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* 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
1.1 KiB
Python
51 lines
1.1 KiB
Python
# -.- coding: latin-1 -.-
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"""
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Combinatoric selections
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Problem 53
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There are exactly ten ways of selecting three from five, 12345:
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123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
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In combinatorics, we use the notation, 5C3 = 10.
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In general,
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nCr = n!/(r!(n−r)!),where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.
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It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
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How many, not necessarily distinct, values of nCr, for 1 ≤ n ≤ 100, are greater
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than one-million?
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"""
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from __future__ import print_function
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from math import factorial
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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 combinations(n, r):
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return factorial(n) / (factorial(r) * factorial(n - r))
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def solution():
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"""Returns the number of values of nCr, for 1 ≤ n ≤ 100, are greater than
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one-million
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>>> solution()
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4075
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"""
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total = 0
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for i in xrange(1, 101):
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for j in xrange(1, i + 1):
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if combinations(i, j) > 1e6:
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total += 1
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return total
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if __name__ == "__main__":
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print(solution())
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