A vampire number is a natural decimal number with an even number of digits,   that can be factored into two integers.

These two factors are called the   fangs,   and must have the following properties:

   they each contain half the number of the decimal digits of the original number
   together they consist of exactly the same decimal digits as the original number
   at most one of them has a trailing zero


An example of a vampire number and its fangs:    1260 : (21, 60) 



Task

 Print the first   25   vampire numbers and their fangs. 
 Check if the following numbers are vampire numbers and,   if so,   print them and their fangs: 
 16758243290880, 24959017348650, 14593825548650 



Note that a vampire number can have more than one pair of fangs.



See also

 numberphile.com.
 vampire search algorithm
 vampire numbers on OEIS


use std::cmp::{max, min};
 
static TENS: [u64; 20] = [
    1,
    10,
    100,
    1000,
    10000,
    100000,
    1000000,
    10000000,
    100000000,
    1000000000,
    10000000000,
    100000000000,
    1000000000000,
    10000000000000,
    100000000000000,
    1000000000000000,
    10000000000000000,
    100000000000000000,
    1000000000000000000,
    10000000000000000000,
];
 
/// Get the number of digits present in x
fn ndigits(mut x: u64) -> u64 {
    let mut n = 0;
 
    while x != 0 {
        n += 1;
        x /= 10;
    }
 
    n
}
 
fn dtally(mut x: u64) -> u64 {
    let mut t = 0;
 
    while x != 0 {
        t += 1 << ((x % 10) * 6);
        x /= 10;
    }
 
    t
}
 
/// Get a list of all fangs of x. Get only the first divider of each fang. The second one can be found simply with x / fang.
fn fangs(x: u64) -> Vec<u64> {
    let mut nd = ndigits(x) as usize;
 
    let mut fangs = vec![];
 
    if nd & 1 != 1 {
        nd /= 2;
 
        let lo = max(TENS[nd - 1], (x + TENS[nd] - 2) / (TENS[nd] - 1));
        let hi = min(x / lo, (x as f64).sqrt() as u64);
 
        let t = dtally(x);
 
        for a in lo..(hi + 1) {
            let b = x / a;
            if a * b == x && ((a % 10) > 0 || b % 10 > 0) && t == dtally(a) + dtally(b) {
                fangs.push(a);
            }
        }
    }
 
    fangs
}
 
/// Pretty print the fangs of x
fn print_fangs(x: u64, fangs: Vec<u64>) {
    print!("{} = ", x);
 
    if fangs.is_empty() {
        print!("is not vampiric");
    } else {
        for fang in fangs {
            print!("{} x {}, ", fang, x / fang);
        }
    }
    print!("\n");
}
 
fn main() {
    println!("The first 25 vampire numbers are :");
 
    let mut nfangs = 0;
    let mut x = 1;
 
    while nfangs < 25 {
        let fangs = fangs(x);
        if !fangs.is_empty() {
            nfangs += 1;
            print_fangs(x, fangs);
        }
 
        x += 1;
    }
 
    println!("\nSpecial requests :");
 
    print_fangs(16758243290880, fangs(16758243290880));
    print_fangs(24959017348650, fangs(24959017348650));
    print_fangs(14593825548650, fangs(14593825548650));
}
 
#[test]
fn test() {
    assert_eq!(
        fangs(16758243290880),
        vec![1982736, 2123856, 2751840, 2817360]
    );
 
    assert_eq!(
        fangs(24959017348650),
        vec![2947050, 2949705, 4125870, 4129587, 4230765]
    );
 
    assert_eq!(fangs(14593825548650), vec![]);
}