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"""
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.")