Mirror a Binary Tree in DSA Java - 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.

intermediate

Which traversal method is commonly used to mirror a binary tree?

A post-order traversal is commonly used because it processes children before the parent, allowing safe swapping of left and right subtrees.

beginner

Java method signature to mirror a binary tree node named 'root'?

public void mirrorTree(TreeNode root) { ... }

beginner

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

The base case is when the current node is null, meaning there is no subtree to mirror, so the function returns immediately.

beginner

After mirroring, what happens to the left and right subtrees of each node?

The left subtree becomes the right subtree and the right subtree becomes the left subtree, effectively swapping their positions.

What is the first step in mirroring a binary tree recursively?

A Check if the current node is null

B Swap the left and right children of the current node

C Recursively mirror the right subtree

D Recursively mirror the left subtree

The first step is to check if the current node is null to handle the base case and stop recursion.

Which of these best describes the effect of mirroring a binary tree?

A Swaps left and right children of all nodes

B Deletes all leaf nodes

C Reverses the order of nodes in each level

D Duplicates the tree

Mirroring swaps the left and right children of every node, creating a mirror image.

In Java, what data structure is typically used to represent a binary tree node?

A Array

B TreeNode class with left and right references

C HashMap

D LinkedList

A TreeNode class with left and right child references is used to represent nodes in a binary tree.

What traversal order is best suited for mirroring a binary tree?

A Pre-order

B In-order

C Post-order

D Level-order

Post-order traversal processes children before the parent, allowing safe swapping of subtrees.

What happens if you try to mirror a null node?

A Swaps null with itself

B Throws an error

C Creates a new node

D Returns immediately without changes

The base case for recursion returns immediately when the node is null, so no changes occur.

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 flipping the tree around its center.

Practice

1. What does it mean to mirror a binary tree?

easy

A. Remove all leaf nodes from the tree

B. Swap the left and right children of every node in the tree

C. Convert the tree into a linked list

D. Sort the nodes in ascending order

Solution

1. Step 1: Understand the mirror operation

   Mirroring a binary tree means swapping the left and right children of every node.

2. Step 2: Apply the definition to the tree

   By swapping children at every node, the tree becomes a mirror image of the original.

3. Final Answer:

   Swap the left and right children of every node in the tree -> Option B

4. Quick Check:

   Mirror = Swap children [OK]

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

Common Mistakes:

• Thinking mirror means deleting nodes
• Confusing mirror with sorting
• Assuming mirror flattens the tree

2. Which of the following Java method signatures correctly represents a function to mirror a binary tree node?

easy

A. public void mirrorTree(Node root)

B. public int mirrorTree(Node root)

C. void mirrorTree(Node root) throws Exception

D. public Node mirrorTree()

Solution

1. Step 1: Identify correct return type

   Mirroring modifies the tree in place, so void return type is appropriate.

2. Step 2: Check method parameters

   The method should accept the root node to start mirroring from.

3. Final Answer:

   public void mirrorTree(Node root) -> Option A

4. Quick Check:

   Void return + root parameter = correct signature [OK]

Hint: Mirror modifies tree in place, so use void with root parameter [OK]

Common Mistakes:

• Using return type int instead of void
• Missing root parameter
• Adding unnecessary exceptions

3. Given the following binary tree and the mirror function below, what will be the preorder traversal output after mirroring?

    1
   / \
  2   3
 /     \
4       5

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

medium

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

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

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

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

Solution

1. Step 1: Understand the mirror function

   The function swaps left and right children at every node recursively.

2. Step 2: Apply mirror to the tree

   Original tree preorder: 1,2,4,3,5. After mirror, left and right children swap: - Root 1: left=3, right=2 - Node 3: left=5, right=null - Node 2: left=null, right=4

3. Step 3: Preorder traversal after mirror

   Visit root, then left subtree, then right subtree: 1, 3, 5, 2, 4

4. Final Answer:

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

5. Quick Check:

   Mirror swaps children; preorder = [1,3,5,2,4] [OK]

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

Common Mistakes:

• Not swapping children correctly
• Confusing preorder with inorder
• Missing recursive calls

4. The following code attempts to mirror a binary tree but causes a NullPointerException. What is the error?

public void mirrorTree(Node root) {
  Node temp = root.left;
  root.left = root.right;
  root.right = temp;
  mirrorTree(root.left);
  mirrorTree(root.right);
}

medium

A. Swapping left and right children incorrectly

B. Recursive calls should be after swapping

C. Missing null check before accessing root.left

D. Method should return a Node instead of void

Solution

1. Step 1: Identify cause of NullPointerException

   The code accesses root.left without checking if root is null.

2. Step 2: Fix by adding null check

   Adding "if (root == null) return;" at the start prevents errors when root is null.

3. Final Answer:

   Missing null check before accessing root.left -> Option C

4. Quick Check:

   NullPointerException = missing null check [OK]

Hint: Always check if node is null before accessing children [OK]

Common Mistakes:

• Ignoring null checks
• Thinking swap order causes error
• Changing return type unnecessarily

5. You have a binary tree where some nodes have only one child. After mirroring the tree using the standard mirror function, which of the following statements is true about the structure of the mirrored tree?

hard

A. Leaf nodes become internal nodes after mirroring

B. Nodes with one child will have two children after mirroring

C. The tree height will always increase by 1

D. Nodes with only left child will have only right child after mirroring

Solution

1. Step 1: Understand mirroring effect on children

   Mirroring swaps left and right children at every node.

2. Step 2: Analyze nodes with one child

   If a node has only a left child, after mirroring it will have only a right child (the left child moves to right).

3. Step 3: Check other options

   Tree height does not necessarily increase; leaf nodes remain leaves; nodes do not gain extra children.

4. Final Answer:

   Nodes with only left child will have only right child after mirroring -> Option D

5. Quick Check:

   Mirror swaps children, so left-only becomes right-only [OK]

Hint: Mirror swaps children, so single left child becomes single right child [OK]

Common Mistakes:

• Assuming tree height changes
• Thinking nodes gain extra children
• Confusing leaf and internal nodes