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import math
class sieve:
def __init__(self, limit):
self.limit = limit
self.number_list = [False] + [True]*(self.limit-1)
self.list_len = len(self.number_list)
def next_prime(self, i):
x = i+1
while(x <= self.list_len):
if self.number_list[x-1] == True:
break
x += 1
return x
def primes(self):
i = 2
while(i*i <= self.list_len):
x = i*i
while(x <= self.list_len):
self.number_list[x-1] = False
x += i
i = self.next_prime(i)
primeset = set()
for i in xrange(1, self.limit+1):
if self.number_list[i-1]:
primeset.add(i)
return primeset
class pandigital:
# create n-digit pandigital numbers
def __init__(self, start, end):
self.digits = set()
for d in range(start, end+1):
self.digits.add(d)
# return set of digits that are not in x
def missing(self, x):
d = set()
while x > 0:
d.add(x % 10)
x /= 10
return self.digits - d
def numbers(self, r):
result = set()
result |= self.digits
for i in range(2, r):
new = set()
for x in result:
for y in self.missing(x):
new.add(x*10 + y)
result |= new
return result
def ggt(a, b): # Stein's algorithm
k = 0
t = 0
while a&1==0 and b&1==0:
a = a>>1
b = b>>1
k += 1
if a&1==1:
t = -b
else:
t = a
while t != 0:
while t&1==0:
t = t>>1
if t>0:
a = t
else:
b = -t
t = a - b
return a*(1<<k)
def composite(n): # check if n = c^b
primes = sieve(int(math.sqrt(n))+1).primes()
for c in primes:
number = c
while number < n:
number *= c
if number == n:
return True
return False
def order(n, r):
res = n % r
k = 1
while res != 1:
res = (res * n) % r
k += 1
return k
def phi(x):
primes = sieve(x+1).primes()
product = x
for p in primes:
if x % p != 0:
continue
product *= (1 - 1.0/p)
return int(product)
def prime_test(n): # aks test
if composite(n):
return False
logn = math.log(n, 2)
o = 0
r = 0
while o <= logn:
r += 1
o = order(n, r)
a = 1
while a <= r:
g = ggt(a, n)
if g < n and g > 1:
return False
a += 1
if n <= r*r:
return True
#for a in xrange(1, math.floor(math.sqrt(phi(r))*logn)):
# # TODO if math.pow(x+a, n) !=
return True
def permutation(p, q): # checks whether p is a permuation of q
digits_p = [0]*10
digits_q = [0]*10
while p > 0:
digit = p % 10
digits_p[digit] += 1
p /= 10
while q > 0:
digit = q % 10
digits_q[digit] += 1
q /= 10
return digits_p == digits_q
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