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"""
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.
"""
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"""
x += 2 x = x + 2
x -= 3 x = x - 3
(+=, -=, *=, /=, //=, %=, **=, <<=, >>=, &=, ^=, |=)
"""
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def findDecimalRepeatingSequence(num, den, searchDepth):
"""For a fraction num/den, returns the decimal repeating sequence, up to searchDepth in length.
Otherwise returns None. Can be modified to also return the division result."""
reps = []
rep =[]
result = []
resNum = num // den
num = (num-resNum*den)*10
while len(result) < searchDepth:
resNum = num // den
rep = [num,resNum,den]
if rep not in reps:
result.append(resNum)
reps.append(rep)
num = (num-resNum*den)*10
else:
return result
return None
def maxRepSeqBelowD(d,sD):
"""Returns maximum repeating decimal sequence for 1/d."""
currSeq = []
lenCurrSeq = 0
currI = 0
for i in range(1,d):
seq = findDecimalRepeatingSequence(1,i,sD)
if seq:
seqlen = len(seq)
if seqlen > lenCurrSeq:
currSeq = seq
lenCurrSeq = seqlen
currI = i
return currI
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maxRepSeqBelowD(1000,1000)
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