def test_pytriplets_2_c_lt300():
"""Testing pytriples with c values less than 100"""
vals = set()
gen = pytriple_gen(300)
while len(vals) < len(lt300):
vals.add(next(gen))
assert vals == lt300
def p009():
"""
for each possible pythagorean triplet:
if 1000 is divisible by the sum of the triplet:
RETURN: multiply product and the multiplier cubed
"""
for tri in pytriple_gen(int(1000 // 2)):
if 1000 % sum(tri) == 0:
return iter_product(tri) * (1000 // sum(tri))**3
def pytiles(max_perimeter):
"""
we are looking for triangles where the hypotenuse is divisible by the side
mag of the inner square, which is the difference in the RAT legs,
:param max_perimeter: max right triangle perimeter
:return: number of triangles
"""
count = 0
for tri in pytriple_gen(max_perimeter // 2):
if tri[2] % (tri[1] - tri[0]) == 0:
count += max_perimeter // sum(tri)
return count
def almost_equilateral(max_perimeter):
"""
Generates almost equilateral triangles
Almost-equilateral-triangles (AET):
A triangle for which two sides are equal and the third differs by no
more than one unit.
An AET is really just 2 pythag-triple-triangles (back 2 back), where double
the shortest leg in the triple +/-1 is equal to the hypotenuse (c). For an
AET max perimeter of p, we look at pythagorean triples with c < p/3.
"""
return ((tri[0] * 2, tri[-1], tri[-1])
for tri in pytriple_gen((max_perimeter + 3) // 3)
if abs(tri[-1] - (tri[0] * 2)) == 1)
def test_pytriplets_c_lt300(self):
"""
"""
p_set = {t for t in pytriple_gen(300)}
assert self.lt300 == p_set
def test_pytriplets_c_lt100(self):
"""
Testing the primative pytriplet generator
"""
p_set = {t for t in pytriple_gen(100)}
assert self.lt100 == p_set
from math import sqrt
from pupy.maths import pytriple_gen
def tri_area(two_sides_len, other_side_length):
return (sqrt(two_sides_len**2 - (other_side_length / 2.0)**2) *
(other_side_length / 2.0)) % 1 == 0
print sum(
sum(triple) for triple in [(tri[0] * 2, tri[2], tri[2]) for tri in [
x for x in pytriple_gen((3 + 10**9) // 3) if abs(x[2] - 2 * x[0]) == 1
]])
# sum = 0
# for i in range(2, 1000000000//3):
# if tri_area(i, i+1):
# sum += 3*i+1
# if tri_area(i, i-1):
# sum += 3*i -1
#
# print sum
def test_pytriplets_2_c_lt100():
"""Testing pytriples with c values less than 100"""
assert lt100 == set(pytriple_gen(100))
def test_pytriplets_c_lt300():
"""Testing pytriples with c values less than 100"""
p_set = {t for t in pytriple_gen(300)}
assert lt300 == p_set
def test_pytriplets_c_lt100():
"""Testing pytriples with c values less than 100"""
assert {t for t in pytriple_gen(100)} == lt100