mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
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
1.1 KiB
Python
51 lines
1.1 KiB
Python
# -.- coding: latin-1 -.-
|
||
"""
|
||
Combinatoric selections
|
||
Problem 53
|
||
|
||
There are exactly ten ways of selecting three from five, 12345:
|
||
|
||
123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
|
||
|
||
In combinatorics, we use the notation, 5C3 = 10.
|
||
|
||
In general,
|
||
|
||
nCr = n!/(r!(n−r)!),where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.
|
||
It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
|
||
|
||
How many, not necessarily distinct, values of nCr, for 1 ≤ n ≤ 100, are greater
|
||
than one-million?
|
||
"""
|
||
from __future__ import print_function
|
||
from math import factorial
|
||
|
||
try:
|
||
xrange # Python 2
|
||
except NameError:
|
||
xrange = range # Python 3
|
||
|
||
|
||
def combinations(n, r):
|
||
return factorial(n) / (factorial(r) * factorial(n - r))
|
||
|
||
|
||
def solution():
|
||
"""Returns the number of values of nCr, for 1 ≤ n ≤ 100, are greater than
|
||
one-million
|
||
|
||
>>> solution()
|
||
4075
|
||
"""
|
||
total = 0
|
||
|
||
for i in xrange(1, 101):
|
||
for j in xrange(1, i + 1):
|
||
if combinations(i, j) > 1e6:
|
||
total += 1
|
||
return total
|
||
|
||
|
||
if __name__ == "__main__":
|
||
print(solution())
|