Lock test case generator

def generate_initial(level = 0):
    import random
    if random.random() > 0.8 ** level: # generate more branches near root
        return random.randint(1, 12) # limit amount of distinct keys for more interesting test cases
    else:
        return [generate_initial(level + 1), random.choice(["&", "|"]), generate_initial(level + 1)]

def stringify_tree(tree = None):
    tree = tree if tree is not None else generate_clean()
    return str(tree) if isinstance(tree, (int, str, bool)) else "(" + "".join(map(stringify_tree, tree)) + ")"

def get_keys(tree):
    return {tree} if isinstance(tree, int) else get_keys(tree[0]) | get_keys(tree[2])

def powerset(iterable):
    import itertools
    s = list(iterable)
    return list(itertools.chain.from_iterable(itertools.combinations(s, r) for r in range(len(s) + 1)))

def replace_keys(tree, keys, newkeys):
    if isinstance(tree, int):
        return newkeys[keys.index(tree)]
    return [replace_keys(tree[0], keys, newkeys), tree[1], replace_keys(tree[2], keys, newkeys)]

def get_security(tree):
    keys = sorted(get_keys(tree))
    combs = powerset(keys)
    valid = []
    for comb in combs:
        newkeys = [key in comb for key in keys]
        modify = replace_keys(tree, keys, newkeys)
        if eval(stringify_tree(modify)):
            valid.append(comb[::-1])
    return sorted(valid)[0]

trees = [generate_initial() for n in range(10)]
keys = set()
for tree in trees:
    keys |= get_keys(tree)
keys = sorted(keys)
for tree in trees:
    tree = replace_keys(tree, keys, range(1, len(keys) + 1))
    print(tree)
    print(get_security(tree))