diff --git a/8/example.txt b/8/example.txt new file mode 100644 index 0000000..c9f629b --- /dev/null +++ b/8/example.txt @@ -0,0 +1,10 @@ +be cfbegad cbdgef fgaecd cgeb fdcge agebfd fecdb fabcd edb | fdgacbe cefdb cefbgd gcbe +edbfga begcd cbg gc gcadebf fbgde acbgfd abcde gfcbed gfec | fcgedb cgb dgebacf gc +fgaebd cg bdaec gdafb agbcfd gdcbef bgcad gfac gcb cdgabef | cg cg fdcagb cbg +fbegcd cbd adcefb dageb afcb bc aefdc ecdab fgdeca fcdbega | efabcd cedba gadfec cb +aecbfdg fbg gf bafeg dbefa fcge gcbea fcaegb dgceab fcbdga | gecf egdcabf bgf bfgea +fgeab ca afcebg bdacfeg cfaedg gcfdb baec bfadeg bafgc acf | gebdcfa ecba ca fadegcb +dbcfg fgd bdegcaf fgec aegbdf ecdfab fbedc dacgb gdcebf gf | cefg dcbef fcge gbcadfe +bdfegc cbegaf gecbf dfcage bdacg ed bedf ced adcbefg gebcd | ed bcgafe cdgba cbgef +egadfb cdbfeg cegd fecab cgb gbdefca cg fgcdab egfdb bfceg | gbdfcae bgc cg cgb +gcafb gcf dcaebfg ecagb gf abcdeg gaef cafbge fdbac fegbdc | fgae cfgab fg bagce diff --git a/8/input.txt b/8/input.txt new file mode 100644 index 0000000..df64473 --- /dev/null +++ b/8/input.txt @@ -0,0 +1,200 @@ +defabc gcb dbafcg gc gcbed fbecgd begfdac fcbde cfge debag | gfce fgce bdefgca aebgd +eabdc egbda bagcef eg fdageb beg bcfdag egdf agbfd cbgdafe | fdbga bge ebg eg +gfbda feg eg afgcbe fbdcag bfedg gead ecfdabg dfecb gedafb | gedbfa dgae degbf gefdb +ecadfb edg defgcb ecbda fbagcde ge dbeag gacbed agec bdfga | debcaf geafdbc gedab egabd +gcedbf bfeag bcgfdea bcgdaf eg gfe gace cgefab gabcf edfba | gbcfa gfe gef eg +bd bcdgefa dab gcdbaf dabfec cedab gcafde bgcae cafed debf | efcdab dba ebdca edafcb +cdaef fbcedg gdaeb gedcfa cgaed bcfaed gc ceg cgaf eadfbcg | cdfae acfg adbcefg cg +cagbed fbedca cfgdabe ecbda aedfg bcge dfagbc dceag cdg cg | abdec cgd bagdecf eadbc +adbfc fdcabg bg ceabfd bfg bcefga cgbd fgaed fdbag cfbeadg | bfadg bagfcd aefbgcd bg +agbefc aebc cbg cb dafgce deafbgc ebgdf ecfga cgfeb fgdbac | bdfge gefca dgefac ecbfg +cgb cbefgd debac ceadfbg bgceaf gbecd fgdeb cg dgfeab cfdg | fbeacg eafbgcd abcde bfcgdae +aedf fcged abfdcg fcadg ef bgcde efc dgacef fcgbea acebgfd | edbgc geacdf cagdfe bgcfea +gdeba bcafed efbacgd efdacg febadg eg gacdb fadeb bgef ega | bdgae cagbfde cdgba edfbac +gdcae dab bgac cegafdb ab ebafcd gbadce dcefag gfdeb degab | fedabc bcag adceg egbfd +fgcda bgedfa abec bcedfg dgeac dagbe cdeagb ecd ec cfegdba | ecd ce acgde aecdg +dfage becg dceabf beacgf eab acfdgbe gbdcaf bafge fgcab be | dfgcba gcfab eacbfd gaebf +dfabc ecgad fcdabe gfc bedfcg cdagbf dacgf bdgfeac bfag gf | dcfab fagb cgfda agbf +gefcd fad bgfea cgfdea da fbecgd bdgafc dgbfcea cdae edagf | cgfbda gefdc cdea adf +fg efgb fga bdgea adbegf cfeadg fbdag abgdce bdaefcg afbcd | bgfe gebf afgdcbe dbegaf +cagbe dbca gcedfa cga dabfcge ac dgbace fbage cdgeb edcfbg | adfecbg cagedb abcd gbdce +eabdf efb be efcda cabgfd gedfab cdefabg eagb cfedgb gdfba | aebdfcg gecbfd efb efb +ecd fadce acgfd cdgfeb ec edbafg dfcaeb fcegabd abdef ebca | fdeac adcfe dfgeabc dfacbe +egcadbf fca cafbd dceba fa agcfbe fgcdba defgcb afdg cgdfb | gfbcd efdbgc af caf +beca ea fbdegca cafdbg ecagf fae bfgaed efagbc gbafc ecdgf | aegfc adbegcf ea ebgfca +bgacfed gbc fbdeac gc bgfae adcg ecbad begac dabcge gfcdbe | gcb bceagd agcd daebc +ba fgbcead gbaefd ebcfag dagcfe dfeag bdcfg adeb gadfb afb | deba eadb gbefda aecdfg +ab cgfdea dgcbfa aedgc agb efbcadg bagced gbdfe gabde aecb | aefbdgc bfdcag egbda agb +gfcd fecdb fdbeag dcb dgefb ecfab bdecfag bgdeac cd cfgbde | cbaef ecgdbf gdfbe cd +bae dgeabc fdgae aedfb be gfbcad dbecaf cbfda gfcedab cfeb | gfdea fdabc abfcegd gfaed +cegfd dcefba daefc agdcfe cgebfda fg edgcb dgf debgfa cgfa | cfegd debcfa gfd edgfc +dceabg bgcfae fb cfgeb bfc dfceg bcfdea dcfbaeg acebg gfab | aegbdfc bcefg egbac egbfc +ceadgfb cfgadb eagfb eagbcd gebcfa ge age eabdf bacfg gecf | abdef ecagdb bgfea adgbfec +gdcaf egc cebfa cfdaeg cgdfbe eg eagfc gaed fabgced dbcgfa | afgce dcafbeg eadg dgfac +cfdbe dfcgeab ab abgdcf ageb cba eadgc cgadef cdaeb deabcg | efagdc cadeb ab eabg +bgfaedc gcdfe gfbdc fbga cbaedg dcagb gbdcaf bf bfd dacfbe | cgaebd fdgce bf fbdeca +gdabcf acgbefd egafc cda adbe gbadec fgdecb ad cdegb edgca | ecagd ad dcebg gbced +afdebc ebgcfda fabge ecfgdb caefdg dcbg cb fgecd gbcef cfb | eagfb fedgc ebgfc cbfedg +eb fgcade debgfc ebc gadec dfacb ecadb aegb ebcdga dagcfbe | efacbdg cdbaf fdcegb cbdage +gdefac gbdefca aec ce fecagb bfcgda gcafd dceg aefdb cdeaf | cbfaedg cdefag cgdfa cegd +bdegaf fda da ceda edfacg efbacg agdcf bfdgc faecg cgebafd | fdcga daf afd cdgbf +gec fbdgc abdceg febgdc gbacfed decgf facgdb fcbe fadge ec | agdfe cegdf gadcbef cfedg +fbeag bgcea cg cabfed agebcd acgd cadeb cge bgedfc cgaebfd | dfgbce efcbad cge bdcae +gdaef gbafdc gafdce fcadg gedc efbgdca de dfe baefg bcfdae | abcdfe gaefd cgfade dfe +gbcdf gcfa bgdaf dagbe dcegfb bfedca afb cgebdaf fa bafdcg | af fbegadc aegbd gfac +dbgacef ceagfb cfbd ebfdga bd edb bcged aecdg bcgfe fdbceg | db gbeafc befgad dfbegc +bdf bfadeg dbfgeac degcf aebf cgfadb gfdeb bf gdeab bgcdae | fb bgdaec gcfed feba +bgdeaf gbafe cdfeag gecfba debca adgcebf dfe df fdgb efabd | bfdeagc gdbaef fgeabc acdeb +edfcga fdab df fcbead bcagefd dbcage fgebc dcaeb befdc dfe | afbd caedb ebdac cdagef +dcbeg bcag bdaec fcdbeg adcef dfgaeb gcbaed ba begacfd bea | febgdc dbceg agecdbf dbceg +agbc eafbd dgcefb afdbg gaf gdecfa dfgbc fbgcad defcgba ag | edcgfb fadbg dfaeb abefd +abfdcge fadcge gde dcfgb cdgafb gbefd eg fcdgeb ecbg faebd | cgfdb ge dbgafc cegb +ab fbcge fegdbc gab fegad gebaf bgacef ceab fcdbega bcafdg | dgfbac gfacbe gba ab +bed fdage bcafge afebd cdegba fabce fdecab bd dfcb aebfcgd | dbe dgbeafc adebcgf eabfd +cbfdeg gbafe egf bdfgea dfea abceg ef gbdfa daecgfb bdgafc | edaf fabdge ebgac fgaeb +dgba bdcgaf bcdfg bg cgdfe cgb afcdeb bdfcega bdfca gcbeaf | aefdcb dbga cgfed cdfge +gefda gfbed cgfdbea feb dbcgf bgecfd becd fgabec be dfgbac | fgeda agcbdf bdce be +bcfge ab cagbed bea acdeg gdab aecbg fcegbad bcefda adfcge | bgadce dcgea febcg aeb +dagc dcefg gfcdaeb da fgecdb bfeac ead dgfcae eacdf begfda | bdeagf cfedgab dcbgaef ead +dg eadcb fcgd eafgbd fcdgbe bfegc gecbd deg dgcbafe cfegba | ebcad gecfbd ebgcd gfcbeda +bc bgc edbcfg gbafd ecgbfa ebdc gdcaef dfbecag bgfdc egfdc | bgfda fcdgb cgeafb fcbgd +abgf dbfcgae adegf gdabe cbdeg ab bae dgecfa caefdb aedbgf | daefg fbag badfce gbdefac +cabed gabcdf eb cegad fabcgde ebd ebaf fcdeba badfc egdbcf | dbeac cdafb edbfacg eb +degfac adgcf fbgade fae ef egcabfd egacb decf efagc agbcdf | ef fcadeg edcf cgafdb +adcefg agbefcd acdfe cdfba ecfdbg ed eagfc aged edf cegbfa | fcdea gbafec efd fecdgb +dfeacb fge fbgca gfcbe dbeg eg cdefb fbedgc fdbcaeg adecgf | gef dbeg efg becfgd +ae fbdegc gfcdae fbgda fecabd gfecd gdafe edgfcab afe acge | facged adcgfe cgae bacdgef +gfbac cfebda dfg degfca dfgbc cbgdfe dg dcefb edagcbf gbed | caedgfb gdf gd ecgdbf +gcdfea dafbcg gadfc aecdbf cab ba gcbaf abdg cebfgad ecbgf | bca gcfad dcfbage efbcg +gbceaf baegd gab ga agcd gecdb deabgc afedb agebcdf fdbgec | cdgeb gab eagfbc aebdg +ebagcd dgacef gbc gdefcba cbeagf bfadc bedg acdeg bgcda bg | aegdbfc cbg fagecbd agfedc +fcbage dfbage acdebgf ed faed bafge fdegb dge bfdcg egcabd | deg dgfbc bgdefca abcgef +aeg acegd degb dagfcb fadec bgeafc bfagcde eg bdecag gbdac | acefd defca degb cgeabd +bfce fadeg fegdb cdgeb cfdabge bf acdfgb bfd edbcga cebgfd | begadc edfcbag dcefbg bgfed +gc gfac fegcd fedcagb gaedbc cafed edbfg gedafc fecadb gec | adcfe cgdeba egfdc cfedg +egcfb dbac beafcdg cbgea fdeabg gadecb cdgaef cga gadbe ca | dfcabeg cbdgea ca egbca +edgbc fdeb dcfegb cgeafdb dfcaeg gebfc daebcg bfagc fe fec | bgdefc ebdgc ebfd dgbec +bgacde abfgecd caedg ba ebfdc ecfadg bagc eba dbeac gdebfa | cdefag bafedg agbc bcfed +febacg fegda gdbacf ceab cfa cbfeg fgabcde cgaef dgefbc ac | gbcfe beca deafg eagbfcd +debg fgbade gecabf dfaeg fdaegbc gad eagbf fedac dfabcg dg | egbacfd cfead fegadb gd +agfeb cf gcead fgcea gfcdba edagfc bcadeg dfec fca cdfabeg | geacf fbage gdfacb cf +dbfae geacfd eabgc cebfga gd cbgd dfbaecg edbgac adgbe gda | dag gd caefgd gfdceab +edabcg dgaf cgbfe bcdfa efdabc edcfgba ga cag dbgfca gacfb | fdcbag gac ag bdaecg +bf efb efcabd gfba agebdfc deafcg afegd gfeadb gebcd gdbef | bfga bfeadc bcegd fbe +edfgbc fgdc cf bgecf dcaefb efagdcb gdecb bfage cfe dcgeab | dfcg ebgdc fgdc aecbgd +bdgea dgebf ebcdaf ebf fe fabcgd gcfe bgedcf ecgdfab bgfdc | egfc gbcdef bfe fdbcg +ca gdbaef adecg acdfbe cefadg caedbgf afedg eac afcg ecdbg | eadgf dgefab dgeac gadce +dfgecb adcf becfadg cgfdea gfdae dcgae fd dgcaeb dfe egbaf | efcdbg caedfg eacdg dgeafc +agcbe fba dfag fgbca cdagbef fgdcb gcefdb acfdeb af dcbgfa | dcbafe afbcg bfa cdbfg +cead ce dcefga fce afgedb cfebagd agfebc fecgd dafeg cbgfd | fedagb cgbaef egcfba gadfec +dfebga bcadge gdfebac ed beagf eabdf gbafce gdef bdfca ade | ade abcdf bagcde fabcd +adg fgdbce abfgcd ecdgaf cebgdaf gcbad ga bgaf fcbgd edbac | beacd dag fgdcb gda +dbeacf edfcbga bgcde edbac gbac dgb dcegf bcgdea gdafeb bg | cbdge bg cbag