def pythagorean_triples(n=None):
"""Generate n Pythagorean triples ordered by the value of c ascending. If n
is None or not given, generate infinitly. Default is None.
Examples:
>>> list(pythagorean_triples(5))
[(3, 4, 5), (5, 12, 13), (15, 8, 17), (7, 24, 25), (21, 20, 29)]
"""
iterator = _count() if n is None else range(n)
iterator = iter(iterator)
base_mat = ((1, 2, 2),
(2, 1, 2),
(2, 2, 3))
multiplier = ((1, -1, 1), (1, 1, 1), (-1, 1, 1))
matrices = []
for multip in multiplier:
mat = []
for row, elem in zip(base_mat, multip):
mat.append(tuple(map(lambda e: e * elem, row)))
matrices.append(tuple(mat))
matrices = tuple(matrices)
heap = [(5, (3, 4, 5))]
for i in iterator:
_, triple = _heappop(heap)
yield triple
for matrix in matrices:
next_triple = tuple(map(lambda col: sum(_starmap(_mul,
zip(triple, col))), zip(*matrix)))
_heappush(heap, (next_triple[2], next_triple))
def elements(self):
# apply repeat function on each item
# chained inputs from a single iterabe
# iteritems()
# Return an iterator over the dictionary's (key, value) pairs.
# items()
# Return a copy of dictionary's list of (key, value) pairs.
return _chain.from_iterable(_starmap(_repeat, self.iteritems()))
def elements(self):
"""Iterator over elements repeating each as many times as its count.
>>> c = Counter('ABCABC')
>>> sorted(c.elements())
['A', 'A', 'B', 'B', 'C', 'C']
# Knuth's example for prime factors of 1836: 2**2 * 3**3 * 17**1
>>> prime_factors = Counter({2: 2, 3: 3, 17: 1})
>>> product = 1
>>> for factor in prime_factors.elements(): # loop over factors
... product *= factor # and multiply them
>>> product
1836
Note, if an element's count has been set to zero or is a negative
number, elements() will ignore it.
"""
return _chain.from_iterable(_starmap(_repeat, self.iteritems()))
def elements(self):
'''Iterator over elements repeating each as many times as its count.
>>> c = Counter('ABCABC')
>>> sorted(c.elements())
['A', 'A', 'B', 'B', 'C', 'C']
# Knuth's example for prime factors of 1836: 2**2 * 3**3 * 17**1
>>> prime_factors = Counter({2: 2, 3: 3, 17: 1})
>>> product = 1
>>> for factor in prime_factors.elements(): # loop over factors
... product *= factor # and multiply them
>>> product
1836
Note, if an element's count has been set to zero or is a negative
number, elements() will ignore it.
'''
# Emulate Bag.do from Smalltalk and Multiset.begin from C++.
return _chain.from_iterable(_starmap(_repeat, self.items()))
def elements(self):
'''Iterator over elements repeating each as many times as its count.
>>> from scikits.crab.utils.counter import Counter
>>> c = Counter('ABCABC')
>>> sorted(c.elements())
['A', 'A', 'B', 'B', 'C', 'C']
# Knuth's example for prime factors of 1836: 2**2 * 3**3 * 17**1
>>> prime_factors = Counter({2: 2, 3: 3, 17: 1})
>>> product = 1
>>> for factor in prime_factors.elements(): # loop over factors
... product *= factor # and multiply them
>>> product
1836
Note, if an element's count has been set to zero or is a negative
number, elements() will ignore it.
'''
# Emulate Bag.do from Smalltalk and Multiset.begin from C++.
return _chain.from_iterable(_starmap(_repeat, self.iteritems()))
def elements(self):
return _chain.from_iterable(_starmap(_repeat, self.iteritems()))
def transform_items_to_values(dct, func):
""" apply a function to each value
"""
return dict(zip(dct.keys(), _starmap(func, dct.items())))
def elements(self):
return _chain.from_iterable(_starmap(_repeat, self.iteritems()))
def elements(self):
'Iterator returning each element as many times as its multiplicity.'
return _chain.from_iterable(_starmap(_repeat, self._ms.items()))