2021 fall cs61a hw05
网址 https://inst.eecs.berkeley.edu/~cs61a/fa21/hw/hw05/#required-questions
def gen_perms(seq):
"""Generates all permutations of the given sequence. Each permutation is a
list of the elements in SEQ in a different order. The permutations may be
yielded in any order.
>>> perms = gen_perms([100])
>>> type(perms)
<class 'generator'>
>>> next(perms)
[100]
>>> try: #this piece of code prints "No more permutations!" if calling next would cause an error
... next(perms)
... except StopIteration:
... print('No more permutations!')
No more permutations!
>>> sorted(gen_perms([1, 2, 3])) # Returns a sorted list containing elements of the generator
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
>>> sorted(gen_perms((10, 20, 30)))
[[10, 20, 30], [10, 30, 20], [20, 10, 30], [20, 30, 10], [30, 10, 20], [30, 20, 10]]
>>> sorted(gen_perms("ab"))
[['a', 'b'], ['b', 'a']]
"""
"*** YOUR CODE HERE ***"
if not seq:
yield []
else:
for prem in gen_perms(seq[1:]):
for i in range(len(seq)):
yield prem[:i] + [seq[0]] + prem[i:]
def path_yielder(t, value):
"""Yields all possible paths from the root of t to a node with the label
value as a list.
>>> t1 = tree(1, [tree(2, [tree(3), tree(4, [tree(6)]), tree(5)]), tree(5)])
>>> print_tree(t1)
1
2
3
4
6
5
5
>>> next(path_yielder(t1, 6))
[1, 2, 4, 6]
>>> path_to_5 = path_yielder(t1, 5)
>>> sorted(list(path_to_5))
[[1, 2, 5], [1, 5]]
>>> t2 = tree(0, [tree(2, [t1])])
>>> print_tree(t2)
0
2
1
2
3
4
6
5
5
>>> path_to_2 = path_yielder(t2, 2)
>>> sorted(list(path_to_2))
[[0, 2], [0, 2, 1, 2]]
"""
"*** YOUR CODE HERE ***"
if label(t) == value:
yield [label(t)]
for b in branches(t):
for path in path_yielder(b, value):
yield [label(t)] + path
"*** YOUR CODE HERE ***"
def preorder(t):
"""Return a list of the entries in this tree in the order that they
would be visited by a preorder traversal (see problem description).
>>> numbers = tree(1, [tree(2), tree(3, [tree(4), tree(5)]), tree(6, [tree(7)])])
>>> preorder(numbers)
[1, 2, 3, 4, 5, 6, 7]
>>> preorder(tree(2, [tree(4, [tree(6)])]))
[2, 4, 6]
"""
"*** YOUR CODE HERE ***"
ans = [label(t)]
for i in branches(t):
ans += preorder(i)
return ans
def generate_preorder(t):
"""Yield the entries in this tree in the order that they
would be visited by a preorder traversal (see problem description).
>>> numbers = tree(1, [tree(2), tree(3, [tree(4), tree(5)]), tree(6, [tree(7)])])
>>> gen = generate_preorder(numbers)
>>> next(gen)
1
>>> list(gen)
[2, 3, 4, 5, 6, 7]
"""
"*** YOUR CODE HERE ***"
yield from preorder(t)
def remainders_generator(m):
"""
Yields m generators. The ith yielded generator yields natural numbers whose
remainder is i when divided by m.
>>> import types
>>> [isinstance(gen, types.GeneratorType) for gen in remainders_generator(5)]
[True, True, True, True, True]
>>> remainders_four = remainders_generator(4)
>>> for i in range(4):
... print("First 3 natural numbers with remainder {0} when divided by 4:".format(i))
... gen = next(remainders_four)
... for _ in range(3):
... print(next(gen))
First 3 natural numbers with remainder 0 when divided by 4:
4
8
12
First 3 natural numbers with remainder 1 when divided by 4:
1
5
9
First 3 natural numbers with remainder 2 when divided by 4:
2
6
10
First 3 natural numbers with remainder 3 when divided by 4:
3
7
11
"""
"*** YOUR CODE HERE ***"
def my(i):
if i == 0:
while True:
i += m
yield i
j = i
while True:
yield j
j += m
for i in range(m):
yield my(i)
class Tree:
"""
>>> t = Tree(3, [Tree(2, [Tree(5)]), Tree(4)])
>>> t.label
3
>>> t.branches[0].label
2
>>> t.branches[1].is_leaf()
True
"""
def __init__(self, label, branches=[]):
for b in branches:
assert isinstance(b, Tree)
self.label = label
self.branches = list(branches)
def is_leaf(self):
return not self.branches
def __repr__(self):
if self.branches:
branch_str = ', ' + repr(self.branches)
else:
branch_str = ''
return 'Tree({0}{1})'.format(self.label, branch_str)
def __str__(self):
def print_tree(t, indent=0):
tree_str = ' ' * indent + str(t.label) + "\n"
for b in t.branches:
tree_str += print_tree(b, indent + 1)
return tree_str
return print_tree(self).rstrip()
tree = lambda label, branches=[]: Tree(label, branches)
label = lambda t: t.label
branches = lambda t: t.branches
print_tree = lambda t: print(t)
def naturals():
"""A generator function that yields the infinite sequence of natural
numbers, starting at 1.
>>> m = naturals()
>>> type(m)
<class 'generator'>
>>> [next(m) for _ in range(10)]
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
"""
i = 1
while True:
yield i
i += 1
