def triples():
""" generates all Pythagorean triplets triplets x<y<z
sorted by hypotenuse z, then longest side y
"""
prim=[] #list of primitive triples up to now
key=lambda x:(x[2],x[1])
samez=SortedCollection(key=key) # temp triplets with same z
buffer=SortedCollection(key=key) # temp for triplets with smaller z
for pt in primitive_triples():
z=pt[2]
if samez and z!=samez[0][2]: #flush samez
while samez:
yield samez.pop(0)
samez.insert(pt)
#build buffer of smaller multiples of the primitives already found
for i,pm in enumerate(prim):
p,m=pm[0:2]
while True:
mz=m*p[2]
if mz < z:
buffer.insert(tuple(m*x for x in p))
elif mz == z:
# we need another buffer because next pt might have
# the same z as the previous one, but a smaller y than
# a multiple of a previous pt ...
samez.insert(tuple(m*x for x in p))
else:
break
m+=1
prim[i][1]=m #update multiplier for next loops
while buffer: #flush buffer
yield buffer.pop(0)
prim.append([pt,2]) #add primitive to the list
def sorted_iterable(iterable, key=None, buffer=100):
"""sorts an almost sorted (infinite) iterable
:param iterable: iterable
:param key: function used as sort key
:param buffer: int size of buffer. elements to swap should not be further than that
"""
from Goulib.container import SortedCollection
b=SortedCollection(key=key)
for x in iterable:
if len(b)>=buffer:
yield b.pop(0)
b.insert(x)
for x in b: yield x # this never happens if iterable is infinite
def sorted_iterable(iterable, key=None, buffer=100):
"""sorts an "almost sorted" (infinite) iterable
:param iterable: iterable
:param key: function used as sort key
:param buffer: int size of buffer. elements to swap should not be further than that
"""
key = key or identity
from Goulib.container import SortedCollection
b = SortedCollection(key=key)
for x in iterable:
if len(b) >= buffer:
res = b.pop(0)
yield res
b.insert(x)
for x in b: # this never happens if iterable is infinite
yield x
def primitive_triples():
""" generates primitive Pythagorean triplets x<y<z
sorted by hypotenuse z, then longest side y
through Berggren's matrices and breadth first traversal of ternary tree
:see: https://en.wikipedia.org/wiki/Tree_of_primitive_Pythagorean_triples
"""
key = lambda x: (x[2], x[1])
triples = SortedCollection(key=key)
triples.insert([3, 4, 5])
A = [[1, -2, 2], [2, -1, 2], [2, -2, 3]]
B = [[1, 2, 2], [2, 1, 2], [2, 2, 3]]
C = [[-1, 2, 2], [-2, 1, 2], [-2, 2, 3]]
while triples:
(a, b, c) = triples.pop(0)
yield (a, b, c)
# expand this triple to 3 new triples using Berggren's matrices
for X in [A, B, C]:
triple = [
sum(x * y for (x, y) in zip([a, b, c], X[i])) for i in range(3)
]
if triple[0] > triple[1]: # ensure x<y<z
triple[0], triple[1] = triple[1], triple[0]
triples.insert(triple)
def primitive_triples():
""" generates primitive Pythagorean triplets x<y<z
sorted by hypotenuse z, then longest side y
through Berggren's matrices and breadth first traversal of ternary tree
:see: https://en.wikipedia.org/wiki/Tree_of_primitive_Pythagorean_triples
"""
key=lambda x:(x[2],x[1])
triples=SortedCollection(key=key)
triples.insert([3,4,5])
A = [[ 1,-2, 2], [ 2,-1, 2], [ 2,-2, 3]]
B = [[ 1, 2, 2], [ 2, 1, 2], [ 2, 2, 3]]
C = [[-1, 2, 2], [-2, 1, 2], [-2, 2, 3]]
while triples:
(a,b,c) = triples.pop(0)
yield (a,b,c)
# expand this triple to 3 new triples using Berggren's matrices
for X in [A,B,C]:
triple=[sum(x*y for (x,y) in zip([a,b,c],X[i])) for i in range(3)]
if triple[0]>triple[1]: # ensure x<y<z
triple[0],triple[1]=triple[1],triple[0]
triples.insert(triple)
def triples():
""" generates all Pythagorean triplets triplets x<y<z
sorted by hypotenuse z, then longest side y
"""
prim = [] #list of primitive triples up to now
key = lambda x: (x[2], x[1])
samez = SortedCollection(key=key) # temp triplets with same z
buffer = SortedCollection(key=key) # temp for triplets with smaller z
for pt in primitive_triples():
z = pt[2]
if samez and z != samez[0][2]: #flush samez
while samez:
yield samez.pop(0)
samez.insert(pt)
#build buffer of smaller multiples of the primitives already found
for i, pm in enumerate(prim):
p, m = pm[0:2]
while True:
mz = m * p[2]
if mz < z:
buffer.insert(tuple(m * x for x in p))
elif mz == z:
# we need another buffer because next pt might have
# the same z as the previous one, but a smaller y than
# a multiple of a previous pt ...
samez.insert(tuple(m * x for x in p))
else:
break
m += 1
prim[i][1] = m #update multiplier for next loops
while buffer: #flush buffer
yield buffer.pop(0)
prim.append([pt, 2]) #add primitive to the list