# Tree Classless Tree: def __init__(self, entry, branches=()): self.entry = entry

for branch in branches:

assert isinstance(branch, Tree)

self.branches = list(branches)

def __repr__(self):

if self.branches:

branches_str = ‘, ‘ + repr(self.branches)

else:

branches_str = ”

return ‘Tree({0}{1})’.format(self.entry, branches_str)

def __str__(self):

def print_tree(t, indent=0):

tree_str = ‘ ‘ * indent + str(t.entry) + “n”

for b in t.branches:

tree_str += print_tree(b, indent + 1)

return tree_str

return print_tree(self).rstrip()

def is_leaf(self):

return not self.branches

Question 1 Part 1: Tree Map

Define the function tree_map, which takes in a tree and a one-argument function as arguments and returns a new tree which is the result of mapping the function over the entries of the input tree.

def tree_map(fn, t):
    """Maps the function fn over the entries of t and returns the
    result in a new tree.
    >>> numbers = Tree(1,
    ...                [Tree(2,
    ...                      [Tree(3),
    ...                       Tree(4)]),
    ...                 Tree(5,
    ...                      [Tree(6,
    ...                            [Tree(7)]),
    ...                       Tree(8)])])
    >>> print(tree_map(lambda x: 2**x, numbers))
    2
      4
        8
        16
      32
        64
          128
        256
    >>> print(numbers)
    1
      2
        3
        4
      5
        6
          7
        8
    """
    "*** YOUR CODE HERE ***"

Part 2: Add Leaves

Implement add_d_leaves, a function that takes in a Tree instance t and mutates it so that at each depth d in the tree, d leaves with labels v are added to each node at that depth. For example, we want to add 1 leaf with v in it to each node at depth 1, 2 leaves to each node at depth 2, and so on.

Recall that the depth of a node is the number of edges from that node to the root, so the depth of the root is 0. The leaves should be added to the end of the list of branches.

def add_d_leaves(t, v):
    """Add d leaves containing v to each node at every depth d.

    >>> t1 = Tree(1, [Tree(3)])
    >>> add_d_leaves(t1, 4)
    >>> t1
    Tree(1, [Tree(3, [Tree(4)])])
    >>> t2 = Tree(2, [Tree(5), Tree(6)])
    >>> t3 = Tree(3, [t1, Tree(0), t2])
    >>> add_d_leaves(t3, 10)
    >>> print(t3)
    3
      1
        3
          4
            10
            10
            10
          10
          10
        10
      0
        10
      2
        5
          10
          10
        6
          10
          10
        10
    """
    def add_leaves(t, d):
        "*** YOUR CODE HERE ***"
    add_leaves(t, 0)

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