diff --git a/CHANGELOG.md b/CHANGELOG.md --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -1,9 +1,9 @@ -# Revision history for aoc - -## 0.1.0.1 -- 2025-03-26 - -* Exported HashMap and Set types to prevent conflicts in type signatures - -## 0.1.0.0 -- 2025-03-16 - -* First version. Released on an unsuspecting world. +# Revision history for aoc + +## 0.1.0.1 -- 2025-03-26 + +* Exported HashMap and Set types to prevent conflicts in type signatures + +## 0.1.0.0 -- 2025-03-16 + +* First version. Released on an unsuspecting world. diff --git a/LICENSE b/LICENSE --- a/LICENSE +++ b/LICENSE @@ -1,29 +1,29 @@ -Copyright (c) 2025, M1n3c4rt - - -Redistribution and use in source and binary forms, with or without -modification, are permitted provided that the following conditions are met: - - * Redistributions of source code must retain the above copyright - notice, this list of conditions and the following disclaimer. - - * Redistributions in binary form must reproduce the above - copyright notice, this list of conditions and the following - disclaimer in the documentation and/or other materials provided - with the distribution. - - * Neither the name of the copyright holder nor the names of its - contributors may be used to endorse or promote products derived - from this software without specific prior written permission. - -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT -LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT -HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, -SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT -LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, -DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY -THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT -(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE -OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +Copyright (c) 2025, M1n3c4rt + + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: + + * Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + + * Redistributions in binary form must reproduce the above + copyright notice, this list of conditions and the following + disclaimer in the documentation and/or other materials provided + with the distribution. + + * Neither the name of the copyright holder nor the names of its + contributors may be used to endorse or promote products derived + from this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/aoc.cabal b/aoc.cabal --- a/aoc.cabal +++ b/aoc.cabal @@ -1,77 +1,81 @@ -cabal-version: 3.0 --- The cabal-version field refers to the version of the .cabal specification, --- and can be different from the cabal-install (the tool) version and the --- Cabal (the library) version you are using. As such, the Cabal (the library) --- version used must be equal or greater than the version stated in this field. --- Starting from the specification version 2.2, the cabal-version field must be --- the first thing in the cabal file. - --- Initial package description 'aoc' generated by --- 'cabal init'. For further documentation, see: --- http://haskell.org/cabal/users-guide/ --- --- The name of the package. -name: aoc - --- The package version. --- See the Haskell package versioning policy (PVP) for standards --- guiding when and how versions should be incremented. --- https://pvp.haskell.org --- PVP summary: +-+------- breaking API changes --- | | +----- non-breaking API additions --- | | | +--- code changes with no API change -version: 0.1.0.1 - --- A short (one-line) description of the package. -synopsis: Utility functions commonly used while solving Advent of Code puzzles - --- A longer description of the package. -description: A collection of miscellaneous utility functions, including but not limited to pathfinding, grid enumeration, coordinate/range operations and extrapolation functions. - --- The license under which the package is released. -license: BSD-3-Clause - --- The file containing the license text. -license-file: