日拱一卒，伯克利CS61A，有这么扎实的作业，还愁学生实力不强吗？

def tree(label, branches=[]):
    """Construct a tree with the given label value and a list of branches."""
    for branch in branches:
        assert is_tree(branch), 'branches must be trees'
    return [label] + list(branches)

def label(tree):
    """Return the label value of a tree."""
    return tree[0]

def branches(tree):
    """Return the list of branches of the given tree."""
    return tree[1:]

def is_tree(tree):
    """Returns True if the given tree is a tree, and False otherwise."""
    if type(tree) != list or len(tree) < 1:
        return False
    for branch in branches(tree):
        if not is_tree(branch):
            return False
    return True

def is_leaf(tree):
    """Returns True if the given tree's list of branches is empty, and False
    otherwise.
    """
    return not branches(tree)

def print_tree(t, indent=0):
    """Print a representation of this tree in which each node is
    indented by two spaces times its depth from the root.

    >>> print_tree(tree(1))
    1
    >>> print_tree(tree(1, [tree(2)]))
    1
      2
    >>> numbers = tree(1, [tree(2), tree(3, [tree(4), tree(5)]), tree(6, [tree(7)])])
    >>> print_tree(numbers)
    1
      2
      3
        4
        5
      6
        7
    """
    print('  ' * indent + str(label(t)))
    for b in branches(t):
        print_tree(b, indent + 1)

def copy_tree(t):
    """Returns a copy of t. Only for testing purposes.

    >>> t = tree(5)
    >>> copy = copy_tree(t)
    >>> t = tree(6)
    >>> print_tree(copy)
    5
    """
    return tree(label(t), [copy_tree(b) for b in branches(t)])

def replace_leaf(t, old, new):
    """Returns a new tree where every leaf value equal to old has
    been replaced with new.

    >>> yggdrasil = tree('odin',
    ...                  [tree('balder',
    ...                        [tree('thor'),
    ...                         tree('loki')]),
    ...                   tree('frigg',
    ...                        [tree('thor')]),
    ...                   tree('thor',
    ...                        [tree('sif'),
    ...                         tree('thor')]),
    ...                   tree('thor')])
    >>> laerad = copy_tree(yggdrasil) # copy yggdrasil for testing purposes
    >>> print_tree(replace_leaf(yggdrasil, 'thor', 'freya'))
    odin
      balder
        freya
        loki
      frigg
        freya
      thor
        sif
        freya
      freya
    >>> laerad == yggdrasil # Make sure original tree is unmodified
    True
    """
    "*** YOUR CODE HERE ***"
    if is_leaf(t):
        val = new if label(t) == old else label(t)
        return tree(val)
    return tree(label(t), [replace_leaf(b, old, new) for b in branches(t)])

def print_move(origin, destination):
    """Print instructions to move a disk."""
    print("Move the top disk from rod", origin, "to rod", destination)

def move_stack(n, start, end):
    """Print the moves required to move n disks on the start pole to the end
    pole without violating the rules of Towers of Hanoi.

    n -- number of disks
    start -- a pole position, either 1, 2, or 3
    end -- a pole position, either 1, 2, or 3

    There are exactly three poles, and start and end must be different. Assume
    that the start pole has at least n disks of increasing size, and the end
    pole is either empty or has a top disk larger than the top n start disks.

    >>> move_stack(1, 1, 3)
    Move the top disk from rod 1 to rod 3
    >>> move_stack(2, 1, 3)
    Move the top disk from rod 1 to rod 2
    Move the top disk from rod 1 to rod 3
    Move the top disk from rod 2 to rod 3
    >>> move_stack(3, 1, 3)
    Move the top disk from rod 1 to rod 3
    Move the top disk from rod 1 to rod 2
    Move the top disk from rod 3 to rod 2
    Move the top disk from rod 1 to rod 3
    Move the top disk from rod 2 to rod 1
    Move the top disk from rod 2 to rod 3
    Move the top disk from rod 1 to rod 3
    """
    assert 1 <= start <= 3 and 1 <= end <= 3 and start != end, "Bad start/end"
    "*** YOUR CODE HERE ***"
    if n == 1:
        print_move(start, end)
    else:
        other = 6 - start - end
        move_stack(n-1, start, other)
        print_move(start, end)
        move_stack(n-1, other, end)

