d22 p2 (stuck)

2019/22.rkt

@@ -53,3 +53,37 @@ cut -1")
 
 ;; 1
 (check-eq? (index-of (run (file->string "22.rktd") 10007) 2019) 4086)
+
+
+;; 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)