Let us call a binary tree symmetric if you can draw a vertical line through the root node and then the right subtree is the mirror image of the left subtree. Write a predicate symmetric/1 to check whether a given binary tree is symmetric. Hint: Write a predicate mirror/2 first to check whether one tree is the mirror image of another. We are only interested in the structure, not in the contents of the nodes.
# Example in Haskell:
# *Main> symmetric (Branch 'x' (Branch 'x' Empty Empty) Empty)
# *Main> symmetric (Branch 'x' (Branch 'x' Empty Empty) (Branch 'x' Empty Empty))
if tree == None:
val, left, right = tree
return (None, mirror(right), mirror(left))
return mirror(mirror(tree)) == mirror(tree)