A function that checks if binary tree is balanced

balanced_binary_tree.py

def height_min_max(tree):
    if not tree:
        return 0, 0
    else:
        _, l, r = tree
        lmin, lmax = height_min_max(l)
        rmin, rmax = height_min_max(r)
        return 1 + min(lmin, rmin), 1 + max(lmax, rmax)
 
 
def is_balanced(tree):
    tmin, tmax = height_min_max(tree)
    return tmax - tmin <= 1
 

Test in Python REPL:

>>> balanced = (1, (2, (3, None, None), (4, None, None)), (5, None, None))

>>> height_min_max(balanced)
(2, 3)

>>> is_balanced(balanced)
True

>>> unbalanced = (1, (2, (3, None, None), (4, (6, None, None), None)), (5, None, None))

>>> is_balanced(unbalanced)
False