The following method avoids computing factorials explicitly, which can be computationally expensive for large values of n and r. Instead, it computes the product of a sequence of values using a generator expression, which is more memory-efficient and faster than computing factorials. You can compute perm(n, r) using a prod function, which is a built-in SageMath function that computes the product of a sequence of values.
See the code:
perm(n, r) = prod(n - i for i in range(r))
Hello! I am assuming nPr means "n permutation r". Unfortunately, SageMath doesn't have a command for that purpose. However, if you remember that
$$nPr = \frac{n!}{(n-r)!} = \binom{n}{r}r!,$$
you can make something like this:
perm(n, r) = factorial(n) / factorial(n - r)
or even:
perm(n, r) = binomial(n, r) * factorial(r)
Hope this helps!
To my surprise, the former is about 12 times faster than the latter :
sage: %timeit Permutations(5,3).cardinality()
2.31 µs ± 450 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
sage: sage: %timeit binomial(5,3)*factorial(3)
27.3 µs ± 860 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
Go figure...
Asked: 2023-07-15 13:42:28 +0100
Seen: 350 times
Last updated: Jul 21 '23
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What is nPr?