RogerBW's Blog

The Weekly Challenge 153: Factoriality 24 February 2022

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.

Comments on this post are now closed. If you have particular grounds for adding a late comment, comment on a more recent post quoting the URL of this one.

Search
Archive
Tags 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010s 3d printing action aeronautics aikakirja anecdote animation anime army astronomy audio audio tech aviation base commerce battletech beer boardgaming book of the week bookmonth chain of command children chris chronicle church of no redeeming virtues cold war comedy computing contemporary cornish smuggler cosmic encounter coup covid-19 crime cycling dead of winter doctor who documentary drama driving drone ecchi economics espionage essen 2015 essen 2016 essen 2017 essen 2018 essen 2019 essen 2022 existential risk falklands war fandom fanfic fantasy feminism film firefly first world war flash point flight simulation food garmin drive gazebo genesys geocaching geodata gin gkp gurps gurps 101 gus harpoon historical history horror hugo 2014 hugo 2015 hugo 2016 hugo 2017 hugo 2018 hugo 2019 hugo 2020 hugo 2022 hugo-nebula reread in brief avoid instrumented life javascript julian simpson julie enfield kickstarter kotlin learn to play leaving earth linux liquor lovecraftiana lua mecha men with beards museum music mystery naval noir non-fiction one for the brow opera parody paul temple perl perl weekly challenge photography podcast politics postscript powers prediction privacy project woolsack pyracantha python quantum rail raku ranting raspberry pi reading reading boardgames social real life restaurant reviews romance rpg a day rpgs ruby rust science fiction scythe second world war security shipwreck simutrans smartphone south atlantic war squaddies stationery steampunk stuarts suburbia superheroes suspense television the resistance the weekly challenge thirsty meeples thriller tin soldier torg toys trailers travel type 26 type 31 type 45 vietnam war war wargaming weather wives and sweethearts writing about writing x-wing young adult
Special All book reviews, All film reviews
Produced by aikakirja v0.1