RogerBW's Blog

I’ve been doing the Weekly Challenges. The latest involved matrix evaluation and integer searching. (Note that this closes today.)

Task 1: Toeplitz Matrix

You are given a matrix m x n.

Write a script to find out if the given matrix is Toeplitz Matrix.

A matrix is Toeplitz if every diagonal from top-left to bottom-right has the same elements.

I don't see any obvious short-cuts here.

Perl:

sub toeplitzmatrix($a) {
  my $ym = $#{$a};
  my $xm = $#{$a->[0]};

Finding one non-consistent diagonal will be enough for a false return. But we have to check all of them to get a true one.

  my $toeplitz = 1;

The X coordinate of the start of every conceivable diagonal runs from -X to +Y.

  foreach my $xb ((1 - $xm)..($ym - 1)) {
    my $init = 1;
    my $tv = 0;

Each possible entry on that diagonal:

    foreach my $x ($xb .. $xb + $xm) {

…may not exist.

      if ($x >= 0 && $x <= $xm) {

Similarly, the Y coordinate may not exist.

        my $y = $x - $xb;

If they do, though, store the value if it's the first one we've met.

        if ($y >= 0 && $y <= $ym) {
          if ($init) {
            $init = 0;
            $tv = $a->[$y][$x];

Otherwise, if it doesn't match that stored value, drop out with a false return.

          } elsif ($a->[$y][$x] != $tv) {
            $toeplitz = 0;
            last;
          }
        }
      }
    }
    unless ($toeplitz) {
      last;
    }
  }
  return $toeplitz;
}

Task 2: Split Same Average

You are given an array of integers.

Write a script to find out if the given array can be split into two separate arrays whose average are the same.

This means generating combinations, and I finally bit the bullet and wrote combination generators for the languages that didn't have them built in (Kotlin, Lua and JavaScript). (I'm not claiming that these don't exist in libraries, but they're not trivially available.)

Raku has a Rat type for rational fractions, but otherwise I used floating-point equality tests. (Rust does too, but I didn't know about it.)

In Rust:

fn splitsameaverage(a: Vec<i32>) -> bool {

Pre-calculate the sum of the list, and store the numnber of entries in it.

    let ss = a.iter().sum::<i32>();
    let ml = a.len();

I'll be checking each combination up to half the length (rounded down).

    let mx = ml / 2;

One positive result will be enough for an early exit.

    let mut ssa = false;

Each combination size:

    for n in 1 ..= mx {

Each combination:

        for c in a.iter().combinations(n) {

Get the sum of the included elements.

            let ca = c.iter().map(|i| *i).sum::<i32>();

If the mean of that equals the mean of everything else, return true.

            if (ca as f64) / (n as f64) == ((ss - ca) as f64) / ((ml - n) as f64) {
                ssa = true;
                break;
            }
        }
        if ssa {
            break;
        }
    }
    ssa
}

Full code on github.