"""
Rows of Pascal's Triangle
See:
http://en.wikipedia.org/wiki/Pascal%27s_triangle
"Calculating an individual row"
Consider a row starting as follows:
1, 12...
Initialize to [1] and multiply by (row_num/1)
to get the next term, row[1].
Then decrement and increment again, getting
(11 / 2), (10 / 3), (9 / 4) and so forth, and multiply
by the last term so far. Stop when the numerator
is 0.
1 * (12/1) = 12
12 * (11 / 2) = 66
66 * (10 / 3) = 220
220 * (9 / 4) = 495
etc.
This is another way of computing successive values
of C(n, k) without using a factorial function and
dividing.
Independently discovered by David Koski,
implemented in Python by Kirby Urner
"""
def pascal_row(row_num):
numer = row_num
denom = 1
# initialize row of Pascal's Triangle
row = [1]
while numer > 0:
row.append((row[-1] * numer/denom))
numer -= 1 # decrement numerator
denom += 1 # increment denominator
return row
def pascal_mod2(row_num = 0):
"""
row integers mod 2, give a binary string which
corresponds to Rule 60 in the Wolfram categorization
scheme for cellular automata
http://www.research.att.com/~njas/sequences/A001317
"""
while True:
therow = pascal_row(row_num)
binary = "".join(str(i % 2) for i in therow)
yield [int(binary,2), binary]
row_num += 1
"""
traditional generator for successive rows, included
for completeness
"""
def pascal_gen():
row = [1]
while True:
yield row
row = [i + j for i,j in zip(row + [0], [0] + row)]
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