RogerBW's Blog

The Weekly Challenge 205: Third Exclusive 26 February 2023

I’ve been doing the Weekly Challenges. The latest involved list parsing and combinations. (Note that this closes today.)

Task 1: Third Highest

You are given an array of integers.

Write a script to find out the Third Highest if found otherwise return the maximum.

My approach here is to get the distinct values in the input list, reverse sort it, and then pull either the third entry (if it exists) or the first. (The problem doesn't specify what's to be done with an empty list; I choose to return zero.)


sub thirdhighest($l) {
  my @v = reverse sort keys %{{map {$_ => 1} @{$l}}};
  if (scalar @v == 0) {
    return 0;
  } elsif (scalar @v <= 2) {
    return $v[0];
  } else {
    return $v[2];

I think the most elegant code here is in Rust (for which I was going to use a HashSet, but it turns out that dedup() is a thing for vectors).

fn thirdhighest(l: Vec<i32>) -> i32 {
    let mut v = l.clone();
    match v.len() {
        0 => 0,
        1..=2 => v[0],
        _ => v[2],

Task 2: Maximum XOR

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.

So it's time to dust off the combinations generator, last seen in 203 task 1. Some languages have this readily available; others don't.


from itertools import combinations

def maximumxor(l):
  m = []
  for c in combinations(l, 2):
    m.append(c[0] ^ c[1])
  return max(m)

I finally got round to implementing Knuth's lexicographic combination algorithm [TAoCP volume 4 §] in PostScript, complete with its slightly odd ordering, and that's now in the library for future use. (The library itself has moved to Codeberg as part of my general disentanglement from github at least for my own projects.)


/combinations {
    4 dict begin
    /k exch def
    /arr exch def
    /c [
        0 1 k 1 sub { } for
        arr length
    ] def
                k 1 sub -1 0 {
                    c exch get arr exch get
                } for
            /j 0 def
                c j get 1 add c j 1 add get ne {
                } if
                c j j put
                /j j 1 add def
            } loop
            j k ge {
            } if
            c j c j get 1 add put
        } loop
} bind def

/maximumxor {
    [ exch
      2 combinations {
          dup 0 get exch 1 get xor
      } forall
    ] listmax
} bind def

Full code on github.

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