def mobile(left, right):
    """Construct a mobile from a left side and a right side."""
    return tree('mobile', [left, right])

def is_mobile(m):
    return is_tree(m) and label(m) == 'mobile'

def sides(m):
    """Select the sides of a mobile."""
    assert is_mobile(m), "must call sides on a mobile"
    return branches(m)

def is_side(m):
    return not is_mobile(m) and not is_weight(m) and type(label(m)) == int

def side(length, mobile_or_weight):
    """Construct a side: a length of rod with a mobile or weight at the end."""
    return tree(length, [mobile_or_weight])

def length(s):
    """Select the length of a side."""
    assert is_side(s), "must call length on a side"
    return label(s)

def end(s):
    """Select the mobile or weight hanging at the end of a side."""
    assert is_side(s), "must call end on a side"
    return branches(s)[0]

def weight(size):
    """Construct a weight of some size."""
    assert size > 0
    "*** YOUR CODE HERE ***"
    return tree(size, [])

def size(w):
    """Select the size of a weight."""
    "*** YOUR CODE HERE ***"
    assert is_weight(w)
    return label(w)

def is_weight(w):
    """Whether w is a weight, not a mobile."""
    "*** YOUR CODE HERE ***"
    return is_leaf(w) and type(label(w)) == int

def balanced(m):
    """Return whether m is balanced.

    >>> t, u, v = examples()
    >>> balanced(t)
    True
    >>> balanced(v)
    True
    >>> w = mobile(side(3, t), side(2, u))
    >>> balanced(w)
    False
    >>> balanced(mobile(side(1, v), side(1, w)))
    False
    >>> balanced(mobile(side(1, w), side(1, v)))
    False
    """
    "*** YOUR CODE HERE ***"
    if is_weight(m):
        return True
    if is_side(m):
        return balanced(end(m))
    
    flag = all([balanced(s) for s in sides(m)])
    left, right = sides(m)[0], sides(m)[1]
    left, right = length(left) * total_weight(end(left)), length(right) * total_weight(end(right))
    return left == right and flag

class Account:
    """An account has a balance and a holder.

    >>> a = Account('John')
    >>> a.deposit(10)
    10
    >>> a.balance
    10
    >>> a.interest
    0.02

    >>> a.time_to_retire(10.25) # 10 -> 10.2 -> 10.404
    2
    >>> a.balance               # balance should not change
    10
    >>> a.time_to_retire(11)    # 10 -> 10.2 -> ... -> 11.040808032
    5
    >>> a.time_to_retire(100)
    117
    """

    interest = 0.02  # A class attribute

    def __init__(self, account_holder):
        self.holder = account_holder
        self.balance = 0

    def deposit(self, amount):
        """Add amount to balance."""
        self.balance = self.balance + amount
        return self.balance

    def withdraw(self, amount):
        """Subtract amount from balance if funds are available."""
        if amount > self.balance:
            return 'Insufficient funds'
        self.balance = self.balance - amount
        return self.balance

    def time_to_retire(self, amount):
        """Return the number of years until balance would grow to amount."""
        assert self.balance > 0 and amount > 0 and self.interest > 0
        "*** YOUR CODE HERE ***"
        import math
        return math.ceil(math.log(amount / self.balance) / math.log(1 + Account.interest))

class FreeChecking(Account):
    """A bank account that charges for withdrawals, but the first two are free!

    >>> ch = FreeChecking('Jack')
    >>> ch.balance = 20
    >>> ch.withdraw(100)  # First one's free
    'Insufficient funds'
    >>> ch.withdraw(3)    # And the second
    17
    >>> ch.balance
    17
    >>> ch.withdraw(3)    # Ok, two free withdrawals is enough
    13
    >>> ch.withdraw(3)
    9
    >>> ch2 = FreeChecking('John')
    >>> ch2.balance = 10
    >>> ch2.withdraw(3) # No fee
    7
    >>> ch.withdraw(3)  # ch still charges a fee
    5
    >>> ch.withdraw(5)  # Not enough to cover fee + withdraw
    'Insufficient funds'
    """
    withdraw_fee = 1
    free_withdrawals = 2

    "*** YOUR CODE HERE ***"
    def __init__(self, account_holder):
        self.holder = account_holder
        self.balance = 0
        self.free_withdrawals = FreeChecking.free_withdrawals

    def withdraw(self, amount):
        amount += self.withdraw_fee if self.free_withdrawals == 0 else 0
        if self.free_withdrawals > 0:
            self.free_withdrawals -= 1
        if self.balance < amount:
            return 'Insufficient funds'
        self.balance -= amount
        return self.balance

def make_counter():
    """Return a counter function.