ebcda +gafcd dcae cd cgaef bfedcga gfdab cbgfea cdgebf dagcef gdc | afcdg gcd gafdb bgcdaef +edabfg gecfdb adcf abf cfgbade gbace bcfed af bface febdac | eadcbf efabgd fa fba +af eaf daebg fgebac dfaeg geadcfb cfad fedgc dcefgb fadcge | afdge ecgfabd fa fa +dcfga agfdbc db gcbefad baefg fdb gefadc dgabf fgcbde bcad | gdcfa adgbf fbd cgfdeb +cbega fgb agfceb dfbcage dbfca efga dbgefc bcagf bedcag fg | dafbc dbcfa fdbcge ebdgac +eac cbaeg ce acbfg daefcg abgfde bgdeca dbgaecf ebagd cbde | abcedfg cae gbdae ec +gadef daebgfc fge beagd fcebad cbfgde gf afced gfdace agfc | bedfcg geadb gdefbc gf +adbfcg cdbge cfeg beagdfc cbegfd bfdaeg eacbd eg fbgcd egd | ge gdcfab cgebd dacbe +ca cbega abcefdg bfcdea bgdcea abc dgac ebdag ecfbg aebfgd | adgebf debagc bgcae bca +bg edcbg gbd dabegfc dcgae aefdgc cbga dbaegf eadgcb dbefc | cbga cgab adcgeb bgca +egbdf becfga gdcae cdgef cf cdgfea faegcbd dacf cgadeb fcg | cdfge gcdabe befagc cgf +fbade ca eca eabcd cefbag ebacdf fdbaeg cdgbe facd dbagfce | fcbgdae dbace debfgca cbade +fbdceg fgade egfcd fbdacg dgcbf cbed gec ec dgbacef ecagfb | aegdf egdaf gecdf feagd +aef bacedf aedcg bfge efabcg fcbagd fe gfbac fegca abdfceg | cgafb agcfdb gbcafe acfge +bgfc defgbc cf deagf gbcdea baedcf ecfgd ebgdc dcagfeb cdf | fgaed fedcab cdefg dfega +afecbgd bgefca eca gbcaf cgfe bgcdfa bceadf ec cabeg dgabe | ce efbcagd aec fceg +gaeb eafcd dbeafg egf dbfag adfbcg bfcaedg aefgd eg decgfb | fegbda bgfecd adgfe gef +cgb baecd begdc cbdefa adbg ebafgc gcfbead cgfde bgdcea gb | cfedg ebdca adbg eabcd +egafc ac fecdg acfgdb aceb befgcad eadgfb fbgcea cga ebfga | daecbgf bcea fegba ac +afde cefbgda gabdfe cegdab feb bdgae dbcgfe fbgca eabfg fe | dgeba dgcbfe bafge gaecbfd +ceabgd ba cfbagde afdce dba ebcdg abcg fdaegb adbce defcgb | fdgbcea bacg dba agcb +gbcfed eag dceabgf eagfdc febgc bfag eagbcf abdec ag cgeba | gae aeg gfdbace gbfa +gb gbfeda cbead gebdcaf gbdf cgabef beg fgaed gdabe cfgeda | gdbf bgfeac bcead cdefag 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bgcafde dbcfga bafdcg +aebfcg gfedabc eadgb bf cafgdb bfg fbce fgcea gcdfae gebaf | afgebc fb fb bgf +gc fgecbd egc gaebf gecbda acbed fcaebd cagd bcgae gfabdce | gacd egbacd abefg egfba +dcfab bgdc efagd acg gc aedcfb cdafg begcfad dabgcf cbefga | cdagf gcfda dbfac cdgb +bcdfea dgce cadfg dae agfde cgdeaf adfegcb bafge ed cdbfga | cgedaf bgfae gafdc fbgae +adgcfe dfagecb gfbcda ba cafegb fbdce eagb agefc cafbe cab | bcedf bac ba fbcde +bfeacd fcdebg fg dbaeg egdaf dcgfae gcfa efadc bcegdfa fge | acdef fgaed gf bdeag +dcgefa ceabfg fagbc beagd df fagcdeb dbafg fgabcd dcfb fgd | egafdc gabde beagd dfbc +ef bgdaefc cagdbe fbcda fgbade aef gfce eagbcf gcabe cfbea | fcdab fgce bcfad acebf +efagbc fbdag afdcb fg bgf begda aedfbcg deafgb gedf cdgbea | dfgab acfdb gf gf +edcagb ecfbadg ebdfg ega fbaedc fecdag ga dacef gfac gaedf | dgbfe ga dcafe ag +bedfacg acbfge cbg badfeg begfc fbcde ecag facdgb gbfea gc | fbced gcb eagc agebdfc +fdgca fbgce gfecd gdeb cdfagbe ed ecd