euler/python/e090.py

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2021-04-22 03:53:35 +02:00
#
def choose(xs, n):
"""
Computes r choose n, in other words choose n from xs.
Returns combinations and not permutations.
"""
if not xs or n == 0:
return [[]]
if len(xs) == n:
return [xs]
rs = []
x = xs[0]
for r in choose(xs[1:], n - 1):
rs.append([x] + r)
for r in choose(xs[1:], n):
rs.append(r)
return rs
def pairs(xs):
if len(xs) == 2:
return [xs]
r = []
a = xs[0]
for b in xs[1:]:
r.append([a, b])
return r + pairs(xs[1:])
def can_form_squares(pair):
xs, ys = pair
# replace 9s with 6s
for d, e in [(0, 1), (0, 4), (0, 6), (1, 6),
(2, 5), (3, 6), (4, 6), (6, 4), (8, 1)]:
if d in xs and e in ys:
continue
elif e in xs and d in ys:
continue
return False
return True
def euler_090():
# replace 9s with 6s to handle "up-side down usage of 6" without hassle
xs = list(range(0, 9)) + [6]
cs = choose(xs, 6)
ps = pairs(cs)
count = 0
for p in ps:
if can_form_squares(p):
count += 1
return count
if __name__ == "__main__":
solution = euler_090()
print("e090.py: " + str(solution))
assert(solution == 1217)