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#lang racket
(require advent-of-code
threading
graph)
(define input (fetch-aoc-input (find-session) 2023 23 #:cache #true))
(define trails
(for*/hash ([(row r) (in-indexed (string-split input "\n"))]
[(col c) (in-indexed row)]
#:when (not (equal? col #\#)))
; for now, we don't actually need to detect paths and slopes, just not-rocks
; in part 1, all forks in the road go right or down, so we can just infer the path
; direction from the shape of the junction and form a network of junctions from there
; in part 2, the slopes are removed anyway
(values (cons (add1 r) (add1 c)) col)))
(define max-row (~> input (string-split "\n") length))
(define start (findf (λ (p) (= (car p) 1)) (hash-keys trails)))
(define end (findf (λ (p) (= (car p) max-row)) (hash-keys trails)))
(define (get-neighbors posn type)
(match-define (cons r c) posn)
(match type
['junction
(~> (set (cons (add1 r) c) (cons r (add1 c))))]
[_
(~> (list (cons (add1 r) c) (cons (sub1 r) c) (cons r (add1 c)) (cons r (sub1 c)))
(filter (curry hash-has-key? trails) _)
list->set)]))
(define junction-points
(for/set ([(k v) (in-hash trails)]
#:when (not (= (set-count (get-neighbors k v)) 2)))
k))
(define trails-with-junctions
(for/hash ([k (in-hash-keys trails)])
(cond
[(set-member? junction-points k) (values k 'junction)]
[else (values k 'trail)])))
(define (walk-to-next-junction start current [length 1] [seen (set start)])
(define next (~> current
(get-neighbors _ 'trail)
(set-subtract seen) set-first))
(cond
[(equal? (hash-ref trails-with-junctions next) 'junction)
(list (- (add1 length)) start next)] ; weird format is due to graph library
[else
(walk-to-next-junction start next (add1 length) (set-add seen current))]))
(define routes-to-junctions
(for*/list ([j (in-set junction-points)]
[neighbor (in-set (get-neighbors j 'junction))]
#:when (hash-has-key? trails neighbor))
(walk-to-next-junction j neighbor)))
;; part 1 -- using graph library for Bellman-Ford on negative weighted graph
;; Bellman-Ford finds the shortest path, but negating all the path weights
;; will give us the longest path instead
;;
;; unlike Dijkstra which can't handle negative path lengths, Bellman-Ford
;; works as long as the graph is currently directed and acyclic
(define slippery-trail (weighted-graph/directed routes-to-junctions))
(match-define-values (distances _) (bellman-ford slippery-trail start))
(- (hash-ref distances end))
;; part 2 -- rolling my own DFS that can reject seen junctions and dead ends
(define routes-to-junctions-with-traction
(for/fold ([trails (hash)]) ([route (in-list routes-to-junctions)])
(match-define (list (app - weight) from to) route)
(~> trails
(hash-update _ from (curry cons (cons to weight)) '())
(hash-update _ to (curry cons (cons from weight)) '()))))
(define (dfs g from to [acc 0] [seen (set from)])
(cond
[(equal? from to) acc]
[else
(define choices (filter (λ (path) (not (set-member? seen (car path)))) (hash-ref g from)))
(if (empty? choices) 0 ; long dead-ends don't count
(for/fold ([best acc])
([path (in-list choices)]
#:do [(match-define (cons next dist) path)])
(max best (dfs g next to (+ acc dist) (set-add seen next)))))]))
(dfs routes-to-junctions-with-traction start end)
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