#lang scribble/lp2 @(require scribble/manual aoc-racket/helper) @aoc-title[20] @defmodule[aoc-racket/day20] @link["http://adventofcode.com/day/20"]{The puzzle}. Our @link-rp["day20-input.txt"]{input} is a target number of presents, in this case @racket[36000000]. @chunk[ ] @section{What's the first house that gets the target number of presents?} The puzzle imagines infinite elves delivering presents to an infinite sequence of houses. (Already @link["http://practicaltypography.com/the-infinite-pixel-screen.html"]{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["https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes"]{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 @racket[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.) @chunk[ (require racket rackunit (only-in math divisors)) (provide (all-defined-out)) ] @chunk[ (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)] [elf-gifts (apply + (map (curry * gifts-per-elf) elves))]) (>= elf-gifts target-gifts))) house-number))] @section{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 @racket[filter] the list of elves using this condition. @chunk[ (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)] [elf-gifts (apply + (map (curry * gifts-per-elf) elves))]) (>= elf-gifts target-gifts))) house-number)) ] @section{Testing Day 20} @chunk[ (module+ test (define input-str (file->string "day20-input.txt")) (check-equal? (q1 input-str) 831600) (check-equal? (q2 input-str) 884520))]