RogerBW's Blog

The Weekly Challenge 178: Imaginary Date 18 August 2022

I’ve been doing the Weekly Challenges. The latest involved an unusual base representation and date calculations. (Note that this is open until 21 August 2022.)

Task 1: Quater-imaginary Base

Write a script to convert a given number (base 10) to quater-imaginary base number and vice-versa.

As described here: digits alternate for real and imaginary components.

For Perl this doesn't matter much, but for most of the other languages it does: what format do I use for the quater-imaginary representation? I ended up using a string of characters - though a more compressed version could take just two bits per place, since only digits 0..3 are allowed.

In Kotlin, I start with a convenience function (I might as well write the full complex number conversion since it's not much more work than the real-only one).

fun r2qi (n: Int): String {
    return c2qi(n, 0)

Real and imaginary components are treated separately.

fun c2qi (r0: Int, i0: Int): String {
    var l = ArrayList<ArrayList<Int>>()
    for (n0 in listOf(i0, r0)) {
        var n = n0
        var digits = ArrayList<Int>()

A fairly usual base conversion by repeated division, but a modulus operator can return a negative result, so we deal with that here.

        while (n != 0) {
            var digit = n % -4
            n /= -4
            if (digit < 0) {
                digit += 4
                n += 1

Take the difference in length between the two arrays (for real and imaginary parts), and pad with zeroes as needed. (There are probably more efficient ways of doing this.)

    val ld = l[0].size - l[1].size
    if (ld < 0) {
        for (x in 1..-ld-1) {
    } else if (ld > 1) {
        for (x in 1..ld) {
    var o = ""
    for (i in l[1].size-1 downTo 0) {
        for (b in listOf(0,1)) {
            if (l[b].size > i) {
                o += l[b][i]
    return o

Convenience function for the string-to-number conversion.

fun qi2r(n: String): Int {
    return qi2c(n)[0]

fun qi2c(n: String): List<Int> {
    var pow = 1
    var ri = 0
    var r = 0
    var i = 0

This is rather simpler: for each digit, flip between real and imaginary components, and increment the power. However, there's apparently a bug in Kotlin, and I had to write this:

    for (ch in n.reversed().toList()) {
        if (ri == 0) {
            r += (ch.digitToInt()) * pow
        } else {
            i += (ch.digitToInt()) * pow

rather than, as in all the other languages, simply using an array o and incrementing o[ri].

Increment loop variables.

        ri += 1
        pow *= 2
        if (ri == 2) {
            ri = 0
            pow = -pow
    return listOf(r,i)

This is one of the few times when Lua's 1-based arrays actually make the code simpler.

JavaScript has a % operator like all the other languages, but unlike them it's not a true modulus; it's a remainder. (Which is the same thing if both the numbers are positive.) Should you need one:

function mod(n, m) {
  return ((n % m) + m) % m;

Task 2: Business Date

You are given $timestamp (date with time) and $duration in hours.

Write a script to find the time that occurs $duration business hours after $timestamp. For the sake of this task, let us assume the working hours is 9am to 6pm, Monday to Friday. Please ignore timezone too.

That last bit is really hard in languages with good date handling, and worryingly easy in others. Again I ignored Lua; in PostScript I used a two-element array of (julian date) and (minutes since midnight). In Raku, though:

sub addbizhours($start, $delta) {

One of the few languages that doesn't provide a strptime-like date parser.

    $start ~~ /(<[0..9]>+)\D(<[0..9]>+)\D(<[0..9]>+)\D(<[0..9]>+)\D(<[0..9]>+)/;
    my $current = => $0,
                               month => $1,
                               day => $2,
                               hour => $3,
                               minute => $4,
                               second => 0);
    my $seconds = 3600 * $delta;
    my $bizdaylength = 3600 * 9;

If the current time isn't in business hours, advance to the next start of business hours.

    unless (isbiz($current)) {
        $current = nextbizstart($current);

Find the end of the current business day.

    my $ed = nextbizend($current);

Get the number of seconds between then and current.

    my $remain = ($ed - $current).Int;

If the remaining span won't fit in this day:

    if ($remain < $seconds) {

Knock the rest of day off the remaining span.

        $seconds -= $remain;

Advance to the start of the next day.

        $current = nextbizstart($ed);

And while the remaining span is more than a day length,

        while ($seconds > $bizdaylength) {

Move to the start of the next business day and knock that off the span.

            $current = nextbizstart($current);
            $seconds -= $bizdaylength;

Finally, add any remaining seconds.

    $current = $current.later(seconds => $seconds);

And return the string format (most languages offer something based on strftime).

    return $current.yyyy-mm-dd ~ " " ~ substr($current.hh-mm-ss,0,5);

Are we in a business-day?

sub isbiz($tm) {

Not if it's Saturday or Sunday.

    if ($ > 5) {
        return False;

Not if it's before 9am or after 6pm.

    if ($tm.hour < 9 || $tm.hour >= 18) {
        return False;

Otherwise yes.

    return True;

Given a current time, when does the next business day start?

sub nextbizstart($tm0) {
    my $tm = $tm0.clone;

While it's a weekend, advance to 9am on the next day.

    while ($ > 5) {
        $tm = $tm.later(days => 1).
               clone(hour => 9, minute => 0, second => 0);

If it's before 9, advance to 9,

    if ($tm.hour < 9) {
        $tm = $tm.clone(hour => 9, minute => 0, second => 0);
    } else {

Otherwise, add a day and then jump to 9am, repeatedly if needed until we're not at a weekend.

        while (True) {
            $tm = $tm.later(days => 1)
                   .clone(hour => 9, minute => 0, second => 0);
            if ($ <= 5) {
    return $tm;

nextbizend works the same way with fractionally different logic.

Perl's DateTime is pretty good (rather better than the Raku built-in clearly inspired by it), but I think Rust's chrono crate was my favourite of the date libraries; alas, the date support in Ruby (using the Time class) is shockingly bad, especially given my generally positive experience of the rest of the language. You can't even set the hours part of a time entity without parsing it out into compnents and then reassembling:

def sethour(tm,hour)
  ar = tm.to_a
  ar[2] = hour
  return Time.utc(*ar)

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.

Tags 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010s 3d printing action advent of code 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 cthulhu eternal cycling dead of winter doctor who documentary drama driving drone ecchi economics en garde espionage essen 2015 essen 2016 essen 2017 essen 2018 essen 2019 essen 2022 essen 2023 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 mpd 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 scala 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