Python Binomial Coefficient

Question

import math
x = int(input("Enter a value for x: "))
y = int(input("Enter a value for y: "))

if y == 1 or y == x:
    print(1)

if y > x:
    print(0)        
else:
    a = math.factorial(x)
    b = math.factorial(y)
    div = a // (b*(x-y))
    print(div)  

This binomial coefficient program works but when I input two of the same number which is supposed to equal to 1 or when y is greater than x it is supposed to equal to 0.

Answer 1

This question is old but as it comes up high on search results I will point out that scipy has two functions for computing the binomial coefficients:

1. scipy.special.binom()

2. scipy.special.comb()

   import scipy.special
   
   # the two give the same results 
   scipy.special.binom(10, 5)
   # 252.0
   scipy.special.comb(10, 5)
   # 252.0
   
   scipy.special.binom(300, 150)
   # 9.375970277281882e+88
   scipy.special.comb(300, 150)
   # 9.375970277281882e+88
   
   # ...but with `exact == True`
   scipy.special.comb(10, 5, exact=True)
   # 252
   scipy.special.comb(300, 150, exact=True)
   # 393759702772827452793193754439064084879232655700081358920472352712975170021839591675861424
   

Note that scipy.special.comb(exact=True) uses Python integers, and therefore it can handle arbitrarily large results!

Speed-wise, the three versions give somewhat different results:

num = 300

%timeit [[scipy.special.binom(n, k) for k in range(n + 1)] for n in range(num)]
# 52.9 ms ± 107 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)

%timeit [[scipy.special.comb(n, k) for k in range(n + 1)] for n in range(num)]
# 183 ms ± 814 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)each)

%timeit [[scipy.special.comb(n, k, exact=True) for k in range(n + 1)] for n in range(num)]
# 180 ms ± 649 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)

(and for n = 300, the binomial coefficients are too large to be represented correctly using float64 numbers, as shown above).