day 13 part 2

2020/13.rkt

@@ -1,5 +1,5 @@
 #lang br
-(require racket/file rackunit)
+(require racket/file rackunit racket/dict)
 
 (match-define (cons target buses-all)
   (for/list ([tok
@@ -8,13 +8,34 @@
                         (string-replace (file->string "13.rktd") "," " ")))])
     tok))
 
-(define buses (filter integer? buses-all))
-
 (define (overshoot bus)
   (for/last ([i (in-naturals)]
              #:final (> (* i bus) target))
     (- (* i bus) target)))
 
-(define winner (argmin overshoot buses))
+(define (solve-1)
+  (define winner (argmin overshoot (filter integer? buses-all)))
+  (* winner (overshoot winner)))
+
+(check-equal? (solve-1) 246)
+
+(define (solve-2)
+  (define pairs (for/list ([(b i) (in-indexed buses-all)]
+                           #:when (integer? b))
+                  (cons b i)))
+  (for/fold ([t 0]
+             [increment 1]
+             #:result t)
+            ([(bus overshoot) (in-dict pairs)])
+    (define mod-target (let loop ([overshoot overshoot])
+                         (cond
+                           [(zero? overshoot) 0]
+                           [(< overshoot bus) (- bus overshoot)]
+                           [else (loop (- overshoot bus))])))
+    (define multiplier
+      (for/first ([multiplier (in-naturals)]
+                  #:when (= (modulo (+ t (* increment multiplier)) bus) mod-target))
+        multiplier))
+    (values (+ t (* increment multiplier)) (* increment bus))))
 
-(check-equal? (* winner (overshoot winner)) 246)
+(check-equal? (solve-2) 939490236001473)