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Day 18: Part 2 complete.

This commit is contained in:
Jonathan Chan 2019-12-25 21:00:30 -08:00
parent eedf2c6391
commit 35437aeb6a
6 changed files with 393 additions and 201 deletions
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(require racket/set
data/heap
graph
(only-in 2htdp/batch-io read-lines)
(except-in "../lib.rkt" transpose))
(define input
(read-lines filename))
(define list-grid
(map string->list input))
(define vector-grid
(lists->vectors list-grid))
(define width
(length (car list-grid)))
(define height
(length list-grid))
(define (show-grid)
(for-each displayln
(map (λ (s)
(string-replace (string-replace s "#" "█") "." " "))
input)))
;; keys : (setof char)
(define keys
(list->set
(cons #\@
(map integer->char
(range (char->integer #\a)
(add1 (char->integer #\z)))))))
;; coord : (list number number)
;; get-char : coord -> char
(define (get-char coord)
(match-let ([(list x y) coord])
(if (or (< x 0) (< y 0)
(>= x width)
(>= y height))
#\#
(vector-ref (vector-ref vector-grid y) x))))
;; neighbours : coord -> (listof coord)
;; If the coordinate is occupiable (by a key, door, or bot),
;; return the neighbouring coordinates that are also occupiable
(define (neighbours coord)
(if (char=? #\# (get-char coord)) '()
(match-let ([(list x y) coord])
(let ([U (list x (sub1 y))]
[D (list x (add1 y))]
[L (list (sub1 x) y)]
[R (list (add1 x) y)])
(filter-not
(∘ (∂ char=? #\#) (∂ get-char))
(list U D L R))))))
;; graph-grid : unweighted, undirected graph
;; Vertices are (char . coord)
;; Edges between traversable coordinates
(define graph-grid
(let* ([coords (cartesian-product (range 1 (sub1 width))
(range 1 (sub1 height)))]
[graph (unweighted-graph/undirected '())])
(for ([coord coords])
(let ([ncoords (neighbours coord)])
(for ([ncoord ncoords])
(add-edge! graph
(cons (get-char coord) coord)
(cons (get-char ncoord) ncoord)))))
graph))
;; keys-hash : (hashof (char => coord))
;; A hashmap from keys to their coordinates, including #\@
(define keys-hash
(let ([hash (make-immutable-hash)]
[coords (cartesian-product (range 1 (sub1 width))
(range 1 (sub1 height)))])
(foldl (λ (coord hash)
(let ([char (get-char coord)])
(if (or (char=? #\@ char)
(char-lower-case? char))
(hash-set hash char coord)
hash)))
hash coords)))
;; start : (char . coord)
;; Char-coord pair of #\@, for convenience
(define start
(cons #\@ (hash-ref keys-hash #\@)))
;; visited : (setof char)
;; Assume that we already have any key that does not
;; show up in the hash, as well as the starting point #\@
(define visited
(set-add (set-subtract keys (list->set (hash-keys keys-hash))) #\@))
;; inter-keys-hash : (hashof (char => char))
;; A hashmap from keys to the keys that must be collected
;; when taking the shortest path from #\@ to that key
(define inter-keys-hash
(let ([hash (make-immutable-hash)])
(foldl (λ (keycoord hash)
(match-let* ([(cons key _) keycoord]
[path (map car (fewest-vertices-path graph-grid start keycoord))]
[inter-keys (remove* (list #\@ key) (filter char-lower-case? path))])
(hash-set hash key inter-keys)))
hash (hash->list keys-hash))))
;; doors : (hashof (char => (listof char)))
;; A hashmap from keys to the list of keys for the doors
;; that stand between the starting point #\@ and that key
(define doors-hash
(let ([hash (make-immutable-hash)])
(foldl (λ (keycoord hash)
(match-let* ([(cons key _) keycoord]
[path (map car (fewest-vertices-path graph-grid start keycoord))]
[doors (map char-downcase (filter char-upper-case? path))])
(hash-set hash key doors)))
hash (hash->list keys-hash))))
;; key-graph : weighted, undirected graph
;; Vertices are char (keys)
;; Edges between neighbouring keys
;; Weights are distances between keys
(define key-graph
(let ([graph (weighted-graph/undirected '())]
[key-pairs (combinations (hash-keys keys-hash) 2)])
(for ([pair key-pairs])
(match-let* ([(list key1 key2) pair]
[keycoord1 (cons key1 (hash-ref keys-hash key1))]
[keycoord2 (cons key2 (hash-ref keys-hash key2))]
[path (fewest-vertices-path graph-grid keycoord1 keycoord2)]
[distance (sub1 (length path))])
(add-edge! graph key1 key2 distance)))
graph))
;; visitable? : (setof char) -> char -> boolean
;; Given a set of visited keys and a prospective key,
;; return whether we visit that key based on three conditions:
;; - There isn't a closer key we could visit;
;; - The key has not yet been visited; and
;; - We have the keys needed to open all doors leading to that key.
