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957ede8215
Dumbest solution ever, but so fast to implement. And finally runs in less than 2 seconds on my Netbook. I really wonder even why search for optimization. Python int to str conversion is so useful for those problems.
53 lines
1.5 KiB
Python
53 lines
1.5 KiB
Python
#!/usr/bin/env python
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"""
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##---
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# Julien Lengrand-Lambert
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#Created on : 16 - 10 - 2012
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#
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# DESCRIPTION : Solves problem 40 of Project Euler
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An irrational decimal fraction is created by concatenating the positive 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 d_n represents the nth digit of the fractional part, find the value of the following expression.
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d_1 * d_10 * d_100 * d_1000 * d_10000 * d_100000 * d_1000000
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This first version is going to be over dumb. We are actually going to create the fractional part.
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We first need to know how much elements we need to sum.
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##---
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"""
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def el_to_go(max_val=1000000):
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"""
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Returns the maximum number of the range we are going to need to be able to get d_1000000
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"""
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return 1000000 # max index is 100000. Dumbest limit is thus 1000000
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def get_index(myfrac, el):
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"""
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Given the string representation of the fractional part, return the elth element
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"""
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return int(myfrac[el - 1])
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def sum_elements():
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"""
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Returns the value of the following expression.
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d_1 d_10 d_100 d_1000 d_10000 d_100000 d_1000000
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"""
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els_to_go = [1, 10, 100, 1000, 10000, 100000, 1000000]
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max_el = el_to_go()
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sum_res = 1
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frac = ''.join(map(str, range(1, max_el + 1)))
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for el in els_to_go:
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sum_res *= get_index(frac, el)
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return sum_res
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if __name__ == '__main__':
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print "Answer : %d " % (sum_elements())
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