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12. Symmetric Tree

easyAsked at Expedia

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).

Constraints

  • The number of nodes is 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. Inorder list

Inorder traversal then check palindrome (fails on duplicates).

Time
O(n)
Space
O(n)
// fragile: equal values can fake symmetry
const arr=[]; function dfs(n){if(!n) return arr.push(null);
  dfs(n.left);arr.push(n.val);dfs(n.right);} dfs(root);

Tradeoff:

2. Mirror recursion

Recursively check that left.left mirrors right.right and left.right mirrors right.left. Expedia uses similar logic to validate balanced bundle structures.

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:

Expedia-specific tips

Expedia favors clean recursive solutions; mention how the same pattern applies to verifying paired outbound/inbound legs of round-trip itineraries.

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Output

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