(define (visitable? visited key)
(let* ([visitable-inter-keys (filter-not (∂ set-member? visited) (hash-ref inter-keys-hash key))])
(and (empty? visitable-inter-keys)
(not (set-member? visited key))
(andmap (∂ set-member? visited) (hash-ref doors-hash key)))))
;; We do a breadth-first search over an implicit graph.
;; The nodes of this graph are visit states, which consist of
;; the current key we are at, as well as the keys we have visited.
;; This is why state=? only compares key and visited when removing
;; states from the heap.
;; States are ordered by the total number of steps taken,
;; which is also saved in the state struct.
;; This is why state<? only orders by steps.
;; Starting from the state with the fewest steps taken so far,
;; we visit all of its neighbours, which are the visitable keys
;; with the accumulated visited keys at that point.
;; The visitable keys are given by the conditions above in visitable?
;; For each neighbouring state, if the steps taken to get there
;; is smaller than the same existing state already in the heap,
;; we "update" the state by removing the old state from the heap
;; and adding the same state with the new number of steps into the heap.
;; Using a hashmap from states to steps allows us to find the old steps
;; if it exists (since data/heap doesn't have a find operation).
(struct state (key visited steps) #:transparent)
(define (state=? st1 st2)
(and (equal? (state-key st1) (state-key st2))
(equal? (state-visited st1) (state-visited st2))))
(define (state<? st1 st2)
(< (state-steps st1) (state-steps st2)))
(define (search key-count)
(let ([heap (make-heap state<?)]
[memo (make-hash)])
(heap-add! heap (state #\@ visited 0))
(match-let loop ([(state key visited steps) (heap-min heap)])
(heap-remove-min! heap)
(if (= (set-count visited) key-count)
steps
(let* ([visitable (filter (∂ visitable? visited) (get-neighbors key-graph key))])
(for ([nkey visitable])
(let* ([visited (set-add visited nkey)]
[steps (+ steps (edge-weight key-graph key nkey))]
[memo-steps (hash-ref memo (cons nkey visited) +inf.0)]
[st (state nkey visited steps)])
(when (< steps memo-steps)
(hash-set! memo (cons nkey visited) steps)
(heap-remove! heap st #:same? state=?)
(heap-add! heap st))))
(loop (heap-min heap)))))))
(search (set-count keys))

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#lang racket #lang racket/load
(require racket/set (require "../lib.rkt")
data/heap
graph
(only-in 2htdp/batch-io read-lines)
(except-in "../lib.rkt" transpose))
(define input (define filename "../input/18.txt")
(read-lines "../input/18.txt"))
(define list-grid
(map string->list input))
(define vector-grid
(lists->vectors list-grid))
(define width
(length (car list-grid)))
(define height
(length list-grid))
(define (show-grid)
(for-each displayln
(map (λ (s)
(string-replace (string-replace s "#" "█") "." " "))
input)))
;; keys : (setof char)
(define keys
(list->set
(cons #\@
(map integer->char
(range (char->integer #\a)
(add1 (char->integer #\z)))))))
;; coord : (list number number)
;; get-char : coord -> char
(define (get-char coord)
(match-let ([(list x y) coord])
(if (or (< x 0) (< y 0)
(>= x width)
(>= y height))
#\#
(vector-ref (vector-ref vector-grid y) x))))
;; neighbours : coord -> (listof coord)
;; If the coordinate is occupiable (by a key, door, or bot),
;; return the neighbouring coordinates that are also occupiable
(define (neighbours coord)
(if (char=? #\# (get-char coord)) '()
(match-let ([(list x y) coord])
(let ([U (list x (sub1 y))]
[D (list x (add1 y))]
[L (list (sub1 x) y)]
[R (list (add1 x) y)])
(filter-not
(∘ (∂ char=? #\#) (∂ get-char))
(list U D L R))))))
;; graph-grid : unweighted, undirected graph
;; Vertices are (char . coord)
;; Edges between traversable coordinates
(define graph-grid
(let* ([coords (cartesian-product (range 1 (sub1 width))
(range 1 (sub1 height)))]
[graph (unweighted-graph/undirected '())])
(for ([coord coords])
(let ([ncoords (neighbours coord)])
(for ([ncoord ncoords])
(add-edge! graph
(cons (get-char coord) coord)
(cons (get-char ncoord) ncoord)))))
graph))
;; keys-hash : (hashof (char => coord))
;; A hashmap from keys to their coordinates, including #\@
(define keys-hash
(let ([hash (make-immutable-hash)]
[coords (cartesian-product (range 1 (sub1 width))
(range 1 (sub1 height)))])
(foldl (λ (coord hash)
(let ([char (get-char coord)])
(if (or (char=? #\@ char)
(char-lower-case? char))
(hash-set hash char coord)
hash)))
hash coords)))
;; start : (char . coord)
;; Char-coord pair of #\@, for convenience
(define start
(cons #\@ (hash-ref keys-hash #\@)))
;; visited : (setof char)
;; Assume that we already have any key that does not
;; show up in the hash, as well as the starting point #\@
