Day 24: Finished part 2.

src/24.rkt

@@ -6,6 +6,10 @@
 (define input
   (problem-input 24))
 
+;; coord : (list number number)
+;; grid : (vectorof (vectorof char))
+;; side : ('U | 'D | 'L | 'R)
+
 (define width
   (string-length (car input)))
 
@@ -21,19 +25,27 @@
 (define vector-grid
   (list->vector (map (∘ list->vector string->list) input)))
 
+;; make-empty-grid : -> grid
+;; Create a (height × width) vector grid of #\.
 (define (make-empty-grid)
   (build-vector height (λ (_) (make-vector width #\.))))
 
+;; outer-edge? : coord -> boolean
+;; Return whether the given coordinate is on the edge of the grid
 (define (outer-edge? coord)
   (match-let ([(list x y) coord])
     (or (= x 0) (= y 0)
         (= x (sub1 width)) (= y (sub1 height)))))
 
+;; inner-edge? : coord -> boolean
+;; Return whether the given coordinate is adjacent to the centre tile
 (define (inner-edge? coord)
   (match-let ([(list x y) coord])
-    (or (= x mid-x)
+    (or (and (= x mid-x) (<= (sub1 mid-y) y (add1 mid-y)))
-        (= y mid-y))))
+        (and (= y mid-y) (<= (sub1 mid-x) x (add1 mid-x))))))
 
+;; edge-bugs : grid -> side -> number
+;; Return the number of bugs on the top/bottom/left/right edge
 (define (edge-bugs grid side)
   (match side
     ['U (vector-count (∂ char=? #\#) (vector-ref grid 0))]
@@ -41,12 +53,16 @@
     ['L (vector-count (∂ char=? #\#) (vector-map (∂ vector-first) grid))]
     ['R (vector-count (∂ char=? #\#) (vector-map (∂ vector-last)  grid))]))
 
+;; edges-bugs? : grid -> boolean
+;; Return whether any of the edges have bugs
 (define (edges-bugs? grid)
   (!= 0 (+ (edge-bugs grid 'U)
            (edge-bugs grid 'D)
            (edge-bugs grid 'L)
            (edge-bugs grid 'R))))
 
+;; middle-bug : grid -> side -> number
+;; Return the number of bugs on the tile above/below/leftof/rightof the centre tile
 (define (middle-bug grid side)
   (match side
     ['U (if (char=? #\# (vector-grid-ref* grid (list mid-x (sub1 mid-y)) #\.)) 1 0)]
@@ -54,12 +70,16 @@
     ['L (if (char=? #\# (vector-grid-ref* grid (list (sub1 mid-x) mid-y) #\.)) 1 0)]
     ['R (if (char=? #\# (vector-grid-ref* grid (list (add1 mid-x) mid-y) #\.)) 1 0)]))
 
+;; middle-bugs? : grid -> boolean
+;; Return whether any of the tiles adjacent to the centre tile has bugs
 (define (middle-bugs? grid)
   (!= 0 (+ (middle-bug grid 'U)
            (middle-bug grid 'D)
            (middle-bug grid 'L)
            (middle-bug grid 'R))))
 
+;; adjacent-bugs : grid -> coord -> number
+;; Count the number of bugs adjacent to the given tile
 (define (adjacent-bugs grid coord)
   (match-let* ([(list x y) coord]
                [U (vector-grid-ref* grid (list x (sub1 y)) #\.)]
@@ -68,14 +88,39 @@
                [R (vector-grid-ref* grid (list (add1 x) y) #\.)])
     (count (∂ char=? #\#) (list U D L R))))
 
-(define (adjacent-bugs* grids level coord)
+;; adjacent-bugs* : level -> grid -> coord
+;; Count the number of bugs adjacent to the given tile
+;; on the grid on the given level
+;; However! If the coordinate is on the edge, instead of treating the other side
+;; like empty space, we look at the corresponding tile adjacent to the centre tile
+;; on the previous level's grid, as if the current grid were embedded
+;; Furthermore! If the coordinate is adjacent to the centre tile, instead of looking
+;; at the centre tile, we look at the corresponding edge of the next level's grid,
+;; as if that grid were embedded in the current one.
+;; By "corresponding", it means, for instance, if the current coordinate were on
+;; the top edge, we need to look at the tile above the centre tile in the previous grid;
+;; if the current coordinate were above the centre tile, we need to look at the top edge
+;; of the next grid.
+(define (adjacent-bugs* level grids coord)
   (match-let* ([(list x y) coord]
                [grid (list-ref grids level)]
                [level-bugs (adjacent-bugs grid coord)])
     (cond
       [(and (outer-edge? coord) (> level 0))
-       (let* ([outer-grid (list-ref grids (sub1 level))])
+       (let* ([outer-grid (list-ref grids (sub1 level))]
+              [U (middle-bug outer-grid 'U)]
+              [D (middle-bug outer-grid 'D)]
+              [L (middle-bug outer-grid 'L)]
+              [R (middle-bug outer-grid 'R)])
          (cond
+           [(and (= x 0) (= y 0))
+            (+ level-bugs L U)]
+           [(and (= x 0) (= y (sub1 height)))
+            (+ level-bugs L D)]
+           [(and (= x (sub1 width)) (= y 0))
+            (+ level-bugs R U)]
+           [(and (= x (sub1 width)) (= y (sub1 height)))
+            (+ level-bugs R D)]
            [(= x 0)
             (+ level-bugs (middle-bug outer-grid 'L))]
            [(= y 0)
@@ -95,39 +140,49 @@
             (+ level-bugs (edge-bugs inner-grid 'L))]
            [(and (= y mid-y) (> x mid-x))
             (+ level-bugs (edge-bugs inner-grid 'R))]
-           [else level-bugs]))]
+           [else 0]))]
       [else level-bugs])))
 
