Project Euler 40

problem

Consider the following decimal irrational number obtained by concatenating positive integers in order:

   0.123456789101112131415161718192021...

The 12th decimal place is 1.

Represent the nth decimal place with dn. Find d1 x d10 x d100 x d1000 x d10000 x d100000 x d1000000. http://odz.sakura.ne.jp/projecteuler/index.php?cmd=read&page=Problem%2040

Answer

From the number of digits of each number, which digit is which number can be obtained ...

However, it became annoying, and after simply combining each number as a character string, the specified number of digits of the generated character string was calculated.

def main():
  ans = 1
  ls = ''.join([str(i) for i in range((10**5)*2)])
  for d in [10**j for j in range(7)]:
    ans *= int(ls[d])
  print ans
main()

I tried using log. I thought this would save memory, but it didn't work due to a log bug. It took me about an hour to identify this bug.

from math import log

def main2():
  digits = [10**i for i in range(7)]
  N = 10
  ans = 1
  s = 0
  i = 1
  while digits:
    s += int(log(i,N))+1
    if s >= digits[0]:
      ans *= int(str(i)[digits.pop(0)-s-1])
    i+=1
  print ans
main2()

log bug http://bugs.python.org/issue3724

>>>log(1000,10)
2,9999999999999996

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