def max_square(anagram_pair):
s1, s2 = anagram_pair
letters = sorted(list(set(s1)))
l = len(letters)
max_val = 0
if l <= 10:
for tup in permutations([str(i) for i in range(10)], l):
number_s1 = s1
number_s2 = s2
for i in xrange(l):
number_s1 = number_s1.replace(letters[i], tup[i])
number_s2 = number_s2.replace(letters[i], tup[i])
if number_s1[0] != "0" and number_s2[0] != "0":
if is_square(int(number_s1)) and is_square(int(number_s2)):
max_val = max(max_val, int(number_s1), int(number_s2))
return max_val
def f(n):
"""
>>> sum(set(map(sum,f(120000))))
30758397
>>> sum(map(sum,f(20000)))
679255
>>> map(sum, f(1000))
[784]
"""
d = defaultdict(set)
for r in range(2, n):
for q in range(1, min(r, n - r)):
if is_square(r * r + r * q + q * q):
for p in d[q] & d[r]:
if p < q and p + q + r <= n:
yield p, q, r
assert p < q < r
d[q].add(r)
d[r].add(q)
def f(n):
"""
c^2d, cbd, b^2d (c < b)
cb^3d^2 + c^2b=m^2
求出所有x = m^2 = cb^3d^2 + c^2b < n (c, b, d, m 为整数)
>>> sum(set(f(10 ** 5)))
124657
>>> sum(set(f(10 ** 12)))
878454337159
"""
for b in count(2):
b3 = b ** 3
if b3 > n:
break
for c in range(1, b):
for d in count(1):
x = c * b3 * d * d + c * c * d
if x > n:
break
if is_square(x):
yield x