#### Check Tree Is Symmetric

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```package com.thealgorithms.datastructures.trees;

import com.thealgorithms.datastructures.trees.BinaryTree.Node;

/**
* Check if a binary tree is symmetric or not.
* A binary tree is a symmetric tree if the left and right subtree of root are mirror image.
* Below is a symmetric tree
*                               1
*                   /                         \
*                2                           2
*         /                \             /             \
*      3                    4         4                3
*
* Below is not symmetric because values is different in last level
*                               1
*                   /                         \
*                 2                           2
*         /                \             /             \
*      3                    5         4                3
* <p>
* Approach:
* Recursively check for left and right subtree of root
* 1. left subtrees root's values should be equal right subtree's root value
* 2. recursively check with left subtrees' left child VS right subtree's right child AND
* left subtree's right child VS right subtree left child
* Complexity
* 1. Time: O(n)
* 2. Space: O(lg(n)) for height of tree
*
* @author kumanoit on 10/10/22 IST 12:52 AM
*/
public final class CheckTreeIsSymmetric {
private CheckTreeIsSymmetric() {
}

public static boolean isSymmetric(Node root) {
if (root == null) {
return true;
}
return isSymmetric(root.left, root.right);
}

private static boolean isSymmetric(Node leftSubtreeRoot, Node rightSubtreeRoot) {
if (leftSubtreeRoot == null && rightSubtreeRoot == null) {
return true;
}

if (isInvalidSubtree(leftSubtreeRoot, rightSubtreeRoot)) {
return false;
}

return isSymmetric(leftSubtreeRoot.right, rightSubtreeRoot.left) && isSymmetric(leftSubtreeRoot.left, rightSubtreeRoot.right);
}

private static boolean isInvalidSubtree(Node leftSubtreeRoot, Node rightSubtreeRoot) {
return leftSubtreeRoot == null || rightSubtreeRoot == null || leftSubtreeRoot.data != rightSubtreeRoot.data;
}
}
```