Can you explain the concept of symmetry in the context of algorithms or data structures?

In the context of algorithms and data structures, symmetry usually means that a structure or algorithm possesses a property of reflection or equality under certain transformations. For example, in binary trees, a symmetric tree is one that is a mirror reflection of itself with respect to the root.

Example: checking whether a binary tree is symmetric (mirror):

public boolean isSymmetric(TreeNode root) {
    return root == null || isMirror(root.left, root.right);
}

private boolean isMirror(TreeNode t1, TreeNode t2) {
    if (t1 == null && t2 == null) return true;
    if (t1 == null || t2 == null) return false;
    return (t1.val == t2.val)
        && isMirror(t1.left, t2.right)
        && isMirror(t1.right, t2.left);
}

Here, symmetry means that the left subtree is a mirror reflection of the right. In algorithms, symmetry can be used for optimization, simplifying logic, or verifying data correctness.