11. Symmetric Tree
easyAsked at DigitalOceanDetermine if a binary tree is a mirror of itself around its center — DigitalOcean uses this to assess paired-recursion fluency that surfaces in cross-region failover-pair validation.
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. Return true if symmetric.
Constraints
1 <= number of nodes <= 1000-100 <= node.val <= 100
Examples
Example 1
root=[1,2,2,3,4,4,3]trueExample 2
root=[1,2,2,null,3,null,3]falseApproaches
1. Inorder serialize
Serialize the tree, check if the string is a palindrome.
- Time
- O(n)
- Space
- O(n)
function ser(n){return n? '('+ser(n.left)+n.val+ser(n.right)+')' : '_'}
const s = ser(root);
return s === s.split('').reverse().join('');Tradeoff:
2. Mirror recursion
Compare left.left with right.right and left.right with right.left simultaneously.
- Time
- O(n)
- Space
- O(h)
function isSymmetric(root) {
const mirror = (a, b) => {
if (!a && !b) return true;
if (!a || !b) return false;
if (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:
DigitalOcean-specific tips
DigitalOcean grades the mirror-recursion version higher because it short-circuits on the first asymmetry — important when validating that paired region replicas match without serializing the entire topology.
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