Q5: Merge
Write a generator function merge that takes in two infinite generators a and b that are in increasing order without duplicates and returns a generator that has all the elements of both generators, in increasing order, without duplicates.
def merge(a, b):
"""
>>> def sequence(start, step):
... while True:
... yield start
... start += step
>>> a = sequence(2, 3) # 2, 5, 8, 11, 14, ...
>>> b = sequence(3, 2) # 3, 5, 7, 9, 11, 13, 15, ...
>>> result = merge(a, b) # 2, 3, 5, 7, 8, 9, 11, 13, 14, 15
>>> [next(result) for _ in range(10)]
[2, 3, 5, 7, 8, 9, 11, 13, 14, 15]
"""
prev = float('-inf') # 省去了多写一遍循环内内容的麻烦
while True:
next_a, next_b = next(a), next(b)
while next_a <= prev:
next_a = next(a)
while next_b <= prev:
next_b = next(b)
if next_a != next_b:
if next_a < next_b:
yield next_a
yield next_b
else:
yield next_b
yield next_a
else:
yield next_a
prev = max(next_a, next_b)
Q6: Primes Generator
Write a function primes_gen that takes a single argument n and yields all prime numbers less than or equal to n in decreasing order. Assume n >= 1. You may use the is_prime function included below, which we implemented in Discussion 3.
Optional Challenge: Now rewrite the generator so that it also prints the primes in ascending order.
def is_prime(n):
"""Returns True if n is a prime number and False otherwise.
>>> is_prime(2)
True
>>> is_prime(16)
False
>>> is_prime(521)
True
"""
def helper(i):
if i > (n ** 0.5): # Could replace with i == n
return True
elif n % i == 0:
return False
return helper(i + 1)
return helper(2)
def primes_gen(n):
"""Generates primes in decreasing order.
>>> pg = primes_gen(7)
>>> list(pg)
[7, 5, 3, 2]
"""
if n < 2:
return
if is_prime(n):
yield n
yield from primes_gen(n - 1)
Q7: (Optional) Mystery Reverse Environment Diagram
Fill in the lines below so that the variables in the global frame are bound to the values below. Note that the image does not contain a full environment diagram. You may only use brackets, colons, p and q in your answer.
Hint: If you get stuck, feel free to try out different combinations in PythonTutor!
def mystery(p, q):
p[1].extend(q)
q.append(p[1:])
p = [2, 3]
q = [4, [p]]
mystery(q, p)
这题是常规的CS61A交换变量名类型以增加思考难度的题，看多了就习惯了。
pythontutor中的结果如下：
