def genPerms():
"""Create the 9! permutations of the digits 1-9.
>>> from euler32 import genPerms
>>> permList= list(genPerms())
>>> len(permList) # 9! = 362880
362880
>>> permList[:2]
[[1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 9, 8]]
>>> permList[-2:]
[[9, 8, 7, 6, 5, 4, 3, 1, 2], [9, 8, 7, 6, 5, 4, 3, 2, 1]]
"""
permN= Permutation( range(1,10) ) # 1 to 9
return permN.nextPerm()
def PDSD_gen():
"""Generate pan-digital numbers with the substring divisibility property.
The number is represented as a sequence of digits.
>>> from euler43 import PDSD_gen
>>> numbers= list( PDSD_gen() )
>>> 1406357289 in numbers
True
>>> numbers
[1406357289, 1430952867, 1460357289, 4106357289, 4130952867, 4160357289]
"""
pandigital10= Permutation(range(10))
for i in pandigital10.nextPerm():
if substringDivisibility(i):
yield number(i)
def pandigitalPrimes(size):
"""Generate all pan-digital primes of a given size.
>>> from euler41 import pandigitalPrimes
>>> pd4 = list( pandigitalPrimes(4) )
>>> 2143 in pd4
True
>>> pd4
[1423, 2143, 2341, 4231]
"""
permN= Permutation( range(1,size+1) )
for p in permN.nextPerm():
ld= p[-1]
if ld % 2 == 0: continue # skip even numbers
if ld == 5: continue # skip 5's, also
n= number( p )
if isprime(n):
yield n