day20

aoc-racket.scrbl

@@ -40,3 +40,4 @@ You can install this package (if you haven't already) with
 @include-section[(submod "day17.rkt" doc)]
 @include-section[(submod "day18.rkt" doc)]
 @include-section[(submod "day19.rkt" doc)]
+@include-section[(submod "day20.rkt" doc)]

day20-input.txt

@@ -0,0 +1 @@
+36000000

day20.rkt

@@ -0,0 +1,72 @@
+#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[<day20>
+       <day20-setup>
+       <day20-q1>
+       <day20-q2>
+       <day20-test>]
+
+@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[<day20-setup>
+       (require racket rackunit (only-in math divisors))
+       (provide (all-defined-out))
+       ]
+
+@chunk[<day20-q1>
+       
+       (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[<day20-q2>
+       
+       (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 18}
+
+@chunk[<day20-test>
+       (module+ test
+         (define input-str (file->string "day20-input.txt"))
+         (check-equal? (q1 input-str) 831600)
+         (check-equal? (q2 input-str) 884520))]
+
+