mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-07 06:09:28 +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()'
58 lines
1.6 KiB
Python
58 lines
1.6 KiB
Python
"""
|
||
Starting in the top left corner of a 2×2 grid, and only being able to move to
|
||
the right and down, there are exactly 6 routes to the bottom right corner.
|
||
How many such routes are there through a 20×20 grid?
|
||
"""
|
||
from math import factorial
|
||
|
||
|
||
def lattice_paths(n):
|
||
"""
|
||
Returns the number of paths possible in a n x n grid starting at top left
|
||
corner going to bottom right corner and being able to move right and down
|
||
only.
|
||
|
||
bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 50
|
||
1.008913445455642e+29
|
||
bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 25
|
||
126410606437752.0
|
||
bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 23
|
||
8233430727600.0
|
||
bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 15
|
||
155117520.0
|
||
bruno@bruno-laptop:~/git/Python/project_euler/problem_15$ python3 sol1.py 1
|
||
2.0
|
||
|
||
>>> lattice_paths(25)
|
||
126410606437752
|
||
>>> lattice_paths(23)
|
||
8233430727600
|
||
>>> lattice_paths(20)
|
||
137846528820
|
||
>>> lattice_paths(15)
|
||
155117520
|
||
>>> lattice_paths(1)
|
||
2
|
||
|
||
"""
|
||
n = (
|
||
2 * n
|
||
) # middle entry of odd rows starting at row 3 is the solution for n = 1,
|
||
# 2, 3,...
|
||
k = n / 2
|
||
|
||
return int(factorial(n) / (factorial(k) * factorial(n - k)))
|
||
|
||
|
||
if __name__ == "__main__":
|
||
import sys
|
||
|
||
if len(sys.argv) == 1:
|
||
print(lattice_paths(20))
|
||
else:
|
||
try:
|
||
n = int(sys.argv[1])
|
||
print(lattice_paths(n))
|
||
except ValueError:
|
||
print("Invalid entry - please enter a number.")
|