Prime factors generation #9
Description
First of all thank you for this great library.
I don't know if this is strictly in the scope of primal, but I often need to generate the list of prime factors of all the numbers in a range, something like the following:
fn prime_factors(n: usize) -> Vec<Vec<(usize,usize)>> {
let sieve = primal::Sieve::new(n.sqrt()+1);
(0..n).map(|i| sieve.factor(i).unwrap_or(Vec::new())).collect()
}This works just fine but is quite a lot slower than it should be. In fact the following naïve approach if 5 times faster:
#![feature(step_by)]
fn prime_factors_naive(n: usize) -> Vec<Vec<(usize,usize)>> {
let mut f = vec![Vec::new(); n];
for i in 2..n {
// if i is prime
if f[i].is_empty() {
// add it as prime factor to all the multiples of i
for k in (i..n).step_by(i) {
f[k].push((i, 1));
}
// now we handle numbers with several i factors
for p in (0..).scan(i, |a, _| {*a *= i; Some(*a)}) {
if p > n { break; }
for k in (p..n).step_by(p) {
f[k].last_mut().unwrap().1 += 1;
}
}
}
}
f
}So... I filed this bug but this is only for your information, I am not convinced myself that this piece of code should be in primal. For once the space requirements are incompatible with a range of more than of few tens of millions.