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11. Symmetric Tree

easyAsked at Roblox

Check whether a binary tree is a mirror image of itself.

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

Problem

Given the root of a binary tree, determine if the tree is symmetric around its center. The left subtree must be a mirror of the right subtree in both structure and values.

Constraints

  • 1 <= number of 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. Inorder string check

Serialize then compare with its reverse.

Time
O(n)
Space
O(n)
const arr = [];
const dfs = n => { if (!n) { arr.push('#'); return; } arr.push(n.val); dfs(n.left); dfs(n.right); };
dfs(root);
return arr.join(',') === [...arr].reverse().join(',');

Tradeoff:

2. Mirror recursion

Pair left and right; recurse with mirrored children.

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

Tradeoff:

Roblox-specific tips

Roblox often uses this to gauge spatial-symmetry intuition before testing whether you can mirror an avatar rig's left/right limbs.

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Output

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