RogerBW's Blog

I’ve been doing the Weekly Challenges. The latest involved list testing and matrix reconstruction. (Note that this is open until 19 February 2023.)

Task 1: Monotonic Array

You are given an array of integers.

Write a script to find out if the given array is Monotonic. Print 1 if it is otherwise 0.

An array is Monotonic if it is either monotone increasing or decreasing.

This isn't my usual understanding of the term, in which all differences should be equal – i.e. 1, 3, 5 would qualify but 1, 3, 4 would not. But here in effect we're asked to verify that the direction is consistent.

In other words, all the differences are positive-or-zero, or they're all negative-or-zero.

And therefore if I multiply the lowest difference by the highest, the result will be positive or zero.

So that's what I do. The most compact code is in Raku:

sub monotonicarray(@l) {
    my @d = @l.rotor(2 => -1).map({$_[1] - $_[0]});
    return @d.min * @d.max >= 0;
}

but it's not so very much longer in a lanuage such as Lua that doesn't have these convenience functions:

function monotonicarray(l)
   local d = {}
   for i = 1, #l - 1 do
      table.insert(d, l[i + 1] - l[i])
   end
   return math.min(table.unpack(d)) * math.max(table.unpack(d)) >= 0
end

Task 2: Reshape Matrix

You are given a matrix (m x n) and two integers (r) and (c).

Write a script to reshape the given matrix in form (r x c) with the original value in the given matrix. If you can’t reshape print 0.

I do this in three steps:

• flatten the input array of arrays (I've never had a use for flattening in real life);
• check whether we have the right number of entries for the desired output size;
• drop those numbers into an output list, one new row's worth at a time.

JavaScript:

function reshapematrix(m, r, c) {
    let mv = m.flat();
    if (r * c != mv.length) {
        return [[0]];
    }
    let out = [];
    for (let i = 0; i < r; i++) {
        out.push(mv.slice(i * c, (i + 1) * c));
    }
    return out;
}

and PostScript isn't wildly different except for using fewer variables.

/reshapematrix {
    3 dict begin
    /c exch def
    /r exch def
    /mx exch
    [ exch
      {
          {
          } forall
      } forall
    ] def
    r c mul mx length eq {
        [
            0 1 r 1 sub {
                mx exch c mul c getinterval
            } for
        ]
    } {
        [ [ 0 ] ]
    } ifelse
    end
} bind def

Full code on github.