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11. Symmetric Tree

easyAsked at PayPal

Decide whether a binary tree is a mirror of itself. PayPal uses this as a recursion check — testing whether you can write a helper that compares two trees with mirrored axes, the same pattern they use for symmetric-link reconciliation between buyer-side and seller-side transaction graphs.

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

Source citations

Public interview reports confirming this problem appears in PayPal loops.

  • Glassdoor (2025-11)— PayPal SDE-1 phone screen — mirroring helper expected.

Problem

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

Constraints

  • The number of nodes in the tree is in the range [1, 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 level compare

BFS by level. At each level, the list of values should read the same forward and reversed.

Time
O(n)
Space
O(n)
function isSymmetric(root) {
  let q = [root];
  while (q.length) {
    const vals = q.map(n => n ? n.val : null);
    for (let i = 0, j = vals.length - 1; i < j; i++, j--) {
      if (vals[i] !== vals[j]) return false;
    }
    q = q.flatMap(n => n ? [n.left, n.right] : []);
  }
  return true;
}

Tradeoff: Conceptually clean but allocates level-arrays. Less elegant than recursive.

2. Recursive mirror helper (optimal)

Helper mirror(a, b). Both null → true. One null → false. Else a.val == b.val && mirror(a.left, b.right) && mirror(a.right, b.left).

Time
O(n)
Space
O(h)
function isSymmetric(root) {
  function 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: The mirrored recursion (left vs right, right vs left) is the key trick. PayPal looks for this exact shape.

PayPal-specific tips

PayPal's grading rubric here is: did you introduce the two-argument helper? Without it, single-argument recursion can't express the mirror constraint. Bonus signal: mention that this exact two-arg-helper pattern is how PayPal validates buyer-side vs seller-side ledger trees match in mirror across a payment.

Common mistakes

  • Trying to do it with a single-argument helper — can't express mirror without comparing two subtrees in parallel.
  • Mirror calls left-left, right-right (same-tree pattern) — that's Same Tree, not Symmetric.
  • Forgetting the both-null base case at the top.

Follow-up questions

An interviewer at PayPal may pivot to one of these next:

  • Same Tree (LC 100).
  • Invert Binary Tree (LC 226) — same mirror primitive applied to a single tree.
  • Generalize to k-ary trees.

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Output

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FAQ

Why mirror(a.left, b.right)?

Symmetry around the center means a's left subtree mirrors b's right subtree, and vice versa. You're crossing the axis.

Iterative version?

Push pairs of nodes onto a queue: (root.left, root.right). Pop pair, compare, then enqueue (left.left, right.right) and (left.right, right.left). Same crossing-the-axis pattern.

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