Check for Symmetric tree-coding question asked in interviews

Problem Statement:

You are given a binary tree, where the data present in each node is an integer. You have to find whether the given tree is symmetric or not.

Symmetric tree is a binary tree, whose mirror image is exactly the same as the original tree.

Input Format:

the binary tree node elements in the level order form

Output Format:

The output consists of a single line containing “Symmetric” if the given tree is symmetric, else “Asymmetric”.

Sample Input 1:

1 2 2 3 4 4 3 -1 -1 -1 -1 -1 -1 -1 -1

Sample Output 1:

Symmetric

Sample Input 2:

1 2 3 4 -1 -1 -1 -1 -1

Sample Output 2:

Asymmetric

Constraint:

0 <= N <= 10⁵
1 <= Data <= 10⁵

Approach:

A symmetrical binary tree is a tree that forms a mirror of itself around the center. In other words, every node in the left subtree will have a mirror image in the right subtree.

Example of symmetric binary tree

We can ignore the root node as it is lying on the mirror line. In the next level, for a symmetric tree, the node at the root’s left should be equal to the node at the root’s right.

If we take two variables root1 and root2 to represent the left child of root and right child of the root, then root 1 value=root 2 value.

Further, we need to understand that when root1’s value is equal to root2’s value, we need to further check for its children. As we are concerned about node positions through a mirror, root1’s left child should be checked with root2’s right child and root1’s right child should be checked with root2’s left child.

Code:

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