RogerBW's Blog

The Weekly Challenge 188: Divisible Zero 25 October 2022

I’ve been doing the Weekly Challenges. The latest involved more list searching and a variation on the greatest common divisor. (Note that this is open until 30 October 2022.)

Task 1: Divisible Pairs

You are given list of integers @list of size $n and divisor $k.

Write a script to find out count of pairs in the given list that satisfies the following rules.

The pair (i, j) is eligible if and only if
a) 0 <= i < j < len(list)
b) list[i] + list[j] is divisible by k

This has a strong resemblance to 187 task 2, and I used my code from that as the basis for this one: some languages have a combinations generator readily available, others don't and get simple nested loops since I don't have to work to an arbitrary depth.

Lua:

function divisiblepairs(a, k)
   local ct = 0
   for ai = 1,#a-1 do
      for bi = ai+1,#a do
         if (a[ai] + a[bi]) % k == 0 then
            ct = ct + 1
         end
      end
   end
   return ct
end

Or, with a combination generator, Ruby:

def divisiblepairs(a, k)
  ct = 0
  a.combination(2) do |b|
    if (b[0] + b[1]) % k == 0 then
      ct += 1
    end
  end
  return ct
end

Task 2: Total Zero

You are given two positive integers $x and $y.

Write a script to find out the number of operations needed to make both ZERO. Each operation is made up either of the followings:

$x = $x - $y if $x >= $y

or

$y = $y - $x if $y >= $x (using the original value of $x)

This is of course Euclid's algorithm for greatest common divisor, except that we're counting the steps rather than the final result. One could get clever with modulus operations to do multiple steps at once (a variant of the Euclidean algorithm), but it seemed to me that the simplest approach to write and debug was just to do one subtraction at a time.

The end cases in my implementation are:

  • a == b == 0 – we won't reach this so it's special-cased at the start.
  • a == b – one more step gets us to a == b == 0, and everything else terminates here. (So I don't have to worry about temporary variables to do the final double subtraction.)
  • a ≠ b – subtract smaller from larger, increment count and continue.

In Raku:

sub totalzero($aa, $bb) {

The special case for zero steps:

    if ($aa == 0 && $bb == 0) {
        return 0;
    }

Otherwise, set the count to 1.

    my $a = $aa;
    my $b = $bb;
    my $ct = 1;
    while (True) {

Each time the values aren't equal, increment the count and continue.

        if ($a == $b) {
            return $ct;
        }
        $ct++;
        if ($a > $b) {
            $a -= $b;
        } else {
            $b -= $a;
        }
    }
}

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 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 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 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 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