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#lang scribble/lp2
@(require scribble/manual aoc-racket/helper)
@link[""]{The puzzle}. Our @link-rp["day20-input.txt"]{input} is a target number of presents, in this case @racket[36000000].
@isection{What's the first house that gets the target number of presents?}
We're asked to imagine infinite elves delivering presents to an infinite sequence of houses. (Already @link[""]{I like} this puzzle.) The first elf delivers a present to every house equal to 10 times his number (= 10); the second elf, 20 gifts to every second house; the @italic{n}th elf, 10@italic{n} gifts to every @italic{n}th house.
Math jocks will notice that the elf behavior roughly describes a @link[""]{Sieve of Eratosthenes}. Each house is visited by elf @italic{n} only if @italic{n} is a divisor of the house number. (Houses that are primes are therefore only visited by the first elf.) Might there be a Racket function that finds the divisors of a number? Why, yes it's called @iracket[divisors]. We can use it to find the numbers of the elves that visit a house, and loop through house numbers till we reach the target. (The 10-gift multiplier is arbitrary.)
(require racket rackunit (only-in math divisors))
(provide (all-defined-out))
(define (q1 input-str)
(define target-gifts (read (open-input-string input-str)))
(define gifts-per-elf 10)
(for/first ([house-number (in-naturals)]
#:when (let* ([elves (divisors house-number)]
(apply + (map (curry * gifts-per-elf) elves))])
(>= elf-gifts target-gifts)))
@isection{What's the first house that gets the target number of presents, if each elf delivers 11 gifts to 50 houses?}
Going with the math-jock vibe, what this condition means is that the highest-numbered house the @italic{n}th elf will visit is 50@italic{n}. So the answer for this question is like the first, but we'll @iracket[filter] the list of elves using this condition.
(define (q2 input-str)
(define target-gifts (read (open-input-string input-str)))
(define gifts-per-elf 11)
(for/first ([house-number (in-naturals)]
#:when (let* ([elves (divisors house-number)]
[elves (filter
(λ (e) (<= house-number (* 50 e))) elves)]
(apply + (map (curry * gifts-per-elf) elves))])
(>= elf-gifts target-gifts)))
@section{Testing Day 20}
(module+ test
(define input-str (file->string "day20-input.txt"))
(check-equal? (q1 input-str) 831600)
(check-equal? (q2 input-str) 884520))]