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267b5eff40
* Added doctest and more explanation about Dijkstra execution. * tests were not passing with python2 due to missing __init__.py file at number_theory folder * Removed the dot at the beginning of the imported modules names because 'python3 -m doctest -v data_structures/hashing/*.py' and 'python3 -m doctest -v data_structures/stacks/*.py' were failing not finding hash_table.py and stack.py modules. * Moved global code to main scope and added doctest for project euler problems 1 to 14. * Added test case for negative input. * Changed N variable to do not use end of line scape because in case there is a space after it the script will break making it much more error prone. * Added problems description and doctests to the ones that were missing. Limited line length to 79 and executed python black over all scripts. * Changed the way files are loaded to support pytest call. * Added __init__.py to problems to make them modules and allow pytest execution. * Added project_euler folder to test units execution * Changed 'os.path.split(os.path.realpath(__file__))' to 'os.path.dirname()'
62 lines
1.3 KiB
Python
62 lines
1.3 KiB
Python
# -.- coding: latin-1 -.-
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from math import sqrt
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"""
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Amicable Numbers
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Problem 21
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Let d(n) be defined as the sum of proper divisors of n (numbers less than n
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which divide evenly into n).
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If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and
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each of a and b are called amicable numbers.
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For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55
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and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and
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142; so d(284) = 220.
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Evaluate the sum of all the amicable numbers under 10000.
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"""
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try:
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xrange # Python 2
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except NameError:
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xrange = range # Python 3
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def sum_of_divisors(n):
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total = 0
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for i in xrange(1, int(sqrt(n) + 1)):
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if n % i == 0 and i != sqrt(n):
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total += i + n // i
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elif i == sqrt(n):
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total += i
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return total - n
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def solution(n):
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"""Returns the sum of all the amicable numbers under n.
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>>> solution(10000)
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31626
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>>> solution(5000)
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8442
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>>> solution(1000)
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504
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>>> solution(100)
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0
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>>> solution(50)
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0
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"""
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total = sum(
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[
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i
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for i in range(1, n)
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if sum_of_divisors(sum_of_divisors(i)) == i
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and sum_of_divisors(i) != i
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]
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)
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return total
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if __name__ == "__main__":
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print(solution(int(str(input()).strip())))
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