MITx 6.00.1x Python Notes: Mid-term Quiz

Python Code

	def myLog(x, b):
	'''
	x: a positive integer
	b: a positive integer; b >= 2
	returns: log_b(x), or, the logarithm of x relative to a base b.
	'''
	if x < b:
	return 0
	return myLog(x / b, b) + 1
	## test
	# myLog(27, 3)
	# 3
	# myLog(26, 3)
	# 2
	# myLog(4, 16)
	# 0
	def laceStrings(s1, s2):
	"""
	s1 and s2 are strings.
	Returns a new str with elements of s1 and s2 interlaced,
	beginning with s1. If strings are not of same length,
	then the extra elements should appear at the end.
	"""
	s1 = list(s1)
	i = 0
	for j in s2:
	s1.insert(i + 1, j)
	i += 2
	result = ''
	for k in s1:
	result += k
	return result
	## test
	# laceStrings('aaaaaa', 'zzzzzz')
	# 'azazazazazaz'
	# laceStrings('', '')
	# ''
	# laceStrings('af', 'cdizxtau')
	# 'acfdizxtau'
	# laceStrings('mqjkxtav', 'sk')
	# 'msqkjkxtav'
	def laceStringsRecur(s1, s2):
	"""
	s1 and s2 are strings.
	Returns a new str with elements of s1 and s2 interlaced,
	beginning with s1. If strings are not of same length,
	then the extra elements should appear at the end.
	"""
	def helpLaceStrings(s1, s2, out):
	if s1 == '':
	return out + s2
	if s2 == '':
	return out + s1
	else:
	return helpLaceStrings(s1[1:], s2[1:], out + s1[0] + s2[0])
	return helpLaceStrings(s1, s2, '')
	def McNuggets(n):
	"""
	n is an int
	Returns True if some integer combination of 6, 9 and 20 equals n
	Otherwise returns False.
	"""
	if n < 0:
	return False
	elif n == 0:
	return True
	else:
	return any(McNuggets(n - x) for x in [6, 9, 20])
	## test
	# McNuggets(236)
	# True
	# McNuggets(146)
	# True
	# McNuggets(239)
	# True
	# McNuggets(16)
	# False
	def fixedPoint(f, epsilon):
	"""
	f: a function of one argument that returns a float
	epsilon: a small float
	returns the best guess when that guess is less than epsilon
	away from f(guess) or after 100 trials, whichever comes first.
	"""
	guess = 1.0
	for i in range(100):
	if abs(f(guess) - guess) < epsilon:
	return guess
	else:
	guess = f(guess)
	return guess

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