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).