Check if Two Trees are Symmetric in DSA Javascript - Build from Scratch

Check if Two Trees are Symmetric

📖 Scenario: Imagine you have two family trees represented as simple binary trees. You want to check if these two trees are mirror images of each other, meaning they are symmetric in structure and values.

🎯 Goal: Build a program that creates two binary trees, sets up a helper function to check symmetry, and then uses this function to determine if the two trees are symmetric.

📋 What You'll Learn

Create two binary trees using nested objects with val, left, and right properties

Create a helper function called isMirror that takes two nodes and checks if they are mirror images

Create a function called areSymmetric that uses isMirror to check if the two trees are symmetric

Print true or false based on whether the trees are symmetric

💡 Why This Matters

🌍 Real World

Checking if two trees are symmetric is useful in graphics, data organization, and comparing hierarchical data structures.

💼 Career

Understanding tree symmetry helps in coding interviews and software roles involving tree data structures and algorithms.

1

Create Two Binary Trees

Create two binary trees called tree1 and tree2. Each tree node should be an object with val, left, and right properties. Use these exact values:

tree1: root value 1, left child 2, right child 3
tree2: root value 1, left child 3, right child 2

DSA Javascript

# Your code here

Hint

Use nested objects to represent each node with val, left, and right. Use null for empty children.

2

Create Helper Function to Check Mirror

Create a function called isMirror that takes two parameters node1 and node2. It should return true if both nodes are null, or if their values are equal and their left and right children are mirrors of each other. Otherwise, return false.

DSA Javascript

const tree1 = {
  val: 1,
  left: { val: 2, left: null, right: null },
  right: { val: 3, left: null, right: null }
};

const tree2 = {
  val: 1,
  left: { val: 3, left: null, right: null },
  right: { val: 2, left: null, right: null }
};

// Your code here

Hint

Check if both nodes are null first. Then check if values match and recursively check children in mirror order.

3

Create Function to Check if Trees are Symmetric

Create a function called areSymmetric that takes two parameters treeA and treeB. It should return the result of calling isMirror(treeA, treeB).

DSA Javascript

const tree1 = {
  val: 1,
  left: { val: 2, left: null, right: null },
  right: { val: 3, left: null, right: null }
};

const tree2 = {
  val: 1,
  left: { val: 3, left: null, right: null },
  right: { val: 2, left: null, right: null }
};

function isMirror(node1, node2) {
  if (node1 === null && node2 === null) return true;
  if (node1 === null || node2 === null) return false;
  return (node1.val === node2.val) &&
         isMirror(node1.left, node2.right) &&
         isMirror(node1.right, node2.left);
}

// Your code here

Hint

Simply call isMirror with the two trees and return its result.

4

Print if the Two Trees are Symmetric

Use console.log to print the result of calling areSymmetric(tree1, tree2). It should print true if the trees are symmetric, otherwise false.

DSA Javascript

const tree1 = {
  val: 1,
  left: { val: 2, left: null, right: null },
  right: { val: 3, left: null, right: null }
};

const tree2 = {
  val: 1,
  left: { val: 3, left: null, right: null },
  right: { val: 2, left: null, right: null }
};

function isMirror(node1, node2) {
  if (node1 === null && node2 === null) return true;
  if (node1 === null || node2 === null) return false;
  return (node1.val === node2.val) &&
         isMirror(node1.left, node2.right) &&
         isMirror(node1.right, node2.left);
}

function areSymmetric(treeA, treeB) {
  return isMirror(treeA, treeB);
}

// Your code here

Hint

Use console.log(areSymmetric(tree1, tree2)) to print the result.

Practice

1. What does it mean for two binary trees to be symmetric?

easy

A. They have the same root value only.

B. They have the same number of nodes.

C. They are mirror images of each other around their center.

D. They have identical left subtrees only.

Solution

1. Step 1: Understand symmetry in trees

   Two trees are symmetric if one is the mirror reflection of the other around the center.

2. Step 2: Compare structure and node values

   Both structure and node values must match in a mirrored way for symmetry.

