def bell():
"""Bell or exponential numbers: number of ways to partition a set of n labeled elements.
"""
blist, b = [1], 1
yield 1
yield 1
while True:
blist = list(itertools2.accumulate([b]+blist))
b = blist[-1]
yield b
def bell():
"""Bell or exponential numbers: number of ways to partition a set of n labeled elements.
"""
blist, b = [1], 1
yield 1
yield 1
while True:
blist = list(itertools2.accumulate([b]+blist))
b = blist[-1]
yield b
def is_perfect(n):
"""
:return: -1 if n is deficient, 0 if perfect, 1 if abundant
:see: https://en.wikipedia.org/wiki/Perfect_number,
https://en.wikipedia.org/wiki/Abundant_number,
https://en.wikipedia.org/wiki/Deficient_number
"""
# return sign(abundance(n)) #simple, but might be slow for large n
for s in itertools2.accumulate(divisors(n)):
if s>2*n:
return 1
return 0 if s==2*n else -1
def is_perfect(n):
"""
:return: -1 if n is deficient, 0 if perfect, 1 if abundant
:see: https://en.wikipedia.org/wiki/Perfect_number,
https://en.wikipedia.org/wiki/Abundant_number,
https://en.wikipedia.org/wiki/Deficient_number
"""
# return sign(abundance(n)) #simple, but might be slow for large n
for s in itertools2.accumulate(divisors(n)):
if s > 2 * n:
return 1
return 0 if s == 2 * n else -1
def accumulate(self, op=operator.add, init=[]):
return Sequence(chain(init, itertools2.accumulate(self, op, False)))
def accumulate(self,op,skip_first=False):
return Sequence(itertools2.accumulate(self,op,skip_first))
def accumulate(self,op=operator.add,skip_first=False):
return Sequence(itertools2.accumulate(self,op,skip_first))