Python 二项式系数 [英] Python Binomial Coefficient

问题描述

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)  

这个二项式系数程序有效，但是当我输入两个相同的数字时，应该等于 1，或者当 y 大于 x 时，它应该等于 0.

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.

推荐答案

这个问题很老了，但是当它出现在搜索结果的高位时，我会指出 scipy 有两个计算二项式的函数系数:

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. <代码>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

请注意，scipy.special.comb(exact=True) 使用 Python 整数，因此它可以处理任意大的结果！

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

速度方面，三个版本给出的结果有些不同:

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)

(对于 n = 300，二项式系数太大而无法使用 float64 数字正确表示，如上所示).

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

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