def cuboid_routes(m):
total = 0
maxhp = sqrt(1 + (5 * (m**2)))
for p in pytriple_gen(maxhp):
trip = Vuple(p)
while trip[0] <= m:
cubs = set()
for i in range(1, trip[0]):
c = tuple(sorted([i, trip[0] - i, trip[1]]))
if max(c) <= m:
cubs.add(c)
if trip[1] - trip[0] <= trip[0]:
for i in range(trip[1] - trip[0], (trip[1] // 2) + 2):
cubs.add(tuple(sorted([trip[0], trip[1] - i, i])))
total += len(cubs)
trip += Vuple(p)
return total
def highway_dragon(max_order=50, steps=10**16):
dirs = {
0: Vuple((0, 1)),
1: Vuple((1, 0)),
2: Vuple((0, -1)),
3: Vuple((-1, 0))
}
def clockwise(heading):
if heading == 3:
return 0
else:
return heading + 1
def counterclockwise(heading):
if heading == 0:
return 3
else:
return heading - 1
def dee(cur_order, highway, pos=Vuple((0, 0)), heading=0, step=0):
for h in highway:
# print(h)
if h == 'F':
pos += dirs[heading]
step += 1
print(step, pos, heading)
# if step == steps:
if h == 'L':
heading = counterclockwise(heading)
if h == 'R':
heading = clockwise(heading)
if cur_order < max_order:
if h == 'a':
pos, step, heading = dee(cur_order + 1, 'aRbFR', pos,
heading, step)
if h == 'b':
pos, step, heading = dee(cur_order + 1, 'LFaLb', pos,
heading, step)
return pos, step, heading
curlevel = 0
start = 'Fa'
d = ''
dee(0, start)
def dee(cur_order, highway, pos=Vuple((0, 0)), heading=0, step=0):
for h in highway:
# print(h)
if h == 'F':
pos += dirs[heading]
step += 1
print(step, pos, heading)
# if step == steps:
if h == 'L':
heading = counterclockwise(heading)
if h == 'R':
heading = clockwise(heading)
if cur_order < max_order:
if h == 'a':
pos, step, heading = dee(cur_order + 1, 'aRbFR', pos,
heading, step)
if h == 'b':
pos, step, heading = dee(cur_order + 1, 'LFaLb', pos,
heading, step)
return pos, step, heading
def test_gt(self):
a = Vuple((12, 3))
b = Vuple((7, 5))
assert a > b
def test_angle_degrees(self):
v1 = Vuple((10, 10))
v2 = Vuple((1, 0))
assert 45 == round(Vuple.angle(v1, v2, radians=False))
def test_angle_radians(self):
v1 = Vuple((10, 10))
v2 = Vuple((1, 0))
assert 3.1415926535897936 == (4 * Vuple.angle(v1, v2))
def test_unit_vuple(self):
v = Vuple((3, 4))
assert (0.6, 0.8) == Vuple.unit_vuple(v)
v = Vuple((3, 4))
assert (0.6, 0.8) == v.normalize()
def test_idiv_scalar(self):
v = Vuple((6, 8))
v /= 2
assert (3, 4) == v
def test_imul_scalar(self):
v = Vuple((3, 4))
v *= 2
assert (6, 8) == v
def test_mul_scalar(self):
v = Vuple((3, 4))
v = (v * 2)
assert (6, 8) == v
def test_mag(self):
assert 5.0 == Vuple.mag((3, 4))
assert 5 == Vuple((3, 4)).get_mag()
def test_sub(self):
a = Vuple((12, 3))
b = Vuple((7, 5))
assert Vuple((5, -2)) == a - b
assert Vuple((-5, 2)) == b - a
def test_add(self):
a = Vuple((12, 3))
b = Vuple((7, 5))
assert Vuple((19, 8)) == a + b
def test_origin_not_in_triangle(self):
tri = Trigon((-175, 41), (-421, -714), (574, -645))
assert Vuple((0, 0)) not in tri
assert tri.contains_origin() == False
def test_div_scalar(self):
v = Vuple((6, 8)) / 2
assert (3, 4) == v
def point_prob(x, y):
v1 = (xz - x, y)
v2 = (x, yz - y)
return Vuple.angle(v2, v1, radians=False)
def __init__(self, toop):
self.min_xyz = Vuple(toop[:3])
self.dxyz = Vuple(toop[3:])
self.max_xyz = self.min_xyz + Vuple(toop[3:])
self.vol = list_product(self.dxyz)