mirror of
https://github.com/correl/euler.git
synced 2024-11-27 19:19:50 +00:00
45 lines
1,015 B
Python
45 lines
1,015 B
Python
"""Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?
|
|
|
|
Starting in the top left corner of a 22 grid, there are 6 routes (without backtracking) to the bottom right corner.
|
|
[See: p015/p_015.gif]
|
|
|
|
How many routes are there through a 2020 grid?
|
|
"""
|
|
|
|
"""Notes:
|
|
|
|
Calculate the number of possible paths from the top left corner to the bottom
|
|
right, without backtracking (no moving up or left)
|
|
|
|
i.e., for a 2x2 grid:
|
|
_ _
|
|
|_|_|
|
|
|_|_|
|
|
|
|
Paths to each point, forming a Pascal Triangle:
|
|
1 1 1
|
|
1 2 3
|
|
1 3 6
|
|
|
|
001 001 001 001
|
|
001 002 003 004
|
|
001 003 006 010
|
|
001 004 010 020
|
|
"""
|
|
def pascal(row, col):
|
|
val = 1
|
|
r = row + 1
|
|
for c in range(1, col + 1):
|
|
val = (val * ((r - c) / float(c)))
|
|
return int(val)
|
|
def paths(size):
|
|
return pascal(size + (size - 2), size - 1)
|
|
|
|
def main():
|
|
# 20x20 grid
|
|
# Points = cubes + 1
|
|
size = 21
|
|
print 'Paths: ', paths(size)
|
|
|
|
if __name__ == '__main__':
|
|
main()
|