AoC '21, Day 15, first problem, rvc

Find the shortest path through a grid, returning only the value and not the path.

 $ cat 15a.rkt 
 #lang racket 
  
  
 (provide 
   example-a-input 
   example-b-input 
   example-b-input-result 
   (struct-out path-map) 
   path-map:start-state 
   read-input 
   (struct-out risk-path) 
   ) 
  
  
 (require 
   "aoc.rkt" 
   (prefix-in array: "array.rkt") 
   ) 
  
  
 (define (aoc15a) 
  
   ; Return the risk of the minimal risk path for the first half of the 
   ; fifteenth AoC '21 problem. 
  
   (find-minimal-path (read-input))) 
  
  
 (define (find-minimal-path rmap-data) 
  
   ; Return the risk associated with the minimal-risk path from the 
   ; start state to the goal state using the given risk-map data. 
  
   (define path-map (path-map:new rmap-data)) 
  
   (define (run-through paths) 
  
     ; Return a list of paths derived from the given path list.  Each 
     ; path returned is a valid, one-step extension of one of the given 
     ; paths. 
  
     ; Using map to run over the paths makes this a more or less 
     ; breadth-first search. 
  
     (flatten 
       (map 
         (lambda (p) (path-map:extend-path path-map p)) 
         paths))) 
    
  
   ; A brute-force search: look through all paths from start to end, 
   ; return the least risky. 
  
   (let loop ((paths (list (risk-path 0 0 0)))) 
  
     (let ((paths (run-through paths))) 
       (if (null? paths) 
           (path-map:goal-risk path-map) 
           (loop paths))))) 
  
  
 (define read-input (lambda arg? 
  
   ; Return the risk-map described by the problem input.  If no 
   ; argument is given, use the contest problem input; otherwise assume 
   ; the argument is the string representation of a problem input. 
  
   (let ((inp (car (aoc-read-input (if (null? arg?) 15 (car arg?)))))) 
     (map 
       (lambda (l) 
         (map 
           (lambda (c) (- (char->integer c) (char->integer #\0))) 
           (string->list (car l)))) 
       inp)))) 
    
  
 ; The problem only wants the total risk, so the path consists of most 
 ; recent step taken and the risk encountered so far. 
  
 (struct risk-path (x y risk)) 
  
  
 ; The risk-map is a read-only representation of the program input. 
 ; The element at (x, y) in the path-map keeps track of the lowest risk 
 ; of any path reaching (x, y). 
  
 (struct path-map (risk-map path-map)) 
  
  
 (define (path-map:extend-path path-map path) 
  
   ; Return a list of valid paths one step away from the given path 
   ; according to the given path map (which is changed to reflect the 
   ; valid path extensions). 
  
   ; A path is valid if it is in within bounds and it's the least risky 
   ; path to a location so far. 
  
   (foldr 
     (lambda (deltas new-paths) 
       (let* ((pmap (path-map-path-map path-map)) 
              (new-x (+ (risk-path-x path) (car deltas))) 
              (new-y (+ (risk-path-y path) (cdr deltas))) 
              (new-risk (+ (risk-path-risk path) 
                           (array:ref (path-map-risk-map path-map) new-x new-y)))) 
                         
         (if (> (array:ref pmap new-x new-y) new-risk) 
             (begin 
               (array:set! pmap new-x new-y new-risk) 
               (cons (risk-path new-x new-y new-risk) new-paths)) 
             new-paths))) 
     '() 
     '((0 . -1) (-1 . 0) (1 . 0) (0 . 1)))) 
  
  
 (define (path-map:goal-risk path-map) 
  
   ; Return the current goal-state risk, which represents the minimal 
   ; risk of a path from the start state to the goal state.  No such 
   ; path may exist when this function is called, in which case +inf.0 
   ; is returned. 
  
   (let ((pm (path-map-path-map path-map))) 
     (array:ref pm (- (array:cols pm) 1) (- (array:rows pm) 1)))) 
  
  
 (define (path-map:goal-state? path-map path) 
  
   ; Return #t iff the given path ends at the goal state. 
  
   (let ((pm (path-map-path-map path-map))) 
     (and (= (risk-path-y path) (- (array:cols pm) 1)) 
          (= (risk-path-x path) (- (array:rows pm) 1))))) 
  
  
 (define (path-map:new rmap-data) 
  
   ; Return a new path map based on the given risk-map data. 
  
