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11. Symmetric Tree

easyAsked at Box

Check whether a binary tree mirrors itself around the center — Box uses this pattern when validating mirrored backup-tree consistency between primary and DR regions.

By Sam K., 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).

Constraints

  • Number of nodes in [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. Mirror and compare

Build a mirrored copy and check equality.

Time
O(n)
Space
O(n)
function mirror(t) { return !t ? null : { val: t.val, left: mirror(t.right), right: mirror(t.left) }; }
// then compare original with mirror

Tradeoff:

2. Recursive pair check

Recurse left.left vs right.right and left.right vs right.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:

Box-specific tips

Box graders want the helper recursion pattern that walks two subtrees in lockstep — they reuse it in their DR-region replica-consistency checker.

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Output

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