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11. Symmetric Tree

easyAsked at GoDaddy

Determine whether a binary tree is a mirror image of itself about its center.

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

Problem

Given the root of a binary tree, check whether the tree is a mirror of itself (symmetric around its center). The left subtree must be a mirror reflection of the right subtree.

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. BFS level lists

BFS, capture each level (with nulls), check palindrome.

Time
O(n)
Space
O(n)
// BFS recording values level by level then check palindrome per level

Tradeoff:

2. Recursive mirror compare

Recurse on (left.left,right.right) and (left.right,right.left).

Time
O(n)
Space
O(h)
function isSymmetric(root) {
  const mirror = (a, b) => {
    if (!a && !b) return true;
    if (!a || !b || a.val !== b.val) return false;
    return mirror(a.left, b.right) && mirror(a.right, b.left);
  };
  return !root || mirror(root.left, root.right);
}

Tradeoff:

GoDaddy-specific tips

GoDaddy uses tree symmetry to test reasoning about mirrored DNS configurations between a primary and secondary nameserver pair.

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Output

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