LICENSE - --- The package author(s). -author: M1n3c4rt - --- An email address to which users can send suggestions, bug reports, and patches. -maintainer: vedicbits@gmail.com - --- A copyright notice. --- copyright: -category: Utility -build-type: Simple - --- Extra doc files to be distributed with the package, such as a CHANGELOG or a README. -extra-doc-files: CHANGELOG.md - --- Extra source files to be distributed with the package, such as examples, or a tutorial module. --- extra-source-files: - -common warnings - ghc-options: -Wall - -library - -- Import common warning flags. - import: warnings - - -- Modules exported by the library. - exposed-modules: Utility.AOC - - -- Modules included in this library but not exported. - -- other-modules: - - -- LANGUAGE extensions used by modules in this package. - -- other-extensions: - - -- Other library packages from which modules are imported. - build-depends: base ^>=4.17.2.1, heap >= 1.0.4 && < 1.1, unordered-containers >= 0.2.20 && < 0.3, containers >= 0.6.7 && <= 0.7, hashable >= 1.4.7 && < 1.5 - - -- Directories containing source files. - hs-source-dirs: src - - -- Base language which the package is written in. - default-language: Haskell2010 +cabal-version: 3.0 +-- The cabal-version field refers to the version of the .cabal specification, +-- and can be different from the cabal-install (the tool) version and the +-- Cabal (the library) version you are using. As such, the Cabal (the library) +-- version used must be equal or greater than the version stated in this field. +-- Starting from the specification version 2.2, the cabal-version field must be +-- the first thing in the cabal file. + +-- Initial package description 'aoc' generated by +-- 'cabal init'. For further documentation, see: +-- http://haskell.org/cabal/users-guide/ +-- +-- The name of the package. +name: aoc + +-- The package version. +-- See the Haskell package versioning policy (PVP) for standards +-- guiding when and how versions should be incremented. +-- https://pvp.haskell.org +-- PVP summary: +-+------- breaking API changes +-- | | +----- non-breaking API additions +-- | | | +--- code changes with no API change +version: 0.1.0.2 + +-- A short (one-line) description of the package. +synopsis: Utility functions commonly used while solving Advent of Code puzzles + +-- A longer description of the package. +description: A collection of miscellaneous utility functions, including but not limited to pathfinding, grid enumeration, coordinate/range operations and extrapolation functions. + +-- The license under which the package is released. +license: BSD-3-Clause + +-- The file containing the license text. +license-file: LICENSE + +-- The package author(s). +author: M1n3c4rt + +-- An email address to which users can send suggestions, bug reports, and patches. +maintainer: vedicbits@gmail.com + +-- A copyright notice. +-- copyright: +category: Utility +build-type: Simple + +-- Extra doc files to be distributed with the package, such as a CHANGELOG or a README. +extra-doc-files: CHANGELOG.md + +-- Extra source files to be distributed with the package, such as examples, or a tutorial module. +-- extra-source-files: + +common warnings + ghc-options: -Wall + +library + -- Import common warning flags. + import: warnings + + -- Modules exported by the library. + exposed-modules: Utility.AOC + + -- Modules included in this library but not exported. + -- other-modules: + + -- LANGUAGE extensions used by modules in this package. + -- other-extensions: + + -- Other library packages from which modules are imported. + build-depends: base >=4.17.2.1 && < 5 + , heap >= 1.0.4 && < 1.1 + , unordered-containers >= 0.2.20 && < 0.3 + , containers >= 0.6.7 && <= 0.7 + , hashable >= 1.4.7 && < 1.5 + + -- Directories containing source files. + hs-source-dirs: src + + -- Base language which the package is written in. + default-language: Haskell2010 diff --git a/src/Utility/AOC.hs