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#lang scribble/lp2
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@(require scribble/manual aoc-racket/helper)
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@aoc-title[25]
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@defmodule[aoc-racket/day25]
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@link["http://adventofcode.com/day/25"]{The puzzle}. Our @link-rp["day25-input.txt"]{input} is a row and column number for a grid.
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@chunk[<day25>
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<day25-setup>
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<day25-q1>
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<day25-test>]
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@section{What code do you give the machine?}
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The puzzle involves a series of codes in a grid. The first code is @racket[20151125] and subsequent codes are computed by multiplying by @racket[252533] and calculating the remainder after dividing by @racket[33554393]. Then the codes are put into a grid in diagonal fashion, in the order shown:
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@tt{
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| 1 2 3 4 5 6
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@(linebreak)
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++++++++++++++++++++++ @(linebreak)
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1 | 1 3 6 10 15 21 @(linebreak)
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2 | 2 5 9 14 20 @(linebreak)
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3 | 4 8 13 19 @(linebreak)
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4 | 7 12 18 @(linebreak)
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5 | 11 17 @(linebreak)
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6 | 16}
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The grid is described as infinite. But this doesn't play a role in the puzzle, since our job is to find the number at the finite coordinate given in our input. So we need a function for finding the @italic{n}th code in the series, and a function for finding which @italic{n} resides at a given grid location. Short & sweet.
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@chunk[<day25-setup>
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(require racket rackunit)
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(provide (all-defined-out))
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]
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@chunk[<day25-q1>
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(define first-code 20151125)
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(define (next-code code)
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(modulo (* code 252533) 33554393))
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(define (nth-code n)
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(for/fold ([code-so-far first-code])
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([i (in-range (sub1 n))])
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(next-code code-so-far)))
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(define (rc->n row col)
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(define first-col-val (add1 (apply + (range row))))
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(define col-offset-val (apply + (range (add1 row) (+ row col))))
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(+ first-col-val col-offset-val))
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(define (q1 input-str)
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(match-define (list _ row col)
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(map string->number
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(regexp-match #px"row (\\d+), column (\\d+)" input-str)))
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(nth-code (rc->n row col)))
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]
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@section{Testing Day 25}
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@chunk[<day25-test>
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(module+ test
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(define input-str (file->string "day25-input.txt"))
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(check-equal? (q1 input-str) 19980801))]
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