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

@@ -0,0 +1,75 @@
+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))