Farmer John is not good at multitasking. He gets distracted often, making it hard to complete long projects. Currently, he is trying to paint one side of his barn, but he keeps painting small rectangular areas and then getting sidetracked by the needs of tending to his cows, leaving some parts of the barn painted with more coats of paint than others.

We can describe the side of the barn as a 2D x-y plane, on which Farmer John paints N rectangles, each with sides parallel to the coordinate axes, each described by the coordinates of its lower-left and upper-right corner points.

Farmer John wants to apply several coats of paint to the barn so it doesn't need to be repainted again in the immediate future. However, he doesn't want to waste time applying an excessive number of coats of paint. It turns out that K coats of paint is the optimal amount. However, looking at the amount of area covered by K coats of paint, he is not very happy. He is willing to paint up to two additional rectangles to try and increase this area, as long as these two rectangles are disjoint (not sharing any positive amount of area in common). Note that he can also decide to paint zero new rectangles or just one new rectangle if this ends up being the best thing to do.

Problem credits: Nick Wu and Brian Dean

#4110 upload 1 done 1 how_to_reg 1

Painting the Barn timer 2s memory 512MB

#4110

Painting the Barn 2s 512MB