    >>> c = make_counter()
    >>> c('a')
    1
    >>> c('a')
    2
    >>> c('b')
    1
    >>> c('a')
    3
    >>> c2 = make_counter()
    >>> c2('b')
    1
    >>> c2('b')
    2
    >>> c('b') + c2('b')
    5
    """
    "*** YOUR CODE HERE ***"
    dt = {}
    def process(c):
        ret = dt.get(c, 1)
        dt[c] = ret + 1
        return ret
    return process

def make_fib():
    """Returns a function that returns the next Fibonacci number
    every time it is called.

    >>> fib = make_fib()
    >>> fib()
    0
    >>> fib()
    1
    >>> fib()
    1
    >>> fib()
    2
    >>> fib()
    3
    >>> fib2 = make_fib()
    >>> fib() + sum([fib2() for _ in range(5)])
    12
    """
    "*** YOUR CODE HERE ***"
    prev, cur = 1, 0
    def process():
        nonlocal prev, cur
        ret = cur
        prev, cur = cur, prev + cur
        return ret
    return process

def make_withdraw(balance):
    """Return a withdraw function with BALANCE as its starting balance.
    >>> withdraw = make_withdraw(1000)
    >>> withdraw(100)
    900
    >>> withdraw(100)
    800
    >>> withdraw(900)
    'Insufficient funds'
    """
    def withdraw(amount):
        nonlocal balance
        if amount > balance:
           return 'Insufficient funds'
        balance = balance - amount
        return balance
    return withdraw

"Your account is locked. Attempts: [<p1>, <p2>, <p3>]"

def make_withdraw(balance, password):
    """Return a password-protected withdraw function.

    >>> w = make_withdraw(100, 'hax0r')
    >>> w(25, 'hax0r')
    75
    >>> error = w(90, 'hax0r')
    >>> error
    'Insufficient funds'
    >>> error = w(25, 'hwat')
    >>> error
    'Incorrect password'
    >>> new_bal = w(25, 'hax0r')
    >>> new_bal
    50
    >>> w(75, 'a')
    'Incorrect password'
    >>> w(10, 'hax0r')
    40
    >>> w(20, 'n00b')
    'Incorrect password'
    >>> w(10, 'hax0r')
    "Your account is locked. Attempts: ['hwat', 'a', 'n00b']"
    >>> w(10, 'l33t')
    "Your account is locked. Attempts: ['hwat', 'a', 'n00b']"
    >>> type(w(10, 'l33t')) == str
    True
    """
    "*** YOUR CODE HERE ***"
    tried = []
    def withdraw(amount, passw):
        nonlocal balance
        if len(tried) == 3:
            return "Your account is locked. Attempts: ['{}', '{}', '{}'']".format(tried[0], tried[1], tried[2])
        if passw != password:
            tried.append(passw)
            return 'Incorrect password'
        if amount > balance:
            return 'Insufficient funds'
        balance -= amount
        return balance
    return withdraw

j = make_joint(w, 'hax0r', 'secret')
j2 = make_joint(j, 'secret', 'code')

def make_joint(withdraw, old_password, new_password):
    """Return a password-protected withdraw function that has joint access to
    the balance of withdraw.

    >>> w = make_withdraw(100, 'hax0r')
    >>> w(25, 'hax0r')
    75
    >>> make_joint(w, 'my', 'secret')
    'Incorrect password'
    >>> j = make_joint(w, 'hax0r', 'secret')
    >>> w(25, 'secret')
    'Incorrect password'
    >>> j(25, 'secret')
    50
    >>> j(25, 'hax0r')
    25
    >>> j(100, 'secret')
    'Insufficient funds'

    >>> j2 = make_joint(j, 'secret', 'code')
    >>> j2(5, 'code')
    20
    >>> j2(5, 'secret')
    15
    >>> j2(5, 'hax0r')
    10

