PWC205 - Maximum XOR


On with TASK #2 from The Weekly Challenge #205. Enjoy!

The challenge

You are given an array of integers.

Write a script to find the highest value obtained by XORing any two distinct members of the array.

Example 1

Input: @array = (1,2,3,4,5,6,7)
Output: 7

The maximum result of 1 xor 6 = 7.

Example 2

Input: @array = (2,4,1,3)
Output: 7

The maximum result of 4 xor 3 = 7.

Example 3

Input: @array = (10,5,7,12,8)
Output: 15

The maximum result of 10 xor 5 = 15.

The questions

Anything particular we should know about the input values, e.g.:

  • maximum value (to account for big integers, in case)?
  • negative values and their binary representation?

The solution

We’ll go for non-negative integers that fit whatever the language is capable of supporting.

The idea is to build all possible pairs out of the input values, calculate the XOR and take the maximum. This algorithm is $O(n^2)$ on the size of the input array, which is kind of meh and I suspect there must be a better way, but it’s out of my reach at the moment.

In Perl, we iterate over the array in two nested loops, getting one element from each loop’s index:

#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental qw< bitwise signatures >;

say maximum_xor(@ARGV);

sub maximum_xor (@array) {
   my $max = 0;
   for my $i (0 .. $#array - 1) {
      for my $j ($i + 1 .. $#array) {
         my $xor = $array[$i] ^ $array[$j];
         $max = $xor if $xor > $max;
   return $max;

Raku comes with a bit more batteries included, like a combinations method for arrays that allows taking all possible pairs in a single call; this allows us to pack everything in a single line.

#!/usr/bin/env raku
use v6;
sub MAIN (*@args) { put maximum-xor(@args) }

sub maximum-xor (@array) { @array .combinations(2) .map({[+^] $_}) .max }

The calculation of the XOR function is done at the risk of getting the line noise mark that haunted Perl for too long, but whatever. The map takes each pair as input, available as $_; as it is a sequence, it suffices to apply the hyperoperation to do the XOR over its two elements.

Maybe this would be more readable:

sub maximum-xor (@a) { @a.combinations(2).map(->($x,$y){$x +^ $y}).max }

So there you go… if you find my code hermetic, it’s because I wanted it to be like that!

Stay safe and maximized!

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