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aoc-racket/2019/22.rkt

89 lines
2.4 KiB
Racket

5 years ago
#lang br
(require racket/file rackunit)
(define (stack cards)
(reverse cards))
(define (cut n cards)
(define-values (head tail)
(split-at cards (match n
[(? positive?) n]
[_ (- (length cards) (abs n))])))
(append tail head))
(define (increment n cards)
(define len (length cards))
(define vec (make-vector len))
(for ([(card idx) (in-indexed cards)])
(vector-set! vec (modulo (* idx n) len) card))
(vector->list vec))
(define (run program [deck-size 10])
(for/fold ([cards (range deck-size)])
([ln (in-list (string-split program "\n"))])
(match (string-split ln)
[(list "cut" (app string->number num)) (cut num cards)]
[(list _ _ "increment" (app string->number num)) (increment num cards)]
[_ (stack cards)])))
(check-equal?
(run "deal with increment 7
deal into new stack
deal into new stack")
'(0 3 6 9 2 5 8 1 4 7))
(check-equal?
(run "cut 6
deal with increment 7
deal into new stack")
'(3 0 7 4 1 8 5 2 9 6))
(check-equal?
(run "deal into new stack
cut -2
deal with increment 7
cut 8
cut -4
deal with increment 7
cut 3
deal with increment 9
deal with increment 3
cut -1")
'(9 2 5 8 1 4 7 0 3 6))
;; 1
(check-eq? (index-of (run (file->string "22.rktd") 10007) 2019) 4086)
5 years ago
;; 2
#|
The idea is that the numbers are too large to shuffle the deck directly.
Unlike the previous question, this one asks what card is at a certain position.
So we want to go in reverse: just trace that position backwards through each operation
and figure out where we are at the start.
Also, we are likely going to discover a cycle in the transformations
(that is, card 2020 returns to position 2020 after a while)
and we can use this cycle length to reduce the number of times we have to execute the (un)shuffling.
("Likely" because otherwise this puzzle cannot be computed in reasonable time.)
|#
(define (unstack-pos cardlen pos) (- (sub1 cardlen) pos))
(check-eq? (unstack-pos 10 0) 9)
(check-eq? (unstack-pos 10 9) 0)
(define (uncut-pos cardlen pos n)
(define cut-pos (match n
[(? positive?) n]
[_ (- cardlen (abs n))]))
(cond
[(<= (- cardlen cut-pos) pos) (- pos (- cardlen cut-pos))]
[else (+ pos cut-pos)]))
(check-eq? (uncut-pos 10 7 3) 0)
(check-eq? (uncut-pos 10 0 3) 3)
(check-eq? (uncut-pos 10 7 -4) 3)
(check-eq? (uncut-pos 10 0 -4) 6)
(define (unincrement-pos cardlen pos inc)
42)