DSA interview question

Symmetric Binary Tree

Medium · Data structures · Topics: tree, dfs, recursion

The problem

A logo-design tool builds shapes as binary trees and flags designs that are mirror-symmetric around the vertical axis through the root. A tree is symmetric when its left subtree is a mirror image of its right subtree. Two trees mirror each other when their roots are equal, the first tree's left mirrors the second tree's right, and the first tree's right mirrors the second's left. It's the "identical trees" recursion with the children crossed.

Example: [1, 2, 2, 3, 4, 4, 3] → true; [1, 2, 2, null, 3, null, 3] → false.

Function signature

bool isSymmetric(TreeNode* root);

Test cases

Input (level order)	Output	Explanation
`[1, 2, 2, 3, 4, 4, 3]`	`true`
`[1, 2, 2, null, 3, null, 3]`	`false`	Both 3s hang on the right
`[1, 2, 2, 2, null, 2]`	`false`	Values match but the shape doesn't
`[1]`	`true`
`[]`	`true`

(Confirm: both values and structure must mirror; an empty tree is symmetric.)

How interviewers phrase it

"Given the root of a binary tree, check whether it is a mirror of itself" (LeetCode 101), with "solve it both recursively and iteratively" as the follow-up.

Clarifying questions to ask

Must the structure mirror as well as the values? (Yes.)
Is the empty tree symmetric? (Yes.)
How deep can the tree be? (That decides between recursion and a queue.)

Follow-ups to expect

"What exactly is compared?"
"Iterative version?"
"Why can't comparing the inorder traversal with its reverse work?"
"How does it relate to 'invert binary tree'?"
"Complexity?"

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