3. Final Answer:

   They are mirror images of each other around their center. -> Option C

4. Quick Check:

   Symmetry means mirror image = C [OK]

Hint: Symmetric trees mirror each other exactly [OK]

Common Mistakes:

• Thinking same number of nodes means symmetric
• Only comparing root values
• Ignoring structure differences

2. Which of the following is the correct JavaScript function signature to check if two trees are symmetric?

easy

A. function checkSymmetric(tree) {}

B. function isSymmetric(tree1, tree2) {}

C. function symmetricCheck(tree1, tree2, tree3) {}

D. function isSymmetric(tree1) {}

Solution

1. Step 1: Identify parameters needed

   To check symmetry between two trees, we need two tree inputs.

2. Step 2: Match function signature

   Only the function with two parameters for two trees matches the requirement.

3. Final Answer:

   function isSymmetric(tree1, tree2) {} -> Option B

4. Quick Check:

   Two trees need two parameters = B [OK]

Hint: Two trees need two parameters in function [OK]

Common Mistakes:

• Using only one tree parameter
• Adding unnecessary third parameter
• Wrong function naming

3. What will be the output of the following code snippet?

function isMirror(t1, t2) {
  if (!t1 && !t2) return true;
  if (!t1 || !t2) return false;
  return (t1.val === t2.val) && isMirror(t1.left, t2.right) && isMirror(t1.right, t2.left);
}

const tree1 = { val: 1, left: { val: 2, left: null, right: null }, right: { val: 3, left: null, right: null } };
const tree2 = { val: 1, left: { val: 3, left: null, right: null }, right: { val: 2, left: null, right: null } };

console.log(isMirror(tree1, tree2));

medium

A. TypeError

B. false

C. undefined

D. true

Solution

1. Step 1: Check base cases for null nodes

   Both trees have matching null nodes at corresponding mirror positions, so base cases return true.

2. Step 2: Compare node values and recursive calls

   Root values match (1), left of tree1 (2) matches right of tree2 (2), right of tree1 (3) matches left of tree2 (3). All recursive calls return true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   Mirror check returns true for symmetric trees [OK]

Hint: Mirror check compares opposite children recursively [OK]

Common Mistakes:

• Confusing left and right children in recursion
• Ignoring null node base cases
• Assuming order of children doesn't matter

4. Identify the bug in this code snippet that checks if two trees are symmetric:

function isMirror(t1, t2) {
  if (!t1 && !t2) return true;
  if (!t1 || !t2) return false;
  return (t1.val === t2.val) && isMirror(t1.left, t2.left) && isMirror(t1.right, t2.right);
}

medium

A. It compares left with left and right with right instead of mirror sides.

B. It does not check for null nodes.

C. It uses assignment instead of comparison.

D. It returns true too early without recursion.

Solution

1. Step 1: Analyze recursive calls for symmetry

   The function compares t1.left with t2.left and t1.right with t2.right, which checks for identical trees, not mirror symmetry.

2. Step 2: Correct recursive calls for mirror check

   To check symmetry, t1.left should be compared with t2.right and t1.right with t2.left.

3. Final Answer:

   It compares left with left and right with right instead of mirror sides. -> Option A

4. Quick Check:

   Mirror check swaps sides in recursion = A [OK]

Hint: Mirror check swaps left and right children in recursion [OK]

Common Mistakes:

• Comparing same sides instead of mirror sides
• Missing null checks
• Using assignment (=) instead of equality (===)

5. Given two binary trees, write a function to check if they are symmetric. Which approach correctly solves this problem?

hard

A. Use a queue to iteratively compare nodes from left of one tree and right of the other.

B. Compare only the root nodes of both trees.

C. Check if both trees have the same height only.

D. Traverse both trees in preorder and compare node values in order.

Solution

1. Step 1: Understand iterative symmetry check

   Using a queue, we can compare nodes from the left side of one tree with the right side of the other tree iteratively.

2. Step 2: Why other methods fail

   Preorder traversal compares nodes in the same order, not mirror order. Height check or root-only check ignores structure and values.

3. Final Answer:

   Use a queue to iteratively compare nodes from left of one tree and right of the other. -> Option A

4. Quick Check:

   Iterative mirror check uses queue swapping sides = D [OK]

Hint: Use queue to compare opposite sides iteratively [OK]

Common Mistakes:

• Using preorder traversal without mirroring
• Checking only height or root values
• Ignoring iterative approach benefits