(define visited
(set-add (set-subtract keys (list->set (hash-keys keys-hash))) #\@))
;; inter-keys-hash : (hashof (char => char))
;; A hashmap from keys to the keys that must be collected
;; when taking the shortest path from #\@ to that key
(define inter-keys-hash
(let ([hash (make-immutable-hash)])
(foldl (λ (keycoord hash)
(match-let* ([(cons key _) keycoord]
[path (map car (fewest-vertices-path graph-grid start keycoord))]
[inter-keys (remove* (list #\@ key) (filter char-lower-case? path))])
(hash-set hash key inter-keys)))
hash (hash->list keys-hash))))
;; doors : (hashof (char => (listof char)))
;; A hashmap from keys to the list of keys for the doors
;; that stand between the starting point #\@ and that key
(define doors-hash
(let ([hash (make-immutable-hash)])
(foldl (λ (keycoord hash)
(match-let* ([(cons key _) keycoord]
[path (map car (fewest-vertices-path graph-grid start keycoord))]
[doors (map char-downcase (filter char-upper-case? path))])
(hash-set hash key doors)))
hash (hash->list keys-hash))))
;; key-graph : weighted, undirected graph
;; Vertices are char (keys)
;; Edges between neighbouring keys
;; Weights are distances between keys
(define key-graph
(let ([graph (weighted-graph/undirected '())]
[key-pairs (combinations (hash-keys keys-hash) 2)])
(for ([pair key-pairs])
(match-let* ([(list key1 key2) pair]
[keycoord1 (cons key1 (hash-ref keys-hash key1))]
[keycoord2 (cons key2 (hash-ref keys-hash key2))]
[path (fewest-vertices-path graph-grid keycoord1 keycoord2)]
[distance (sub1 (length path))])
(add-edge! graph key1 key2 distance)))
graph))
;; visitable? : (setof char) -> char -> boolean
;; Given a set of visited keys and a prospective key,
;; return whether we visit that key based on three conditions:
;; - There isn't a closer key we could visit;
;; - The key has not yet been visited; and
;; - We have the keys needed to open all doors leading to that key.
(define (visitable? visited key)
(let* ([visitable-inter-keys (filter-not (∂ set-member? visited) (hash-ref inter-keys-hash key))])
(and (empty? visitable-inter-keys)
(not (set-member? visited key))
(andmap (∂ set-member? visited) (hash-ref doors-hash key)))))
;; We do a breadth-first search over an implicit graph.
;; The nodes of this graph are visit states, which consist of
;; the current key we are at, as well as the keys we have visited.
;; This is why state=? only compares key and visited when removing
;; states from the heap.
;; States are ordered by the total number of steps taken,
;; which is also saved in the state struct.
;; This is why state<? only orders by steps.
;; Starting from the state with the fewest steps taken so far,
;; we visit all of its neighbours, which are the visitable keys
;; with the accumulated visited keys at that point.
;; The visitable keys are given by the conditions above in visitable?
;; For each neighbouring state, if the steps taken to get there
;; is smaller than the same existing state already in the heap,
;; we "update" the state by removing the old state from the heap
;; and adding the same state with the new number of steps into the heap.
;; Using a hashmap from states to steps allows us to find the old steps
;; if it exists (since data/heap doesn't have a find operation).
(struct state (key visited steps) #:transparent)
(define (state=? st1 st2)
(and (equal? (state-key st1) (state-key st2))
(equal? (state-visited st1) (state-visited st2))))
(define (state<? st1 st2)
(< (state-steps st1) (state-steps st2)))
(define (search key-count)
(let ([heap (make-heap state<?)]
[memo (make-hash)])
(heap-add! heap (state #\@ visited 0))
(match-let loop ([(state key visited steps) (heap-min heap)])
(heap-remove-min! heap)
(if (= (set-count visited) key-count)
steps
(let* ([visitable (filter (∂ visitable? visited) (get-neighbors key-graph key))])
(for ([nkey visitable])
(let* ([visited (set-add visited nkey)]
[steps (+ steps (edge-weight key-graph key nkey))]
[memo-steps (hash-ref memo (cons nkey visited) +inf.0)]
[st (state nkey visited steps)])
(when (< steps memo-steps)
(hash-set! memo (cons nkey visited) steps)
(heap-remove! heap st #:same? state=?)
(heap-add! heap st))))
(loop (heap-min heap)))))))
(define part1 (define part1
(search (set-count keys))) (load "18-helper.rkt"))
(printf "Part 1: ~a\n" part1) (set! filename "../input/18b1.txt")
(define part2-1
(load "18-helper.rkt"))
(set! filename "../input/18b2.txt")
(define part2-2
(load "18-helper.rkt"))
(set! filename "../input/18b3.txt")
(define part2-3
(load "18-helper.rkt"))
(set! filename "../input/18b4.txt")
(define part2-4
(load "18-helper.rkt"))
(define part2
(+ part2-1 part2-2 part2-3 part2-4))
(show-solution part1 part2)