Problem 027, Incomplete

e027.py

@@ -0,0 +1,72 @@
+"""Find the value of d < 1000 for which 1/d contains the longest recurring cycle.A unit fraction contains 1 in the numerator.
+
+The decimal representation of the unit fractions with denominators 2 to 10 are given:
+    1/2	= 	0.5
+    1/3	= 	0.(3)
+    1/4	= 	0.25
+    1/5	= 	0.2
+    1/6	= 	0.1(6)
+    1/7	= 	0.(142857)
+    1/8	= 	0.125
+    1/9	= 	0.(1)
+    1/10	= 	0.1
+Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
+
+Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
+"""
+
+from decimal import Decimal
+from e003 import pfactor
+
+def coprime(a, b):
+    """Are integers a and b coprime?"""
+
+    primes_a = pfactor(a)
+    primes_b = pfactor(b)
+    primes = [p for p in primes_a if p in primes_b]
+    return bool(primes)
+
+def period_length(numerator, denominator):
+    """Determine the period length of a non-terminating decimal"""
+    
+    length = None
+    numerator = Decimal(numerator)
+    denominator = Decimal(denominator)
+    if numerator == 1:
+        if denominator == 1:
+            return 1
+        primes = pfactor(int(denominator))
+        
+        """
+        From Wikipedia:
+            Terminating decimals represent rational numbers of the form
+            k/2^n5^m
+
+            However, a terminating decimal also has a representation as a
+            repeating decimal, obtained by decreasing the final (nonzero)
+            digit by one and appending an infinitely repeating sequence of
+            nines. 1 = 0.999999... and 1.585 = 1.584999999... are two
+            examples of this.
+        """
+        if len([p for p in primes if p not in [2, 5]]) == 0:
+            return 1
+
+        if coprime(denominator, 10):
+            pass
+    else:
+        raise Exception('Non-reciprocal period detection not yet implemented')
+    return length
+
+def main():
+    MAX = 10
+    longest_cycle = 0
+    for i in xrange((MAX), 1, -1):
+        # The period of 1/k for integer k is always ² k ? 1.
+        if longest_cycle >= i:
+            break
+        
+        cycle = period_length(1, i)
+        fraction = Decimal(1) / Decimal(i)
+        print '1/{0} = {1} ({2})'.format(i, fraction, cycle), fraction.is_subnormal()
+if __name__ == '__main__':
+    main()