-(define (step grid)
+;; step-tile : char -> number -> char
+;; A bug dies unless it has exactly one bug neighbour
+;; A bug spawns if a space has one or two bug neighbours
+(define (step-tile char bugs)
+  (match char
+    [#\. #:when (<= 1 bugs 2) #\#]
+    [#\# #:when (!= 1 bugs)   #\.]
+    [else char]))
+
+;; step : (coord -> number) -> grid -> grid
+;; Return the grid after one minute of bugs dying and spawning
+;; The bug-counter takes a coordinate and returns the number of
+;; bugs adjacent to that coordinate
+;; For part 1, this is simply adjacent-bugs
+;; For part 2, we need to take into account previous and next levels,
+;; and so should be adjacent-bugs* wrt to the current level and grids
+(define (step bug-counter grid)
   (let ([new-grid (make-empty-grid)])
     (for ([coord (cartesian-product (range 0 width) (range 0 height))])
       (match-let* ([(list x y) coord]
                    [char (vector-ref (vector-ref grid y) x)]
-                   [bug-count (adjacent-bugs grid coord)]
+                   [bugs (bug-counter coord)]
-                   [next-char
+                   [next-char (step-tile char bugs)])
-                    (match char
-                      [#\. #:when (<= 1 bug-count 2) #\#]
-                      [#\# #:when (!= 1 bug-count) #\.]
-                      [else char])])
         (vector-set! (vector-ref new-grid y) x next-char)))
     new-grid))
 
+;; step* : grids -> grids
+;; Return the grids after one minute of bugs dying and spawning
+;; The bugs on the edge and near the centre of a given level
+;; will depend on the bugs near the centre and on the edge
+;; of the previous and next levels
+;; If the first (outermost) grid has bugs on the edge, their fate
+;; will depend on a yet outer grid, so we prepend an empty grid
+;; If the last (innermost) grid has bugs near the centre, their fate
+;; will depend on a yet inner grid, so we postpend an empty grid
 (define (step* grids)
   (let* ([grids*
-          (foldl
+          (foldr
            (λ (level grid grids*)
-             (let ([new-grid (make-empty-grid)])
+             (cons (step (∂ adjacent-bugs* level grids) grid) grids*))
-               (for ([coord (cartesian-product (range 0 width) (range 0 height))])
-                 (match-let* ([(list x y) coord]
-                              [char (vector-ref (vector-ref grid y) x)]
-                              [bug-count (adjacent-bugs* grids level coord)]
-                              [next-char
-                               (match char
-                                 [#\. #:when (<= 1 bug-count 2) #\#]
-                                 [#\# #:when (!= 1 bug-count) #\.]
-                                 [else char])])
-                   (vector-set! (vector-ref new-grid y) x next-char)))
-               (cons new-grid grids*)))
            '() (range 0 (length grids)) grids)]
          [grids* (if (edges-bugs? (first grids*))
                      (cons (make-empty-grid) grids*)
@@ -137,6 +192,10 @@
                      grids*)])
     grids*))
 
+;; biodiversity : grid -> number
+;; From left to right and top to bottom, the biodiversity of the grid
+;; is 2 to the power of the index of the tile if they were lined up
+;; in order starting from an index of 0
 (define (biodiversity grid)
   (let ([list-grid (append* (map vector->list (vector->list grid)))])
     (sum (map (λ (char i)
@@ -144,15 +203,25 @@
                     (expt 2 i) 0))
               list-grid (range 0 (length list-grid))))))
 
+;; total-bugs : grids -> number
 (define (total-bugs grids)
   (sum (map (λ (grid)
               (sum (vector->list (vector-map (∂ vector-count (∂ char=? #\#)) grid))))
             grids)))
 
+;; show-grids : grids -> void
+;; Print each grid from outermost to innermost separated by line breaks
+;; for... debugging
+(define (show-grids grids)
+  (for ([grid grids])
+    (for ([row grid])
+      (displayln (list->string (vector->list row))))
+    (displayln "")))
+
 (define part1
   (let loop ([grid vector-grid]
              [set (set vector-grid)])
-    (let ([next-grid (step grid)])
+    (let ([next-grid (step (∂ adjacent-bugs grid) grid)])
       (if (set-member? set next-grid)
           (biodiversity next-grid)
           (loop next-grid (set-add set next-grid))))))
@@ -160,7 +229,7 @@
 (define part2
   (let loop ([count 0]
              [grids (list (make-empty-grid) vector-grid (make-empty-grid))])
-    (if (= count 10)
+    (if (= count 200)
         (total-bugs grids)
         (loop (add1 count) (step* grids)))))