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11. Symmetric Tree

easyAsked at Canva

Check whether a binary tree is a mirror of itself — Canva uses this to gauge how clearly you reason about mirrored layer compositions.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given the root of a binary tree, check whether it is a mirror of itself (symmetric around its center).

Constraints

  • 1 <= nodes <= 1000
  • -100 <= Node.val <= 100

Examples

Example 1

Input
root=[1,2,2,3,4,4,3]
Output
true

Example 2

Input
root=[1,2,2,null,3,null,3]
Output
false

Approaches

1. BFS pairs

BFS treating left and right siblings as pairs.

Time
O(n)
Space
O(n)
const q = [root.left, root.right];
while (q.length) {
  const a = q.shift(), b = q.shift();
  if (!a && !b) continue;
  if (!a || !b || a.val !== b.val) return false;
  q.push(a.left, b.right, a.right, b.left);
}

Tradeoff:

2. Recursive mirror

Helper compares one node's left to the other's right and vice versa. Symmetric iff every paired walk matches.

Time
O(n)
Space
O(h)
function isSymmetric(root) {
  const mirror = (a, b) => {
    if (!a && !b) return true;
    if (!a || !b) return false;
    return a.val === b.val && mirror(a.left, b.right) && mirror(a.right, b.left);
  };
  return !root || mirror(root.left, root.right);
}

Tradeoff:

Canva-specific tips

Canva expects you to walk through a tiny ASCII tree on the whiteboard, since visual reasoning is half the signal at a design-tools company.

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Output

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