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11. Symmetric Tree

easyAsked at Electronic Arts

Determine whether 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 (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 then palindrome

Inorder-traverse with null markers and check palindrome.

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

Tradeoff:

2. Mirror pair recursion

Compare left's left with right's right and left's right with right's left.

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 mirror(root?.left, root?.right);
}

Tradeoff:

Electronic Arts-specific tips

EA evaluators look for the pair-recursion insight — it's the cleanest way to express the mirror invariant and matches how reflection is handled in scene graphs.

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Output

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