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Non-transitive dice: Difference between revisions
→{{header|Python}}: supersede with faster solution
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=={{header|Python}}==
Trivial rotations of the same loop are not shown. It should not be difficult to mentally picture them.
<lang python>from itertools import combinations_with_replacement as cmbr
from time import time
def dice_gen(n, faces, m):
dice = list(cmbr(faces, n))
succ = [set(j for j, b in enumerate(dice)
if j != i and sum((x>y) - (x<y) for x in a for y in b) > 0)
for i, a in enumerate(dice)]
def loops(seq, s, depth):
if not depth:
if seq[0] in s:
yield seq
else:
for d in (x for x in s if x > seq[0]):
yield from loops(seq + (d,), succ[d], depth - 1)
yield from (tuple(''.join(dice[s]) for s in x)
for i, v in enumerate(succ)
for x in loops((i,), v, m - 1))
t = time()
for n, faces, loop_len in [(4, '1234', 3), (4, '1234', 4), (6, '123456', 3), (6, '1234567', 3)]:
for i, x in enumerate(dice_gen(n, faces, loop_len)): pass
print(f'{n}-sided, markings {faces}, loop length {loop_len}:')
print(f'\t{i + 1}*{loop_len} solutions, e.g. {" > ".join(x)} > [loop]')
t, t0 = time(), t
print(f'\ttime: {t - t0:.4f} seconds\n')</lang>
{{out}}
<pre>4-sided, markings 1234, loop length 3:
1*3 solutions, e.g. 1144 > 1333 > 2224 > [loop]
time: 0.0000 seconds
4-sided, markings 1234, loop length 4:
1*4 solutions, e.g. 1144 > 1333 > 2233 > 2224 > [loop]
time: 0.0100 seconds
6-sided, markings 123456, loop length 3:
40666*3 solutions, e.g. 335666 > 555556 > 444666 > [loop]
time: 1.1459 seconds
6-sided, markings 1234567, loop length 3:
423063*3 solutions, e.g. 446777 > 666667 > 555777 > [loop]
time: 6.9465 seconds</pre>
===Alternative===
<lang python>from collections import namedtuple
from itertools import permutations, product
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