mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-25 04:30:15 +00:00
56 lines
1.5 KiB
Python
56 lines
1.5 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.")
|