33 lines
810 B
Python
33 lines
810 B
Python
''' An irrational decimal fraction is created by concatenating the positive
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integers:
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0.123456789101112131415161718192021...
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It can be seen that the 12th digit of the fractional part is 1.
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If dn represents the nth digit of the fractional part, find the value of the following expression.
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d1 * d10 * d100 * d1000 * d10000 * d100000 * d1000000 '''
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from math import log10
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def num(x, i):
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if i > int(log10(x)):
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raise IOError
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else:
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i = int(log10(x)) - i
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while i > 0:
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x /= 10
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i -= 1
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return x % 10
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def d(x):
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elem = [0, 9, 189, 2889, 38889, 488889, 5888889, 68888889]
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for i in xrange(len(elem)):
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if elem[i] >= x:
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break
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x -= elem[i - 1] + 1
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return num(10 ** (i - 1) + x / i, x % i)
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multi = 1
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for i in xrange(7):
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multi *= d(10 ** i)
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#print d(10 ** i)
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print multi
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