Brilliant numbers: Difference between revisions
Added Rust solution
m (C++ - simplified code) |
(Added Rust solution) |
||
Line 638:
First >= 100,000,000 is 573929ᵗʰ in the series: 100,140,049
First >= 1,000,000,000 is 7407841ˢᵗ in the series: 1,000,000,081</pre>
=={{header|Rust}}==
{{trans|C++}}
<lang rust>// [dependencies]
// primal = "0.3"
// indexing = "0.4.1"
fn get_primes_by_digits(limit: usize) -> Vec<Vec<usize>> {
let mut primes_by_digits = Vec::new();
let mut power = 10;
let mut primes = Vec::new();
for prime in primal::Primes::all().take_while(|p| *p < limit) {
if prime > power {
primes_by_digits.push(primes);
primes = Vec::new();
power *= 10;
}
primes.push(prime);
}
primes_by_digits
}
fn main() {
use indexing::algorithms::lower_bound;
use std::time::Instant;
let start = Instant::now();
let primes_by_digits = get_primes_by_digits(1000000000);
println!("First 100 brilliant numbers:");
let mut brilliant_numbers = Vec::new();
for primes in &primes_by_digits {
for i in 0..primes.len() {
let p1 = primes[i];
for j in i..primes.len() {
let p2 = primes[j];
brilliant_numbers.push(p1 * p2);
}
}
if brilliant_numbers.len() >= 100 {
break;
}
}
brilliant_numbers.sort();
for i in 0..100 {
let n = brilliant_numbers[i];
print!("{:4}{}", n, if (i + 1) % 10 == 0 { '\n' } else { ' ' });
}
println!();
let mut power = 10;
let mut count = 0;
for p in 1..2 * primes_by_digits.len() {
let primes = &primes_by_digits[p / 2];
let mut position = count + 1;
let mut min_product = 0;
for i in 0..primes.len() {
let p1 = primes[i];
let n = (power + p1 - 1) / p1;
let j = lower_bound(&primes[i..], &n);
let p2 = primes[i + j];
let product = p1 * p2;
if min_product == 0 || product < min_product {
min_product = product;
}
position += j;
if p1 >= p2 {
break;
}
}
println!("First brilliant number >= 10^{p} is {min_product} at position {position}");
power *= 10;
if p % 2 == 1 {
let size = primes.len();
count += size * (size + 1) / 2;
}
}
let time = start.elapsed();
println!("\nElapsed time: {} milliseconds", time.as_millis());
}</lang>
{{out}}
<pre>
First 100 brilliant numbers:
4 6 9 10 14 15 21 25 35 49
121 143 169 187 209 221 247 253 289 299
319 323 341 361 377 391 403 407 437 451
473 481 493 517 527 529 533 551 559 583
589 611 629 649 667 671 689 697 703 713
731 737 767 779 781 793 799 803 817 841
851 869 871 893 899 901 913 923 943 949
961 979 989 1003 1007 1027 1037 1067 1073 1079
1081 1121 1139 1147 1157 1159 1189 1207 1219 1241
1247 1261 1271 1273 1333 1343 1349 1357 1363 1369
First brilliant number >= 10^1 is 10 at position 4
First brilliant number >= 10^2 is 121 at position 11
First brilliant number >= 10^3 is 1003 at position 74
First brilliant number >= 10^4 is 10201 at position 242
First brilliant number >= 10^5 is 100013 at position 2505
First brilliant number >= 10^6 is 1018081 at position 10538
First brilliant number >= 10^7 is 10000043 at position 124364
First brilliant number >= 10^8 is 100140049 at position 573929
First brilliant number >= 10^9 is 1000000081 at position 7407841
First brilliant number >= 10^10 is 10000600009 at position 35547995
First brilliant number >= 10^11 is 100000000147 at position 491316167
First brilliant number >= 10^12 is 1000006000009 at position 2409600866
First brilliant number >= 10^13 is 10000000000073 at position 34896253010
First brilliant number >= 10^14 is 100000380000361 at position 174155363187
First brilliant number >= 10^15 is 1000000000000003 at position 2601913448897
Elapsed time: 676 milliseconds
</pre>
=={{header|Sidef}}==
| |||