faster combination if y is integer

[DennisMitchell]

That uses floating point arithmetic, making it inaccurate for large values of n.

[kckennylau]

Not really. This formula can guarantee that if left is integer, then all the intermediate values are integers.

[DennisMitchell]

Ah, I see what your intentions were. There are two problems though.

1. / is always floating point division in Python 3, even if the result is exact.
2. Something is off by one. 10C1 should return 10, not 1.

[kckennylau]

1. Then condition on left to see if we use / or //
2. Ok I'll fix that (or you'll fix that?)

[kckennylau]

I forgot to add one to the second argument of range().

[kckennylau]

@DennisMitchell Is it ok now?

[DennisMitchell]

Almost. To match the behavior of the previous code, it should return 0 when the right argument is negative. The case of a negative left argument can be considered undefined behavior for now.

[kckennylau]

But negative left argument is really defined... They are also useful in binomial expansions.

[DennisMitchell]

It is. If you want to implement it correctly, go ahead. I just meant that my code doesn't return anything sensible right now, so there's no reason your code should match its behavior.

[kckennylau]

Thanks!

[DennisMitchell]

Thank you for the contribution!

I made one more functional change to the code, so that nCr(2**256, 2**256-1) is also computed instantly.