Copyright	(c) Eric Mertens 2021
License	ISC
Maintainer	emertens@gmail.com
Safe Haskell	None
Language	Haskell2010

Main

Contents

Segments
N-dimensional boxes

Description

https://adventofcode.com/2021/day/22

This problem is made simple by processing commands by subtracting away all future cuboids. Only the region unique to the current command will affect the final output.

Synopsis

data C
- = Con
- | Coff
main :: IO ()
solve :: [(C, Box n)] -> Int
applyCommand :: [Box n] -> (C, Box n) -> [Box n]
data Seg = Seg !Int !Int
len :: Seg -> Int
intersectSeg :: Seg -> Seg -> Maybe Seg
inSeg :: Int -> Seg -> Bool
data N
- = S N
- | Z
data Box :: N -> Type where
- Pt :: Box 'Z
- (:*) :: Seg -> Box n -> Box ('S n)
size :: Box n -> Int
intersectBox :: Box n -> Box n -> Maybe (Box n)
subBox :: Box n -> Box n -> [Box n]
traverseBox2 :: Applicative f => (Seg -> Seg -> f Seg) -> Box n -> Box n -> f (Box n)

Documentation

data C Source #

On and off commands from the input file

Constructors

Con
Coff

main :: IO () Source #

>>> :main
606484
1162571910364852

solve :: [(C, Box n)] -> Int Source #

Figure out how many lights the given instructions turn on.

applyCommand Source #

Arguments

:: [Box n]	pre-lit boxes
-> (C, Box n)	command
-> [Box n]	post-lit boxes

Apply a command given a list of non-overlapping, illuminated regions.

Segments

data Seg Source #

A segment defined by an inclusive lower-bound and an exclusive upper-bound.

Constructors

Seg !Int !Int

len :: Seg -> Int Source #

Compute the length of a segment

intersectSeg :: Seg -> Seg -> Maybe Seg Source #

Determine if two segments have some overlap

inSeg :: Int -> Seg -> Bool Source #

Determine if a value falls within a segment.

N-dimensional boxes

data N Source #

Natural numbers (used for type index)

Constructors

S N
Z

data Box :: N -> Type where Source #

An n-dimensional box.

Constructors

Pt
Fields :: Box 'Z A single point
(:*) infixr 6
Fields :: Seg -> Box n -> Box ('S n) A box extended along an axis

size :: Box n -> Int Source #

Returns the number of points contained in a box.

>>> size (Seg 1 4 :* Seg 0 3 :* Seg 0 2 :* Pt)
18

intersectBox :: Box n -> Box n -> Maybe (Box n) Source #

The intersection of two boxes is the intersection of their segments.

subBox Source #

Arguments

:: Box n	remove this
-> Box n	from this
-> [Box n]

Subtract the second box from the first box returning a list of boxes that cover all the remaining area.

>>> subBox (Seg 2 3 :* Pt) (Seg 0 4 :* Pt)
[Seg 0 2 :* Pt,Seg 3 4 :* Pt]

>>> subBox (Seg 3 5 :* Pt) (Seg 0 4 :* Pt)
[Seg 0 3 :* Pt]

traverseBox2 :: Applicative f => (Seg -> Seg -> f Seg) -> Box n -> Box n -> f (Box n) Source #

Zip two boxes together.