Data commit

Task/Vampire-number/Python/vampire-number-1.py

@@ -0,0 +1,77 @@
+from __future__ import division
+
+import math
+from operator import mul
+from itertools import product
+from functools import reduce
+
+
+def fac(n):
+    '''\
+    return the prime factors for n
+    >>> fac(600)
+    [5, 5, 3, 2, 2, 2]
+    >>> fac(1000)
+    [5, 5, 5, 2, 2, 2]
+    >>>
+    '''
+    step = lambda x: 1 + x*4 - (x//2)*2
+    maxq = int(math.floor(math.sqrt(n)))
+    d = 1
+    q = n % 2 == 0 and 2 or 3
+    while q <= maxq and n % q != 0:
+        q = step(d)
+        d += 1
+    res = []
+    if q <= maxq:
+        res.extend(fac(n//q))
+        res.extend(fac(q))
+    else: res=[n]
+    return res
+
+def fact(n):
+    '''\
+    return the prime factors and their multiplicities for n
+    >>> fact(600)
+    [(2, 3), (3, 1), (5, 2)]
+    >>> fact(1000)
+    [(2, 3), (5, 3)]
+    >>>
+    '''
+    res = fac(n)
+    return [(c, res.count(c)) for c in set(res)]
+
+def divisors(n):
+    'Returns all the divisors of n'
+    factors = fact(n)   # [(primefactor, multiplicity), ...]
+    primes, maxpowers = zip(*factors)
+    powerranges = (range(m+1) for m in maxpowers)
+    powers = product(*powerranges)
+    return (
+        reduce(mul,
+               (prime**power for prime, power in zip(primes, powergroup)),
+               1)
+        for powergroup in powers)
+
+def vampire(n):
+    fangsets = set( frozenset([d, n//d])
+                    for d in divisors(n)
+                    if (len(str(d)) == len(str(n))/2.
+                        and sorted(str(d) + str(n//d)) == sorted(str(n))
+                        and (str(d)[-1] == 0) + (str(n//d)[-1] == 0) <=1) )
+    return sorted(tuple(sorted(fangs)) for fangs in fangsets)
+
+
+if __name__ == '__main__':
+    print('First 25 vampire numbers')
+    count = n = 0
+    while count <25:
+        n += 1
+        fangpairs = vampire(n)
+        if fangpairs:
+            count += 1
+            print('%i: %r' % (n, fangpairs))
+    print('\nSpecific checks for fangpairs')
+    for n in (16758243290880, 24959017348650, 14593825548650):
+        fangpairs = vampire(n)
+        print('%i: %r' % (n, fangpairs))

Task/Vampire-number/Python/vampire-number-2.py

@@ -0,0 +1,23 @@
+from math import sqrt
+from itertools import imap, ifilter, islice, count
+
+def factor_pairs(n):
+    return ((x, n // x) for x in xrange(2, int(sqrt(n))) if n % x == 0)
+
+def fangs(n):
+    dlen = lambda x: len(str(x))
+    half = dlen(n) // 2
+    digits = lambda (x, y): sorted(str(x) + str(y))
+    halvesQ = lambda xs: all(y == half for y in imap(dlen, xs))
+    dn = sorted(str(n))
+    return [p for p in factor_pairs(n) if halvesQ(p) and dn==digits(p)]
+
+def vampiricQ(n):
+    fn = fangs(n)
+    return (n, fn) if fn else None
+
+for v in islice(ifilter(None, imap(vampiricQ, count())), 0, 25):
+    print v
+
+for n in [16758243290880, 24959017348650, 14593825548650]:
+    print vampiricQ(n) or str(n) + " is not vampiric."