CS61a 2021Fall discussion 5——additional practice

Q7: Perfectly Balanced

Part A: Implement sum_tree, which returns the sum of all the labels in tree t.

Part B: Implement balanced, which returns whether every branch of t has the same total sum and that the branches themselves are also balanced.

Challenge: Solve both of these parts with just 1 line of code each.
第二问还没实现一行解决

def sum_tree(t):
    """
    Add all elements in a tree.
    >>> t = tree(4, [tree(2, [tree(3)]), tree(6)])
    >>> sum_tree(t)
    15
    """
    "*** YOUR CODE HERE ***"
    return label(t) + sum([sum_tree(branch) for branch in branches(t)])

def balanced(t):
    """
    Checks if each branch has same sum of all elements and
    if each branch is balanced.
    >>> t = tree(1, [tree(3), tree(1, [tree(2)]), tree(1, [tree(1), tree(1)])])
    >>> balanced(t)
    True
    >>> t = tree(1, [t, tree(1)])
    >>> balanced(t)
    False
    >>> t = tree(1, [tree(4), tree(1, [tree(2), tree(1)]), tree(1, [tree(3)])])
    >>> balanced(t)
    False
    """
    "*** YOUR CODE HERE ***"
    sum_branches = [sum_tree(branch) for branch in branches(t)]
    if not is_leaf(t) and sum_branches.count(sum_branches[0]) != len(sum_branches):
        return False
    for branch in branches(t):
        if not balanced(branch):
            return False
    return True

Q8: Hailstone Tree

We can represent the hailstone sequence as a tree in the figure below, showing the route different numbers take to reach 1. Remember that a hailstone sequence starts with a number n, continuing to n/2 if n is even or 3n+1 if n is odd, ending with 1. Write a function hailstone_tree(n, h) which generates a tree of height h, containing hailstone numbers that will reach n.

Hint: A node of a hailstone tree will always have at least one, and at most two branches (which are also hailstone trees). Under what conditions do you add the second branch?

def hailstone_tree(n, h):
    """Generates a tree of hailstone numbers that will reach N, with height H.
    >>> print_tree(hailstone_tree(1, 0))
    1
    >>> print_tree(hailstone_tree(1, 4))
    1
        2
            4
                8
                    16
    >>> print_tree(hailstone_tree(8, 3))
    8
        16
            32
                64
            5
                10
    """
    if h == 0:
        return tree(n)
    branches = [hailstone_tree(2 * n, h - 1)]   # 得写成列表形式后面才方便加
    # 注意下一项不能是1
    if (n - 1) % 3 == 0 and (n - 1) // 3 % 2 == 1 and (n - 1) // 3 != 1:
        branches += [hailstone_tree((n - 1) // 3, h - 1)]
    return tree(n, branches)

def print_tree(t):
    def helper(i, t):
        print("    " * i + str(label(t)))
        for b in branches(t):
            helper(i + 1, b)
    helper(0, t)