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11. Symmetric Tree

easyAsked at TripAdvisor

Determine if a binary tree is a mirror of itself around its center.

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

Problem

Given the root of a binary tree, check whether it is a mirror of itself (i.e., symmetric around its center). A tree is symmetric if the left subtree is a mirror reflection of the right subtree.

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. Reverse and compare

Build mirror of right subtree, check structural equality with left.

Time
O(n)
Space
O(n)
// mirror right, then compare with left via deep equal
// fine for small inputs but allocates a parallel tree

Tradeoff:

2. Paired recursion

Recurse on (left.left, right.right) and (left.right, right.left). No tree allocation.

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:

TripAdvisor-specific tips

TripAdvisor uses symmetric structure questions to test if you can spot mirror/duplicate review chains in deep comment graphs.

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