RogerBW's Blog

I’ve been doing the Weekly Challenges. The latest involved various progressions based on factorials. (Note that this is open until 27 February 2022.)

To try to maintain my polyglot mindset, I shuffle the languages I'll be writing the solution in (because I tend to solve the problem in the first one and then copy the algorithm to the others). This time the first one was PostScript, which was fun… at least now that I've got some idea of how to debug it.

Task 1: Left Factorials

Write a script to compute Left Factorials of 1 to 10. Please refer OEIS A003422 for more information.

This turns out to be: the left factorial of N is the sum of all factorials of 0 to N-1.

For efficiency, I calculate those lower factorials just once as needed: the only time I need to know the value of 5! is when I'm calculating term 6, and at that point I already know the value of 4! because I used it to calculate the previous term.

Thus in JavaScript:

function leftfactorial (mx) {
    let out=[];
    let fact=1;
    let sum=0;
    for (let i=0; i < mx; i++) {
        if (i>0) {
            fact *= i;
        }
        sum += fact;
        out.push(sum);
    }
    return out;
}

Task 2: Factorions

You are given an integer, $n.

Write a script to figure out if the given integer is a factorion.

A factorion is a natural number that equals the sum of the factorials of its digits.

Of course it's in the OEIS. And the trivial version would thus be a lookup for the four values; but let's take this seriously and work it out the slightly harder way. Raku:

sub factorion($input) {

Special-casing zero saves trouble later.

    if ($input == 0) {
        return False;
    }

Calculate each digit's factorial. (We may not use all of them but I think that any slight increase in calculation time is justified by the reduced complexity of this approach.)

    my @fd;
    @fd.push(1);
    my $ff=1;
    for (1..9) -> $i {
        $ff *= $i;
        @fd.push($ff);
    }

Now extract the digits and sum their factorial values.

    my $working=$input;
    my $dsum=0;
    while ($working > 0) {
        $dsum += @fd[$working % 10];
        $working=floor($working/10);
    }

Return the boolean calculation.

    return $input==$dsum;
}

One could short-cut if dsum gets larger than input but it hardly seems worth it.

Full code on github.