# Advent of Code 2022 day 4

Day 4 was an exercise in interval relationships, something I've used before in the day job.

## Representation

This followed the problem. An Assignment is a new data type; I represent pairs of Assignments as, well, pairs: 2-tuples. Reading and parsing the datafile is straightforward.

data Assignment = Assignment Int Int deriving (Show, Eq)
type Pair = (Assignment, Assignment)

pairsP = pairP sepBy endOfLine
pairP = (,) <$> assignmentP <* "," <*> assignmentP assignmentP = Assignment <$> decimal <* "-" <*> decimal


## Interval relations

We can say a few things about relations between intervals (assignments).

Inverval p contains interval q if p starts no later than q and p finishes no earlier than q.

Interval p is wholly before interval q if p finishes before q starts.

contains (Assignment lower1 upper1) (Assignment lower2 upper2) =
(lower1 <= lower2) && (upper1 >= upper2)

before (Assignment _lower1 upper1) (Assignment lower2 _upper2) = (upper1 < lower2)


A pair of intervals (p, q) has a containment if p contains q or q contains p.

A pair of intervals (p, q) is disjoint if p is before q or q is before p. p and q overlap if they are not disjoint.

hasContainment (assignment1, assignment2) =
(assignment1 contains assignment2) || (assignment2 contains assignment1)

disjoint (assignment1, assignment2) =
(assignment1 before assignment2) || (assignment2 before assignment1)

overlaps = not . disjoint


## Solution

With these definitions in place, the solutions are just filtering the list of assignment pairs depending on the relations we want.

part1 = length . (filter hasContainment)

part2 = length . (filter overlaps)