RogerBW's Blog

Perl Weekly Challenge 106: Maximum Decimal 31 March 2021

I’ve been doing the Perl Weekly Challenges. The latest involved integer differences and decimal expansion. (Note that this is open until 4 April 2021.)

TASK #1 › Maximum Gap

You are given an array of integers @N.

Write a script to display the maximum difference between two successive elements once the array is sorted.

If the array contains only 1 element then display 0.

I can't see any short-cuts here: we have to subtract every pair of numbers. (I mean, given a sorted list I suppose one might be able to bracket it and skip some comparisons, but it would probably be more work than just doing the calculation.)

A straightforward procedure, therefore: sort the input list, set max-difference to zero, do each subtraction, set max-difference to it if it's higher. Let's have that in Raku:

sub mg(**@aa) {
  my @a=@aa.sort;
  my $g=0;
  for (0..@a.elems-2) -> $i {
    my $d=abs(@a[$i]-@a[$i+1]);
    if ($d>$g) {
      $g=$d;
    }
  }
  return $g;
}

and the other languages all look very much the same.

TASK #2 › Decimal String

You are given numerator and denominator i.e. $N and $D.

Write a script to convert the fraction into decimal string. If the fractional part is recurring then put it in parenthesis.

Clearly the hard part here is working out whether you have a recurring decimal. I had a look at prime-factoring the numbers (any remaining factors that aren't 2 or 5 means an infinite expansion) but then came across this convenient algorithm – so I reimplemented that in Perl (with some tweaks, like using arrays rather than strings where it made sense), then translated the Perl version in the other languages. (It does assume the inputs are positive.)

Let's have that in Perl:

sub ds {
  my $n=shift;
  my $d=shift;
  my $quotient=sprintf('%d.',$n/$d);
  my $c=10*($n % $d);
  while ($c > 0 && $c < $d) {
    $c *= 10;
    $quotient .= "0";
  }
  my @digits;
  my %passed;
  my $i=0;
  while (1) {
    if (exists $passed{$c}) {
      my @cycle=@digits[$passed{$c}..$#digits];
      my $result=$quotient . join('',@digits[0..$passed{$c}-1]);
      if (scalar @cycle > 1 || $cycle[0] != 0) {
        $result .= '('.join('',@cycle).')';
      }
      if (substr($result,-1,1) eq '.') {
        substr($result,-1,1)='';
      }
      return $result;
    }
    my $q=int($c/$d);
    my $r=$c % $d;
    $passed{$c}=$i;
    push @digits,$q;
    $i++;
    $c=10*$r;
  }
}

The other versions look much the same, except for the tweaks needed to shift around between digits and strings.

Full code on github.


  1. Posted by RogerBW at 01:28pm on 05 April 2021

    Looking at other people's blog posts…

    In part 1, my abs was unnecessary, but otherwise nobody came up with anything terribly different except for one rather odd (but effective) recursive approach. One can get cunning with hashes and the zip operator but it all just takes more space.

    For part 2, Raku has a base-repeating function which is essentially defined to solve this problem. (Of course it does!) Someone finished off the prime-factorisation approach that I'd considered, but I don't think their solution was notably simpler than mine. Some people looked at the string expansion, but I think this would fail in too many cases given the limitations of floating-point arithmetic.

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