http://tafakuri.net/?p=66
def num_paths_to_grid_bottom(numRowCells, numColumnCells):
currRow = [1 for x in range(numColumnCells + 1)]
# the number of nodes to consider = numRowCells + 1
for numRow in range(1, numRowCells + 1):
for numColumn in range(1, numColumnCells + 1):
currRow[numColumn] += currRow[numColumn - 1]
return currRow[numColumnCells]
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