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11. Symmetric Tree

easyAsked at Unity

Decide if a tree is a mirror of itself. Unity uses this to test mirrored-rig validation in animation pipelines.

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. Inorder string compare

Serialize left and right subtrees and reverse-compare.

Time
O(n)
Space
O(n)
// build inorder strings for left & reversed-right, compare
// works but allocates; not ideal

Tradeoff:

2. Paired DFS

Recurse on (left.left, right.right) and (left.right, right.left) in lockstep with value check.

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:

Unity-specific tips

Unity wants paired recursion because mirrored rigs in animation must validate left/right bones in lockstep, not by string compare.

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Output

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