   (let ((pmap-data 
           (map (lambda (row) (map (lambda (e) +inf.0) row)) rmap-data))) 
            
   (path-map 
      (array:new rmap-data) 
      (array:new pmap-data)))) 
  
  
 (define (path-map:start-state) 
  
   ; Return a start state. 
  
   (risk-path 0 0 0)) 
  
  
 (define example-a-input 
   (string-join 
    '("1163751742" 
      "1381373672" 
      "2136511328" 
      "3694931569" 
      "7463417111" 
      "1319128137" 
      "1359912421" 
      "3125421639" 
      "1293138521" 
      "2311944581") "\n")) 
  
 (define example-a-input-result 40) 
  
 (define example-b-input 
   (string-join 
    '("11637517422274862853338597396444961841755517295286" 
      "13813736722492484783351359589446246169155735727126" 
      "21365113283247622439435873354154698446526571955763" 
      "36949315694715142671582625378269373648937148475914" 
      "74634171118574528222968563933317967414442817852555" 
      "13191281372421239248353234135946434524615754563572" 
      "13599124212461123532357223464346833457545794456865" 
      "31254216394236532741534764385264587549637569865174" 
      "12931385212314249632342535174345364628545647573965" 
      "23119445813422155692453326671356443778246755488935" 
      "22748628533385973964449618417555172952866628316397" 
      "24924847833513595894462461691557357271266846838237" 
      "32476224394358733541546984465265719557637682166874" 
      "47151426715826253782693736489371484759148259586125" 
      "85745282229685639333179674144428178525553928963666" 
      "24212392483532341359464345246157545635726865674683" 
      "24611235323572234643468334575457944568656815567976" 
      "42365327415347643852645875496375698651748671976285" 
      "23142496323425351743453646285456475739656758684176" 
      "34221556924533266713564437782467554889357866599146" 
      "33859739644496184175551729528666283163977739427418" 
      "35135958944624616915573572712668468382377957949348" 
      "43587335415469844652657195576376821668748793277985" 
      "58262537826937364893714847591482595861259361697236" 
      "96856393331796741444281785255539289636664139174777" 
      "35323413594643452461575456357268656746837976785794" 
      "35722346434683345754579445686568155679767926678187" 
      "53476438526458754963756986517486719762859782187396" 
      "34253517434536462854564757396567586841767869795287" 
      "45332667135644377824675548893578665991468977611257" 
      "44961841755517295286662831639777394274188841538529" 
      "46246169155735727126684683823779579493488168151459" 
      "54698446526571955763768216687487932779859814388196" 
      "69373648937148475914825958612593616972361472718347" 
      "17967414442817852555392896366641391747775241285888" 
      "46434524615754563572686567468379767857948187896815" 
      "46833457545794456865681556797679266781878137789298" 
      "64587549637569865174867197628597821873961893298417" 
      "45364628545647573965675868417678697952878971816398" 
      "56443778246755488935786659914689776112579188722368" 
      "55172952866628316397773942741888415385299952649631" 
      "57357271266846838237795794934881681514599279262561" 
      "65719557637682166874879327798598143881961925499217" 
      "71484759148259586125936169723614727183472583829458" 
      "28178525553928963666413917477752412858886352396999" 
      "57545635726865674683797678579481878968159298917926" 
      "57944568656815567976792667818781377892989248891319" 
      "75698651748671976285978218739618932984172914319528" 
      "56475739656758684176786979528789718163989182927419" 
      "67554889357866599146897761125791887223681299833479") "\n")) 
  
 (define example-b-input-result 315) 
  
 (define problem-a-result 592) 
  
  
 (module+ main 
  
   (aoc15a)) 
  
    
 (module+ test 
  
   (require rackunit) 
  
   (check-equal? 
     (find-minimal-path (read-input example-a-input)) 
     example-a-input-result) 
  
   (check-equal? 
     (find-minimal-path (read-input example-b-input)) 
     example-b-input-result) 
  
   (check-equal? 
     (aoc15a) 
     problem-a-result) 
   ) 
  
 $ raco test 15a.rkt 
 raco test: (submod "15a.rkt" test) 
 3 tests passed 
  
 $