    >>> j2(25, 'password')
    'Incorrect password'
    >>> j2(5, 'secret')
    "Your account is locked. Attempts: ['my', 'secret', 'password']"
    >>> j(5, 'secret')
    "Your account is locked. Attempts: ['my', 'secret', 'password']"
    >>> w(5, 'hax0r')
    "Your account is locked. Attempts: ['my', 'secret', 'password']"
    >>> make_joint(w, 'hax0r', 'hello')
    "Your account is locked. Attempts: ['my', 'secret', 'password']"
    """
    "*** YOUR CODE HERE ***"
    ret = withdraw(0, old_password)
    passw = {}
    if type(ret) == int:
        passw[new_password] = old_password
        def process(amount, password):
            return withdraw(amount, passw.get(password, password))
        return process
    else:
        return ret

def str_interval(x):
    """Return a string representation of interval x."""
    return '{0} to {1}'.format(lower_bound(x), upper_bound(x))

def add_interval(x, y):
    """Return an interval that contains the sum of any value in interval x and
    any value in interval y."""
    lower = lower_bound(x) + lower_bound(y)
    upper = upper_bound(x) + upper_bound(y)
    return interval(lower, upper)

def interval(a, b):
    """Construct an interval from a to b."""
    return [a, b]

def lower_bound(x):
    """Return the lower bound of interval x."""
    "*** YOUR CODE HERE ***"
    return x[0]

def upper_bound(x):
    """Return the upper bound of interval x."""
    "*** YOUR CODE HERE ***"
    return x[1]

def mul_interval(x, y):
    """Return the interval that contains the product of any value in x and any
    value in y."""
    p1 = x[0] * y[0]
    p2 = x[0] * y[1]
    p3 = x[1] * y[0]
    p4 = x[1] * y[1]
    return [min(p1, p2, p3, p4), max(p1, p2, p3, p4)]

def sub_interval(x, y):
    """Return the interval that contains the difference between any value in x
    and any value in y."""
    "*** YOUR CODE HERE ***"
    lower = lower_bound(x) - upper_bound(y)
    upper = upper_bound(x) - lower_bound(y)
    return interval(lower, upper)

def div_interval(x, y):
    """Return the interval that contains the quotient of any value in x divided by
    any value in y. Division is implemented as the multiplication of x by the
    reciprocal of y."""
    "*** YOUR CODE HERE ***"
    assert (lower_bound(y) * upper_bound(y)) > 0, 'can divide zero'
    reciprocal_y = interval(1/upper_bound(y), 1/lower_bound(y))
    return mul_interval(x, reciprocal_y)

par1(r1, r2) = (r1 * r2) / (r1 + r2)
par2(r1, r2) = 1 / (1/r1 + 1/r2)

def par1(r1, r2):
    return div_interval(mul_interval(r1, r2), add_interval(r1, r2))

def par2(r1, r2):
    one = interval(1, 1)
    rep_r1 = div_interval(one, r1)
    rep_r2 = div_interval(one, r2)
    return div_interval(one, add_interval(rep_r1, rep_r2))

def check_par():
    """Return two intervals that give different results for parallel resistors.

    >>> r1, r2 = check_par()
    >>> x = par1(r1, r2)
    >>> y = par2(r1, r2)
    >>> lower_bound(x) != lower_bound(y) or upper_bound(x) != upper_bound(y)
    True
    """
    r1 = interval(2, 4) # Replace this line!
    r2 = interval(2, 4) # Replace this line!
    return r1, r2

def quadratic(x, a, b, c):
    """Return the interval that is the range of the quadratic defined by
    coefficients a, b, and c, for domain interval x.

    >>> str_interval(quadratic(interval(0, 2), -2, 3, -1))
    '-3 to 0.125'
    >>> str_interval(quadratic(interval(1, 3), 2, -3, 1))
    '0 to 10'
    """
    "*** YOUR CODE HERE ***"
    f = lambda x: a * x * x + b * x + c
    extreme_point = -b / (2 * a)
    lower = lower_bound(x)
    upper = upper_bound(x)
    if lower <= extreme_point <= upper:
        left, mid, right = f(lower), f(extreme_point), f(upper)
        return interval(min(left, right, mid), max(left, right, mid))
    else:
        left, right = f(lower), f(upper)
        return interval(min(left, right), max(left, right))