binomial_coefficient.py

defbinomial_coefficient(n: int, r: int) ->int:
"""
 Find binomial coefficient using Pascal's triangle.

 Calculate C(n, r) using Pascal's triangle.

 :param n: The total number of items.
 :param r: The number of items to choose.
 :return: The binomial coefficient C(n, r).

 >>> binomial_coefficient(10, 5)
 252
 >>> binomial_coefficient(10, 0)
 1
 >>> binomial_coefficient(0, 10)
 1
 >>> binomial_coefficient(10, 10)
 1
 >>> binomial_coefficient(5, 2)
 10
 >>> binomial_coefficient(5, 6)
 0
 >>> binomial_coefficient(3, 5)
 0
 >>> binomial_coefficient(-2, 3)
 Traceback (most recent call last):
 ...
 ValueError: n and r must be non-negative integers
 >>> binomial_coefficient(5, -1)
 Traceback (most recent call last):
 ...
 ValueError: n and r must be non-negative integers
 >>> binomial_coefficient(10.1, 5)
 Traceback (most recent call last):
 ...
 TypeError: 'float' object cannot be interpreted as an integer
 >>> binomial_coefficient(10, 5.1)
 Traceback (most recent call last):
 ...
 TypeError: 'float' object cannot be interpreted as an integer
 """
ifn<0orr<0:
raiseValueError("n and r must be non-negative integers")
if0in (n, r):
return1
c= [0foriinrange(r+1)]
# nc0 = 1
c[0] =1
foriinrange(1, n+1):
# to compute current row from previous row.
j=min(i, r)
whilej>0:
c[j] +=c[j-1]
j-=1
returnc[r]


if__name__=="__main__":
fromdoctestimporttestmod

testmod()
print(binomial_coefficient(n=10, r=5))