perform inorder traversal on given tree

   Start at root (5), visit left subtree: node 3 has no left child, so print 3, then visit right child 4, print 4. Then print root 5. Then visit right subtree: node 8 has no left child, print 8, then right child 9, print 9.

2. Step 2: Write the output sequence

   The output is: 3 4 5 8 9.

3. Final Answer:

   3 4 5 8 9 -> Option B

4. Quick Check:

   Inorder visits left, root, right even if child missing [OK]

Hint: Inorder visits left subtree fully before root, even if missing nodes [OK]

Common Mistakes:

• Skipping nodes with only one child
• Printing root before left subtree
• Confusing preorder or postorder output