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Ludic numbers: Difference between revisions
Add Rust implementation
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Ludic triples below 250:
[[1, 3, 7], [5, 7, 11], [11, 13, 17], [23, 25, 29], [41, 43, 47], [173, 175, 179], [221, 223, 227], [233, 235, 239]]
</pre>
=={{header|Rust}}==
<lang rust>
const ARRAY_MAX: usize = 25_000;
const LUDIC_MAX: usize = 2100;
/// Calculates and returns the first `LUDIC_MAX` Ludic numbers.
///
/// Needs a sufficiently large `ARRAY_MAX`.
fn ludic_numbers() -> Vec<usize> {
// The first two Ludic numbers
let mut numbers = vec![1, 2];
// We start the array with an immediate first removal to reduce memory usage by
// collecting only odd numbers.
numbers.extend((3..ARRAY_MAX).step_by(2));
// We keep the correct Ludic numbers in place, removing the incorrect ones.
for ludic_idx in 2..LUDIC_MAX {
let next_ludic = numbers[ludic_idx];
// We remove incorrect numbers by counting the indices after the correct numbers.
// We start from zero and keep until we reach the potentially incorrect numbers.
// Then we keep only those not divisible by the `next_ludic`.
let mut idx = 0;
numbers.retain(|_| {
let keep = idx <= ludic_idx || (idx - ludic_idx) % next_ludic != 0;
idx += 1;
keep
});
}
numbers
}
fn main() {
let ludic_numbers = ludic_numbers();
print!("First 25: ");
print_n_ludics(&ludic_numbers, 25);
println!();
print!("Number of Ludics below 1000: ");
print_num_ludics_upto(&ludic_numbers, 1000);
println!();
print!("Ludics from 2000 to 2005: ");
print_ludics_from_to(&ludic_numbers, 2000, 2005);
println!();
println!("Triplets below 250: ");
print_triplets_until(&ludic_numbers, 250);
}
/// Prints the first `n` Ludic numbers.
fn print_n_ludics(x: &[usize], n: usize) {
println!("{:?}", &x[..n]);
}
/// Calculates how many Ludic numbers are below `max_num`.
fn print_num_ludics_upto(x: &[usize], max_num: usize) {
let num = x.iter().take_while(|&&i| i < max_num).count();
println!("{}", num);
}
/// Prints Ludic numbers between two numbers.
fn print_ludics_from_to(x: &[usize], from: usize, to: usize) {
println!("{:?}", &x[from - 1..to - 1]);
}
/// Calculates triplets until a certain Ludic number.
fn triplets_below(ludics: &[usize], limit: usize) -> Vec<(usize, usize, usize)> {
ludics
.iter()
.enumerate()
.take_while(|&(_, &num)| num < limit)
.filter_map(|(idx, &number)| {
let triplet_2 = number + 2;
let triplet_3 = number + 6;
// Search for the other two triplet numbers. We know they are larger than
// `number` so we can give the searches lower bounds of `idx + 1` and
// `idx + 2`. We also know that the `n + 2` number can only ever be two
// numbers away from the previous and the `n + 6` number can only be four
// away (because we removed some in between). Short circuiting and doing
// the check more likely to fail first are also useful.
let is_triplet = ludics[idx + 1..idx + 3].binary_search(&triplet_2).is_ok()
&& ludics[idx + 2..idx + 5].binary_search(&triplet_3).is_ok();
if is_triplet {
Some((number, triplet_2, triplet_3))
} else {
None
}
})
.collect()
}
/// Prints triplets until a certain Ludic number.
fn print_triplets_until(ludics: &[usize], limit: usize) {
for (number, triplet_2, triplet_3) in triplets_below(ludics, limit) {
println!("{} {} {}", number, triplet_2, triplet_3);
}
}
</lang>
{{out}}
<pre>
First 25: [1, 2, 3, 5, 7, 11, 13, 17, 23, 25, 29, 37, 41, 43, 47, 53, 61, 67, 71, 77, 83, 89, 91, 97, 107]
Number of Ludics below 1000: 142
Ludics from 2000 to 2005: [21475, 21481, 21487, 21493, 21503]
Triplets below 250:
1 3 7
5 7 11
11 13 17
23 25 29
41 43 47
173 175 179
221 223 227
233 235 239
</pre>
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