From cbb9262fbdfee490fa29de4171780fb4c7dd7614 Mon Sep 17 00:00:00 2001
From: Jonathan Chan <jonathanhwchan@gmail.com>
Date: Sun, 22 Dec 2019 00:50:36 -0800
Subject: [PATCH] Day 22: Part 1 complete, part 2... still running?

---
 input/22.txt | 100 +++++++++++++++++++++++++++++++++++++++++++++++++++
 src/22.rkt   |  92 +++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 192 insertions(+)
 create mode 100644 input/22.txt
 create mode 100644 src/22.rkt

diff --git a/input/22.txt b/input/22.txt
new file mode 100644
index 0000000..154b55c
--- /dev/null
+++ b/input/22.txt
@@ -0,0 +1,100 @@
+deal with increment 31
+deal into new stack
+cut -7558
+deal with increment 49
+cut 194
+deal with increment 23
+cut -4891
+deal with increment 53
+cut 5938
+deal with increment 61
+cut 7454
+deal into new stack
+deal with increment 31
+cut 3138
+deal with increment 53
+cut 3553
+deal with increment 61
+cut -5824
+deal with increment 42
+cut -889
+deal with increment 34
+cut 7128
+deal with increment 42
+cut -9003
+deal with increment 75
+cut 13
+deal with increment 75
+cut -3065
+deal with increment 74
+cut -8156
+deal with increment 39
+cut 4242
+deal with increment 24
+cut -405
+deal with increment 27
+cut 6273
+deal with increment 19
+cut -9826
+deal with increment 58
+deal into new stack
+cut -6927
+deal with increment 65
+cut -9906
+deal with increment 31
+deal into new stack
+deal with increment 42
+deal into new stack
+deal with increment 39
+cut -4271
+deal into new stack
+deal with increment 32
+cut -8799
+deal with increment 69
+cut 2277
+deal with increment 55
+cut 2871
+deal with increment 54
+cut -2118
+deal with increment 15
+cut 1529
+deal with increment 57
+cut -4745
+deal with increment 23
+cut -5959
+deal with increment 58
+deal into new stack
+deal with increment 48
+deal into new stack
+cut 2501
+deal into new stack
+deal with increment 42
+deal into new stack
+cut 831
+deal with increment 74
+cut -3119
+deal with increment 33
+cut 967
+deal with increment 69
+cut 9191
+deal with increment 9
+cut 5489
+deal with increment 62
+cut -9107
+deal with increment 14
+cut -7717
+deal with increment 56
+cut 7900
+deal with increment 49
+cut 631
+deal with increment 14
+deal into new stack
+deal with increment 58
+cut -9978
+deal with increment 48
+deal into new stack
+deal with increment 66
+cut -1554
+deal into new stack
+cut 897
+deal with increment 36
diff --git a/src/22.rkt b/src/22.rkt
new file mode 100644
index 0000000..a1b629a
--- /dev/null
+++ b/src/22.rkt
@@ -0,0 +1,92 @@
+#lang racket
+
+(require match-string
+         "../lib.rkt")
+
+(define input
+  (problem-input 22))
+
+(define (parse-technique technique)
+  (match technique
+    ["deal into new stack" deal-into-new-stack]
+    [(string-append "cut " s) (∂ cut-N-cards (string->number s))]
+    [(string-append "deal with increment " s) (∂ deal-with-increment-N (string->number s))]))
+
+(define (deal-into-new-stack cards)
+  (reverse cards))
+
+(define (cut-N-cards n cards)
+  (if (negative? n)
+      (cut-N-cards (+ (length cards) n) cards)
+      (append (drop cards n) (take cards n))))
+
+(define (deal-with-increment-N n cards)
+  (let* ([len (length cards)]
+         [vec (make-vector len)])
+    (for ([index (range 0 len)]
+          [card cards])
+      (vector-set! vec (modulo (* index n) len) card))
+    (vector->list vec)))
+
+(define part1
+  (let loop ([cards (range 0 10007)]
+             [shuffle input])
+    (if (empty? shuffle)
+        (index-of cards 2019)
+        (loop ((parse-technique (first shuffle)) cards) (rest shuffle)))))
+
+;; egcd : number -> number -> (list number number number)
+;; Extended Euclidean algorithm for computing GCD
+;; Given integers a and b, return gcd(a, b), x, and y, where
+;; ax + by = gcd(a, b).
+(define (egcd a b)
+  (if (zero? a)
+      (list b 0 1)
+      (match-let ([(list g x y) (egcd (remainder b a) a)])
+        (list g (- y (* x (quotient b a))) x))))
+
+;; mmi : number -> number -> number
+;; Modular multiplicative inverse
+;; Given an integer n and a modulus m, return x such that
+;; nx ≡ 1 (mod m), i.e. nx + my = 1 for some x, y.
+;; We therefore require that n and m are coprime.
+(define (mmi n m)
+  (match-let ([(list g x y) (egcd n m)])
+    x))
+
+;; The following functions are inverse to those from part 1
+;; with respect to the card indices.
+;; That is, if some shuffling technique s takes a card at index i
+;; and moves it to index s(i) = j, then s^-1(j) = i.
+;; Therefore, if after applying a series of shuffling techniques,
+;; we want to know what card is at position p,
+;; we apply the inverse functions in reverse order to find its original index.
+
+(define (inverse-DINS len i)
+  (sub1 (- len i)))
+
+(define (inverse-CNC len n i)
+  (if (positive? n)
+      (modulo (+ n i) len)
+      (modulo (+ n i len) len)))
+
+(define (inverse-DWIN len n i)
+  (modulo (* (mmi n len) i) len))
+
+(define (inverse-parse len technique)
+  (match technique
+    ["deal into new stack" (∂ inverse-DINS len)]
+    [(string-append "cut " s) (∂ inverse-CNC len (string->number s))]
+    [(string-append "deal with increment " s) (∂ inverse-DWIN len (string->number s))]))
+
+(define (inverse-shuffle len)
+  (apply compose (map (∂ inverse-parse len) input)))
+
+(define (part2)
+  (let loop ([count 101741582076661]
+             [index 2020])
+    (if (zero? count)
+        index
+        (loop (sub1 count) ((inverse-shuffle 119315717514047) index)))))
+
+(show-solution part1 #f)
\ No newline at end of file