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.