/
p015.py
33 lines (27 loc) · 966 Bytes
/
p015.py
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from itertools import permutations, combinations
from math import factorial as f
def main(): # how many lattice-routes (right, down) are there through a 20x20 grid?
n = (20,20)
path_length = n[0]
'''
# n! ouch!
one_route = [0 for i in xrange(n[0])] + [1 for i in xrange(n[0])] # one-route right:0, down:1
all_routes = set(list(permutations(one_route)))
return len(all_routes)
# this method assumes symmetry for grid
# calculating combinations is much faster than permutations... like n^2 ?
return len(list(combinations(range(path_length*2),path_length)))
'''
# I think we can do better...
# oh duh... we don't need a list of all the paths,
# just get the number -> use math:
# n! / ( r! (n - r)! )
n = path_length*2
r = path_length
ret = f(n)/( f(r) * f(n-r) )
return ret
if __name__ == '__main__':
import boilerplate, time, resource
t = time.time()
r = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss
boilerplate.all(main(), t, r)