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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()'
61 lines
1.1 KiB
Python
61 lines
1.1 KiB
Python
"""
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Counting Summations
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Problem 76
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It is possible to write five as a sum in exactly six different ways:
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4 + 1
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3 + 2
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3 + 1 + 1
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2 + 2 + 1
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2 + 1 + 1 + 1
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1 + 1 + 1 + 1 + 1
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How many different ways can one hundred be written as a sum of at least two
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positive integers?
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"""
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from __future__ import print_function
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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 partition(m):
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"""Returns the number of different ways one hundred can be written as a sum
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of at least two positive integers.
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>>> partition(100)
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190569291
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>>> partition(50)
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204225
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>>> partition(30)
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5603
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>>> partition(10)
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41
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>>> partition(5)
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6
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>>> partition(3)
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2
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>>> partition(2)
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1
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>>> partition(1)
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0
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"""
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memo = [[0 for _ in xrange(m)] for _ in xrange(m + 1)]
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for i in xrange(m + 1):
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memo[i][0] = 1
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for n in xrange(m + 1):
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for k in xrange(1, m):
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memo[n][k] += memo[n][k - 1]
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if n > k:
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memo[n][k] += memo[n - k - 1][k]
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return memo[m][m - 1] - 1
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if __name__ == "__main__":
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print(partition(int(str(input()).strip())))
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