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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()'
51 lines
1.0 KiB
Python
51 lines
1.0 KiB
Python
"""
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Problem:
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2520 is the smallest number that can be divided by each of the numbers from 1
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to 10 without any remainder.
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What is the smallest positive number that is evenly divisible(divisible with no
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remainder) by all of the numbers from 1 to N?
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"""
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from __future__ import print_function
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try:
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raw_input # Python 2
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except NameError:
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raw_input = input # Python 3
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""" Euclidean GCD Algorithm """
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def gcd(x, y):
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return x if y == 0 else gcd(y, x % y)
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""" Using the property lcm*gcd of two numbers = product of them """
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def lcm(x, y):
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return (x * y) // gcd(x, y)
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def solution(n):
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"""Returns the smallest positive number that is evenly divisible(divisible
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with no remainder) by all of the numbers from 1 to n.
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>>> solution(10)
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2520
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>>> solution(15)
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360360
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>>> solution(20)
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232792560
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>>> solution(22)
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232792560
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"""
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g = 1
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for i in range(1, n + 1):
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g = lcm(g, i)
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return g
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if __name__ == "__main__":
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print(solution(int(raw_input().strip())))
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