alignment_paths.py

#Author: Aram Comjean  Dec/ 2015

#http://stackoverflow.com/questions/6667201/how-to-define-two-dimensional-array-in-python
Lookup = [[0 for x in range(50)] for x in range(50)]

def alignment_paths (x,y):

    #if we have a 1x1 matrix or are at the left or top edge, there is one path
    if (x == 0 or y == 0):
        return 1;
    else:
        # try looking up in lookup table
        if Lookup[x][y] !=0:
            return Lookup[x][y]

        # the result is the # number of alignment paths from the 3 adjacent squares
        val = alignment_paths(x-1, y-1) + alignment_paths(x-1, y) + alignment_paths (x, y-1)

        #we have the result, store away value for future use
        Lookup[x][y] = val
        return val

#------------
# Main
#------------
#count paths..  Anything above 12 is really long

for i in range (1,50):
    print i,"x",i,": ",
    print alignment_paths(i,i)