fedacb gfabce dgfbec | afcgd deabfc dfagc begcfa +bfeg dge cgadf cgedf gedfbca cebfad dfebc cdabge cdgefb ge | dbcef ged eg ebfacd +ed cebgadf gefdca cfega dcaegb dfce cgaefb dge gbfda dfaeg | aegdf afgce egd deg +aecfgd fgd cedbag fgecd bfagdc feacbdg gceda gf bcdef eagf | dfbce agced gf geadc +gbcfdae fdgea bdgcae edb edgbfc fagdcb ebca be ebgda adgcb | be edb bed gcbaed +gdef df afdgcb fdb ebcgd begadfc gdcbef efbdc baegdc fabec | dgceab acbef fbedc cgbed +dcbgf feg edfacgb efgadc eg fdace afbced fcged eacg aefbdg | cbaedfg ecag aecfdb efdacg +fdbega gcebaf dacgeb eabdc gabcfde fcdea gcbd bd adb agbce | afced efabdcg afced bda +cd dafcbe adegcb edabfgc bdcga adfgb gabecf cdb egcd cbega | daegbfc afbdg cd debacg +bga becfdg gcbfad gcbdf ag baefcg eadbc dcgab fcgadeb afdg | gfbcead edgcbf gdcab bag +aedgfbc fe cgdaef fbec feg agecb bgadf bacefg afebg cgdeba | aebgcfd gfe aegbf efbcga +afcegd gbdec acd afcgbe ad cagfe gdcea fgbedac edaf dgbacf | cad dagec aecgdf da +gfedc eagcfd becagf cafed ace edbaf dgac 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(>>= snd) + g x = sum $ zipWith (curry decode) (map snd x) (map deduce x) + +-- | Parse a line to a tuple of signal values and output values. +-- | The signal values and output values are sorted. +parse :: String -> (Signal, Output) +parse s = let (a, b) = break (== '|') s + signal = map sort $ filter (/= "|") $ words a + output = map sort $ filter (/= "|") $ words b in + (signal, output) + +type Signal = [String] +type Output = [String] + +type Mapping = [Result] + +data Result = Missing String + | Matched Int String + deriving + Show + +-- | Extract the segment combination belonging to the given number. +get :: Mapping -> Int -> String +get m i = head [ s | Matched n s <- m, n == i ] + +-- | Extract the number belonging to the given segment combination. +seg :: Mapping -> String -> Int +seg m v = head [ n | Matched n s <- m, s == v ] + +-- | Deduce what segments correspond to which number. The number +-- | the combination belongs to is its index. +deduce :: (Signal, Output) -> Mapping +deduce (signal, output) = foldl match (map Missing signal) [ 1, 7, 4, 8, 9, 6, 0, 5, 3, 2 ] + +-- | Use the given `Mapping` to match an unmatched set of segments +-- | to the given number. +match :: Mapping -> Int -> Mapping +match m n = match' n pred <$> m + where + pred = matcher n m + match' _ _ v @ (Matched _ _) = v + match' n condition (Missing a) + | condition a = Matched n a + | otherwise = Missing a + + +-- | Map a number to a function that can be used to match that number. +matcher :: Int -> Mapping -> (String -> Bool) +matcher 0 = p + where p _ s = length s == 6 +matcher 1 = p + where p _ s = length s == 2 +matcher 2 = p + where p _ _ = True +matcher 3 = p + where p m s = s == (s `intersect` get m 9) +matcher 4 = p + where p _ s = length s == 4 +matcher 5 = p + where p m s = s == (s `intersect` get m 6) +matcher 6 = p + where p m s = length s == 6 && get m 1 /= (get m 1 `intersect` s) +matcher 7 = p + where p _ s = length s == 3 +matcher 8 = p + where p _ s = length s == 7 +matcher 9 = p + where p m s = get m 4 == get m 4 `intersect` s + +-- | Given a list of output values and a segment mapping, +-- | decode what the output reads. +decode :: (Output, Mapping) -> Int +decode (output, mapping) = read (concatMap (show . seg mapping) output) diff --git a/9/example.txt b/9/example.txt new file mode 100644 index 0000000..6dee4a4 --- /dev/null +++ b/9/example.txt @@ -0,0 +1,5 @@ +2199943210 +3987894921 +9856789892 +8767896789 +9899965678 diff --git a/9/input.txt b/9/input.txt new file mode 100644 index 0000000..44432ed --- /dev/null +++ b/9/input.txt @@ -0,0 +1,100 @@ +5434456789899876598943212349988734679896554212468998765634987654567895454569876745567898765987654678 +4421345997789997987894103458976521398765432101457897664529876543988987353478965434456799974398766789 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+import Data.Maybe + +main :: IO () +main = do + input <- readFile "9/input.txt" + let x = parse $ lines input + -- Problem 1 + print $ f x + -- Problem 2 + print $ g x + where + f = risk + g = solve + +parse :: [String] -> [[Int]] +parse = map (map read . chunksOf 1) + +risk :: [[Int]] -> Int +risk a = sum $ map succ $ mapMaybe index (areas a) + where + index = ($ a) . uncurry idx + +solve :: [[Int]] -> Int +solve x = product $ take 3 $ reverse $ sort $ map (basin x) $ areas x + +-- | Find risk areas (low points). +areas :: [[Int]] -> [(Int,Int)] +areas a = [ (x,y) | y <- [ 0 .. (pred $ length a) ], + x <- [ 0 .. (length (a !! y)) ], + Just n <- [idx x y a], + all ((> n) . snd) (adj x y a) ] + +-- | Get the size of a basin centered on the given point. +basin :: [[Int]] -> (Int, Int) -> Int +basin m (x,y) = length a + where + a = case idx x y m of + Just v -> let t = ((x,y),v) in t : search t m + Nothing -> [] + +-- | Search for neighbors of the given node where the value of the neighbor +-- | is not 9 and is greater than the value of the given node. This search +-- | is then repeated for each result it finds until no nodes satisfying the +-- | constraint can be found in the immediate neighborhood of the cluster. +search :: ((Int, Int), Int) -> [[Int]] -> [((Int, Int), Int)] +search t @ ((x,y),v) b = nub (next ++ (next >>= (`search` b))) + where + neighbors = adj x y b + next = nub $ filter (\(_,n) -> n /= 9 && n > v) neighbors + +-- | Find elements that are directly adjacent to a point in a matrix. +adj :: Int -> Int -> [[a]] -> [((Int, Int), a)] +adj x y m = [ ((a, b), v) | a <- [pred x .. succ x], + b <- [pred y .. succ y], + x /= a || y /= b, + y == b || x == a, + Just v <- [idx a b m] ] + +-- | Index into a matrix safely. If out of bounds on either axis, +-- | returns `Nothing`. +idx :: Int -> Int -> [[a]] -> Maybe a +idx x y m = get y m >>= get x + +-- | Index into a list safely. Returns `Nothing` if out of bounds. +get :: Int -> [a] -> Maybe a +get i l | i < 0 = Nothing + | i >= length l = Nothing + | otherwise = Just (l !! i)