Mirror a Binary Tree in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean to mirror a binary tree?

Mirroring a binary tree means swapping the left and right children of every node in the tree, creating a mirror image of the original tree.

beginner

What is the base case when recursively mirroring a binary tree?

The base case is when the current node is null (empty). In this case, we do nothing and return because there is no subtree to mirror.

beginner

In C#, how do you swap the left and right children of a binary tree node?

You can swap by using a temporary variable:
var temp = node.Left; node.Left = node.Right; node.Right = temp;

intermediate

Why do we recursively call the mirror function on both left and right children?

Because each subtree must also be mirrored to create the full mirror image of the entire tree.

intermediate

What is the time complexity of mirroring a binary tree with n nodes?

The time complexity is O(n) because each node is visited exactly once to swap its children.

What happens to the left and right children of a node when mirroring a binary tree?

A They are duplicated

B They are deleted

C They are swapped

D They remain the same

Mirroring swaps the left and right children of every node.

What is the base case for the recursive mirror function?

A Node is null

B Node has no children

C Node is a leaf

D Node has two children

When the node is null, recursion stops because there is nothing to mirror.

Which traversal order is commonly used to mirror a binary tree recursively?

A Inorder (left, node, right)

B Preorder (process node, then children)

C Postorder (children, then node)

D Level order

Preorder traversal is used because we swap children at the current node before recursively mirroring subtrees.

What is the time complexity of mirroring a binary tree with n nodes?

A O(n)

B O(log n)

C O(n^2)

D O(1)

Each node is visited once, so the time complexity is linear, O(n).

What happens if you call the mirror function on a null node?

A It creates a new node

B It throws an error

C It swaps children

D Nothing, it returns immediately

The function returns immediately on null nodes as the base case.

Explain step-by-step how to mirror a binary tree using recursion.

Think about what happens at each node and how recursion helps.

Describe the changes in the tree structure after mirroring a binary tree.

Imagine folding the tree along its root vertically.

Practice

1. What does mirroring a binary tree mean?

easy

A. Swapping the left and right children of every node

B. Removing all leaf nodes

C. Sorting the nodes in ascending order

D. Counting the total number of nodes

Solution

1. Step 1: Understand the mirror operation

   Mirroring means swapping left and right children at every node in the tree.

2. Step 2: Identify the effect on the tree

   This operation flips the tree horizontally, creating a mirror image.

3. Final Answer:

   Swapping the left and right children of every node -> Option A

4. Quick Check:

   Mirror = Swap children [OK]

Hint: Mirror means swap left and right children at all nodes [OK]

Common Mistakes:

• Thinking mirror means sorting nodes
• Confusing mirror with deleting nodes
• Assuming mirror counts nodes

2. Which of the following C# method signatures correctly represents a recursive function to mirror a binary tree node named root?

easy

A. void MirrorTree(Node root)

B. int MirrorTree(Node root)

C. Node MirrorTree(Node root)

D. bool MirrorTree(Node root)

Solution

1. Step 1: Understand the purpose of the function

   The function modifies the tree in place and does not need to return a value.

2. Step 2: Choose the correct return type

   Since it changes the tree nodes directly, the return type should be void.

3. Final Answer:

   void MirrorTree(Node root) -> Option A

4. Quick Check:

   In-place change means void return [OK]

Hint: Mirror function usually returns void as it modifies tree directly [OK]

Common Mistakes:

• Returning int or bool unnecessarily
• Returning Node when not needed
• Using incorrect parameter types

3. Given the following binary tree and the C# code to mirror it, what will be the output of the inorder traversal after mirroring?

    1
   / \
  2   3
 /     \
4       5

void MirrorTree(Node root) {
  if (root == null) return;
  var temp = root.left;
  root.left = root.right;
  root.right = temp;
  MirrorTree(root.left);
  MirrorTree(root.right);
}

// Inorder traversal prints nodes in order: left, root, right

medium

A. [3, 5, 1, 4, 2]

B. [4, 2, 1, 3, 5]

C. [5, 3, 1, 2, 4]

D. [1, 2, 4, 3, 5]

Solution

1. Step 1: Mirror the tree structure

   Swap left and right children at every node:
   Original root 1: left=2, right=3 -> after mirror left=3, right=2
   Node 2: left=4, right=null -> after mirror left=null, right=4
   Node 3: left=null, right=5 -> after mirror left=5, right=null

2. Step 2: Perform inorder traversal on mirrored tree

   Inorder = left, root, right
   Start at root (1):
   Left subtree (3): left=5, right=null -> inorder: 5,3
   Root: 1
   Right subtree (2): left=null, right=4 -> inorder: 2,4
   Combined inorder: [5, 3, 1, 2, 4]

3. Final Answer:

   [5, 3, 1, 2, 4] -> Option C

4. Quick Check:

   Mirror + inorder = [5,3,1,2,4] [OK]

Hint: Mirror swaps children; inorder visits left-root-right [OK]

Common Mistakes:

• Not swapping children correctly
• Confusing preorder with inorder traversal
• Forgetting to mirror all nodes

4. The following C# code attempts to mirror a binary tree but does not work correctly. What is the main error?

void MirrorTree(Node root) {
  MirrorTree(root.left);
  MirrorTree(root.right);
  var temp = root.left;
  root.left = root.right;
  root.right = temp;
}

medium

A. Swapping children happens after recursive calls, causing incorrect mirror

B. Missing base case for null root

C. Using var instead of explicit type causes error

D. Function should return Node instead of void

Solution

1. Step 1: Analyze the base case

   The code lacks an if (root == null) return; check before recursing on children.

2. Step 2: Understand why this causes error

   Recursing on null children leads to NullReferenceException or stack overflow since there's no termination condition.

3. Final Answer:

   Missing base case for null root -> Option B

4. Quick Check:

   Recursion needs if(root == null) return; [OK]

Hint: Always include null base case in tree recursion [OK]

Common Mistakes:

• Omitting base case for null nodes
• Swapping after recursion instead of before
• Thinking var causes error

5. You have a binary tree where some nodes have only one child (either left or right). You want to mirror this tree using C#. Which approach correctly handles all cases including nodes with single children?

hard

A. Mirror by creating a new tree instead of modifying original

B. Only swap children if both left and right children exist

C. Swap children only at leaf nodes

D. Recursively swap left and right children if node is not null, then recurse on both children

Solution

1. Step 1: Consider nodes with single child

   Nodes with only one child still need swapping; swapping null with a child is valid.

2. Step 2: Choose recursive approach that swaps and recurses regardless of child presence

   Swapping children even if one is null ensures correct mirror. Then recurse on both children to continue mirroring.

3. Final Answer:

   Recursively swap left and right children if node is not null, then recurse on both children -> Option D

4. Quick Check:

   Swap children always, recurse both sides [OK]

Hint: Always swap children even if one is null, then recurse [OK]

Common Mistakes:

• Skipping swap when one child is null
• Swapping only leaf nodes
• Creating new tree unnecessarily