RogerBW's Blog

I’ve been doing the Weekly Challenges. The latest involved finding minimum paths and overlapping rectangles. (Note that this is open until 20 February 2022.)

Task 1: Triangle Sum Path

You are given a triangle array.

Write a script to find the minimum sum path from top to bottom.

With some clarification from the examples, this isn't "descend either left or right" – which would be quite like last week's part 2 – but "pick one entry from each row". Which is therefore pretty simple; in Perl:

sub tsp {
  my $tree = shift;
  my $mp=0;
  foreach my $r (@{$tree}) {
    $mp+=min(@{$r});
  }
  return $mp;
}

Task 2: Rectangle Area

You are given coordinates bottom-left and top-right corner of two rectangles in a 2D plane.

Write a script to find the total area covered by the two rectangles.

The basic approach here is to take the area of each rectangle separately, then subtract the area common to both (if any).

(If you have the outline of a simple polygon there's a rather neat formula for the area, but getting to a single outline would have been more work than doing it this way.)

I'm not sure quite why, but this felt like one to do in an OOP style. (Admittedly in a half-hearted way in PostScript; I think it should be possible to define an object as a dict, as Lua does in effect, and attach methods directly to it, but I just wrote them as plain code blocks.) Here's the JavaScript version.

When we initialise the object, we sort it so that xy1 has the lower left coordinates and xy2 the upper right. (This isn't necessary with the examples given, but.)

function Rect(xy1,xy2) {
    let r=Object.create(Rect.methods);
    r.xy1=[Math.min(xy1[0],xy2[0]),Math.min(xy1[1],xy2[1])];
    r.xy2=[Math.max(xy1[0],xy2[0]),Math.max(xy1[1],xy2[1])];
    return r;
}

Rect.methods = {

We need three methods apart from the constructor. First, the simple area calculator:

    area() {
        let area=1;
        for (let axis=0;axis<=1;axis++) {
            area *= this.xy2[axis]-this.xy1[axis];
        }
        return area;
    },

The overlap calculator (I use other as a contrast with the self in most other languages; I suppose for JS I should have used that contrasting with this). Note that this is just as susceptible to a per-axis approach as the area calculator above; on any given axis, the degree of overlap is the smaller of the two high coordinates, minus the larger of the two low coordinates. If they don't overlap at all, this number will be zero or negative, so we make sure it's not below zero.

    overlap(other) {
        let area=1;
        for (let axis=0;axis<=1;axis++) {
            area *= Math.max(0,
                             Math.min(this.xy2[axis],other.xy2[axis])-
                             Math.max(this.xy1[axis],other.xy1[axis])
                            );
        }
        return area;
    },

And the "full area" calculator: the object's own area, plus the area of the other rectangle, minus the overlap.

    fullarea(other) {
        return this.area()+other.area()-this.overlap(other);
    }
}

Full code on github.