b/src/Utility/AOC.hs --- a/src/Utility/AOC.hs +++ b/src/Utility/AOC.hs @@ -1,249 +1,249 @@ -{-| -Module : AOC -Description : Utility functions commonly used while solving Advent of Code puzzles -Copyright : (c) M1n3c4rt, 2025 -License : BSD-3-Clause -Maintainer : vedicbits@gmail.com -Stability : stable --} - -{-# LANGUAGE FlexibleContexts #-} -{-# LANGUAGE TupleSections #-} -{-# OPTIONS_GHC -Wno-incomplete-patterns #-} -{-# OPTIONS_GHC -Wno-incomplete-uni-patterns #-} -{-# OPTIONS_GHC -Wno-type-defaults #-} - -module Utility.AOC ( - -- * Pathfinding algorithms - -- $cat1 - shortestDistance, - shortestPaths, - shortestDistanceOnMagma, - shortestPathsOnMagma, - -- * Neighbour functions - neighbours4, - neighbours8, - neighbours6, - neighbours26, - -- * Taxicab (Manhattan) distance - taxicab2, - taxicab3, - -- * Grid enumeration - -- $cat2 - enumerate, - enumerateRead, - enumerateHM, - enumerateReadHM, - enumerateFilter, - enumerateFilterSet, - -- * Flood fill - floodFill, - floodFillWith, - -- * List selection - choose, - permute, - -- * Extrapolation - extrapolate, - -- * Miscellaneous - range, - rangeIntersect, - binToDec, - -- Export types/constraints used in top-level function type signatures - Hashable, - HM.HashMap, - S.Set -) where - -import qualified Data.HashMap.Strict as HM -import Data.Hashable (Hashable) -import qualified Data.Set as S -import qualified Data.Heap as H -import Data.List (permutations, genericIndex) - -createMinPrioHeap :: Ord a1 => (a1,a) -> H.MinPrioHeap a1 a -createMinPrioHeap = H.singleton - --- $cat1 --- All of the following functions return distances as a @Maybe Int@, where @Nothing@ is returned if no path is found. --- The graph is a @HashMap@ mapping each node to a sequence of (neighbour, edge weight) pairs. - --- | Returns the shortest distance between two nodes in a graph. -shortestDistance :: (Foldable t, Hashable n, Ord a, Num a) - => HM.HashMap n (t (n, a)) -- ^ Graph - -> n -- ^ Start node - -> n -- ^ End node - -> Maybe a -shortestDistance graph = shortestDistanceOnMagma (repeat graph) - --- | Returns the shortest distance between two nodes in a graph and a list of all possible paths from the ending node to the starting node. --- The starting node is not included in each path. -shortestPaths :: (Foldable t, Hashable n, Ord a, Num a) - => HM.HashMap n (t (n, a)) -- ^ Graph - -> n -- ^ Start node - -> n -- ^ End node - -> (Maybe a, [[n]]) -shortestPaths graph = shortestPathsOnMagma (repeat graph) - --- | Returns the shortest distance between two nodes in a list of graphs where the neighbours of a node in any given graph all lie in the succeeding graph. The ending node must be present in each graph. --- This precondition is not checked. -shortestDistanceOnMagma :: (Foldable t, Hashable n, Ord a, Num a) - => [HM.HashMap n (t (n, a))] -- ^ Graphs - -> n -- ^ Start node - -> n -- ^ End node - -> Maybe a -shortestDistanceOnMagma graphs start end = fst $ shortestPathsOnMagma graphs start end - --- | Returns the shortest distance between two nodes in a list of graphs and a list of all possible paths from the ending node to the starting node. The ending node must be present in each graph. --- This precondition is not checked. --- The starting node is not included in each path. -shortestPathsOnMagma :: (Foldable t, Hashable n, Ord a, Num a) - => [HM.HashMap n (t (n, a))] -- ^ Graphs - -> n -- ^ Start node - -> n -- ^ End node - -> (Maybe a, [[n]]) -shortestPathsOnMagma graphs start end = - let initQueue = createMinPrioHeap (0,start) - initPaths = HM.singleton start (0,[[]]) - helper (paths,queue) = case H.view queue of - Nothing -> (paths,queue) - Just ((_,n),ns) -> - let Just (currentDistance,currentPaths) = HM.lookup n paths - Just neighbours = HM.lookup n (graphs !! length (head currentPaths)) - updateNeighbour (n',d') (p',q') = case HM.lookup n' p' of - Nothing -> (HM.insert n' (currentDistance+d',map (n':) currentPaths) p', H.insert (currentDistance+d',n') q') - Just (d'',ps'') -> - if d'' < currentDistance+d' then - (p',q') - else if d'' > currentDistance+d' then - (HM.insert n' (currentDistance+d',map (n':) currentPaths) p', H.insert (currentDistance+d',n') q') - else - (HM.insert n' (currentDistance+d',ps'' ++ map (n':) currentPaths) p', q') - in helper $ foldr updateNeighbour (paths,ns) neighbours - - in case HM.lookup end $ fst (helper (initPaths,initQueue)) of - Nothing -> (Nothing, []) - Just (d,ps) -> (Just d, ps) - --- | Returns the 4 points orthogonally adjacent to the given point. -neighbours4 :: (Num a, Num b) => (a, b) -> [(a, b)] -neighbours4 (x,y) = [(x+1,y),(x,y+1),(x-1,y),(x,y-1)] - --- | Returns the 8 points orthogonally or diagonally adjacent to the given point. -neighbours8 :: (Enum a, Enum b, Eq a, Eq b, Num a, Num b) => (a, b) -> [(a, b)] -neighbours8 (x,y) = [(x+p,y+q) | p <- [-1..1], q <- [-1..1], p /= 0 || q /= 0] - --- | Returns the 6 points orthogonally adjacent to the given point in 3D space. -neighbours6 :: (Num a, Num b, Num c) => (a, b, c) -> [(a, b, c)] -neighbours6 (x,y,z) = [(x+1,y,z),(x,y+1,z),(x,y,z+1),(x-1,y,z),(x,y-1,z),(x,y,z-1)] - --- | Returns the 26 points orthogonally or diagonally adjacent to the given point in 3D space. -neighbours26 :: (Enum a, Enum b, Enum c, Eq a, Eq b, Eq c, Num a, Num b, Num c) => (a, b, c) -> [(a, b, c)] -neighbours26 (x,y,z) = [(x+p,y+q,z+r) | p <- [-1..1], q <- [-1..1], r <- [-1..1], p /= 0 || q /= 0 || r /= 0] - --- | Returns the Taxicab/Manhattan distance between two points in 2D space. -taxicab2 :: Num a => (a, a) -> (a, a) -> a -taxicab2 (a,b) (c,d) = abs (a-c) + abs (b-d) - --- | Returns the Taxicab/Manhattan distance between two points in 3D space. -taxicab3 :: Num a => (a, a, a) -> (a, a, a) -> a -taxicab3 (a,b,c) (d,e,f) = abs (a-d) + abs (b-e) + abs (c-f) - -enumerateBase :: (Num y, Num x, Enum y, Enum x) => String -> [((x, y), Char)] -enumerateBase s = - let ss = lines s - ys = zipWith (\n l -> map (n,) l) [0..] ss - xs = map (zipWith (\x (y,c) -> ((x,y),c)) [0..]) ys - in concat xs - --- $cat2 --- The following functions operate on a grid of characters as a string with a newline after each row (as seen in several Advent of Code puzzle inputs). - --- | Converts a grid to a list of triples @(x,y,c)@ representing xy coordinates and the character at that location. -enumerate :: (Num y, Num x, Enum y, Enum x) => String -> [(x, y, Char)] -enumerate = map (\((x,y),c) -> (x,y,c)) . enumerateBase - --- | Enumerates a grid along with reading the characters (usually as integers). -enumerateRead :: (Read c, Num y, Num x, Enum y, Enum x) => String -> [(x, y, c)] -enumerateRead = map (\((x,y),c) -> (x,y,read [c])) . enumerateBase - --- | Enumerates a grid and stores it in a @HashMap@ where points are mapped to the character at that location. -enumerateHM :: (Num x, Num y, Enum x, Enum y, Hashable x, Hashable y) => String -> HM.HashMap (x, y) Char -enumerateHM = HM.fromList . enumerateBase - --- | Enumerates a grid and stores it in a @HashMap@ along with reading the characters (usually as integers). -enumerateReadHM :: (Num x, Num y, Enum x, Enum y, Hashable x, Hashable y, Read c) => String -> HM.HashMap (x, y) c -enumerateReadHM = HM.fromList . map (\((x,y),c) -> ((x,y),read [c])) . enumerateBase - --- | Returns a list of points on a grid for which a certain condition is met. -enumerateFilter :: (Num y, Num x, Enum y, Enum x) => (Char -> Bool) -> String -> [(x, y)] -enumerateFilter f = map fst . filter (f . snd) . enumerateBase - --- | Returns a set of points on a grid for which a certain condition is met. -enumerateFilterSet :: (Ord x, Ord y, Num y, Num x, Enum y, Enum x) => (Char -> Bool) -> String -> S.Set (x, y) -enumerateFilterSet f = S.fromList . enumerateFilter f - -floodFill' :: Ord a => (a -> [a]) -> S.Set a -> S.Set a -> S.Set a -> S.Set a -floodFill' neighbours finished frontier blocks - | S.null frontier = finished - | otherwise = floodFill' neighbours (S.union frontier finished) newfrontier blocks - where - newfrontier = S.filter (\n -> n `S.notMember` finished || n `S.notMember` frontier || n `S.notMember` blocks) $ S.unions $ S.map (S.fromList . neighbours) frontier - -floodFillWith' :: Ord a => (a -> a -> Bool) -> (a -> [a]) -> S.Set a -> S.Set a -> S.Set a -floodFillWith' cond neighbours finished frontier - | S.null frontier = finished - | otherwise = floodFillWith' cond neighbours (S.union frontier finished) newfrontier - where - newfrontier = S.filter (\n -> n `S.notMember` finished || n `S.notMember` frontier) $ S.unions $ S.map (S.fromList . (\c -> filter (cond c) $ neighbours c)) frontier - --- | Applies a flood fill algorithm given a function to generate a point's neighbours, a starting set of points, and a set of points to avoid. Returns a set of all points covered. -floodFill :: Ord a - => (a -> [a]) -- ^ Neighbour function - -> S.Set a -- ^ Initial set of points - -> S.Set a -- ^ Set of points to avoid - -> S.Set a -floodFill neighbours = floodFill' neighbours S.empty - --- | Applies a flood fill algorithm given a function to generate a point's neighbours, a condition that filters out points generated by said function, and a starting set of points. Returns a set of all points covered. --- The condition is of the form @a -> a -> Bool@, which returns @True@ if the second point is a valid neighbour of the first point and @False@ otherwise. -floodFillWith :: Ord a - => (a -> a -> Bool) -- ^ Condition - -> (a -> [a]) -- ^ Neighbour function - -> S.Set a -- ^ Initial set of points - -> S.Set a -floodFillWith cond neighbours = floodFillWith' cond neighbours S.empty - --- | Generates a list of all possible lists of length n by taking elements from the provided list of length l. --- Relative order is maintained, and the length of the returned list is \(_{n}C_{l}\). -choose :: (Num n, Eq n) => n -> [a] -> [[a]] -choose n (x:xs) = map (x:) (choose (n-1) xs) ++ choose n xs -choose 0 _ = [[]] -choose _ [] = [] - --- | Generates a list of all possible lists of length n by taking elements from the provided list of length l. --- The length of the returned list is \(_{n}P_{l}\). -permute :: (Num n, Eq n) => n -> [a] -> [[a]] -permute n = concatMap permutations . choose n - --- | Gets the nth element of an infinite list, assuming that each element in the list can be generated using the previous element, for example, a list generated with @iterate@. -extrapolate :: (Integral b, Ord a) => b -> [a] -> a -extrapolate n ls = let (o,p) = helper 0 S.empty ls in ls `genericIndex` (((n-o) `mod` p) + o) - where - helper k finished (l:ls') - | S.null matches = helper (k+1) (S.insert (k,l) finished) ls' - | otherwise = let o = fst $ S.elemAt 0 matches in (o,k-o) - where matches = S.filter ((==l) . snd) finished - --- | Generates a range with @[x..y]@, but reverses the list instead of returning an empty range if x > y. -range :: (Ord a, Enum a) => a -> a -> [a] -range x y = if y < x then [x,pred x..y] else [x..y] - --- | Takes (a,b) and (c,d) as arguments and returns the intersection of the ranges [a..b] and [c..d] as another pair if it is not empty. -rangeIntersect :: Ord b => (b, b) -> (b, b) -> Maybe (b, b) -rangeIntersect (a,b) (c,d) - | b < c || a > d = Nothing - | otherwise = Just (max a c, min b d) - --- | Converts a list of booleans (parsed as a binary number) to an integer. -binToDec :: Num a => [Bool] -> a +{-| +Module : AOC +Description : Utility functions commonly used while solving Advent of Code puzzles +Copyright : (c) M1n3c4rt, 2025 +License : BSD-3-Clause +Maintainer : vedicbits@gmail.com +Stability : stable +-} + +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE TupleSections #-} +{-# OPTIONS_GHC -Wno-incomplete-patterns #-} +{-# OPTIONS_GHC -Wno-incomplete-uni-patterns #-} +{-# OPTIONS_GHC -Wno-type-defaults #-} + +module Utility.AOC ( + -- * Pathfinding algorithms + -- $cat1 + shortestDistance, + shortestPaths, + shortestDistanceOnMagma, + shortestPathsOnMagma, + -- * Neighbour functions + neighbours4, + neighbours8, + neighbours6, + neighbours26, + -- * Taxicab (Manhattan) distance + taxicab2, + taxicab3, + -- * Grid enumeration + -- $cat2 + enumerate, + enumerateRead, + enumerateHM, + enumerateReadHM, + enumerateFilter, + enumerateFilterSet, + -- * Flood fill + floodFill, + floodFillWith, + -- * List selection + choose, + permute, + -- * Extrapolation + extrapolate, + -- * Miscellaneous + range, + rangeIntersect, + binToDec, + -- Export types/constraints used in top-level function type signatures + Hashable, + HM.HashMap, + S.Set +) where + +import qualified Data.HashMap.Strict as HM +import Data.Hashable (Hashable) +import qualified Data.Set as S +import qualified Data.Heap as H +import Data.List (permutations, genericIndex) + +createMinPrioHeap :: Ord a1 => (a1,a) -> H.MinPrioHeap a1 a +createMinPrioHeap = H.singleton + +-- $cat1 +-- All of the following functions return distances as a @Maybe Int@, where @Nothing@ is returned if no path is found. +-- The graph is a @HashMap@ mapping each node to a sequence of (neighbour, edge weight) pairs. + +-- | Returns the shortest distance between two nodes in a graph. +shortestDistance :: (Foldable t, Hashable n, Ord a, Num a) + => HM.HashMap n (t (n, a)) -- ^ Graph + -> n -- ^ Start node + -> n -- ^ End node + -> Maybe a +shortestDistance graph = shortestDistanceOnMagma (repeat graph) + +-- | Returns the shortest distance between two nodes in a graph and a list of all possible paths from the ending node to the starting node. +-- The starting node is not included in each path. +shortestPaths :: (Foldable t, Hashable n, Ord a, Num a) + => HM.HashMap n (t (n, a)) -- ^ Graph + -> n -- ^ Start node + -> n -- ^ End node + -> (Maybe a, [[n]]) +shortestPaths graph = shortestPathsOnMagma (repeat graph) + +-- | Returns the shortest distance between two nodes in a list of graphs where the neighbours of a node in any given graph all lie in the succeeding graph. The ending node must be present in each graph. +-- This precondition is not checked. +shortestDistanceOnMagma :: (Foldable t, Hashable n, Ord a, Num a) + => [HM.HashMap n (t (n, a))] -- ^ Graphs + -> n -- ^ Start node + -> n -- ^ End node + -> Maybe a +shortestDistanceOnMagma graphs start end = fst $ shortestPathsOnMagma graphs start end + +-- | Returns the shortest distance between two nodes in a list of graphs and a list of all possible paths from the ending node to the starting node. The ending node must be present in each graph. +-- This precondition is not checked. +-- The starting node is not included in each path. +shortestPathsOnMagma :: (Foldable t, Hashable n, Ord a, Num a) + => [HM.HashMap n (t (n, a))] -- ^ Graphs + -> n -- ^ Start node + -> n -- ^ End node + -> (Maybe a, [[n]]) +shortestPathsOnMagma graphs start end = + let initQueue = createMinPrioHeap (0,start) + initPaths = HM.singleton start (0,[[]]) + helper (paths,queue) = case H.view queue of + Nothing -> (paths,queue) + Just ((_,n),ns) -> + let Just (currentDistance,currentPaths) = HM.lookup n paths + Just neighbours = HM.lookup n (graphs !! length (head currentPaths)) + updateNeighbour (n',d') (p',q') = case HM.lookup n' p' of + Nothing -> (HM.insert n' (currentDistance+d',map (n':) currentPaths) p', H.insert (currentDistance+d',n') q') + Just (d'',ps'') -> + if d'' < currentDistance+d' then + (p',q') + else if d'' > currentDistance+d' then + (HM.insert n' (currentDistance+d',map (n':) currentPaths) p', H.insert (currentDistance+d',n') q') + else + (HM.insert n' (currentDistance+d',ps'' ++ map (n':) currentPaths) p', q') + in helper $ foldr updateNeighbour (paths,ns) neighbours + + in case HM.lookup end $ fst (helper (initPaths,initQueue)) of + Nothing -> (Nothing, []) + Just (d,ps) -> (Just d, ps) + +-- | Returns the 4 points orthogonally adjacent to the given point. +neighbours4 :: (Num a, Num b) => (a, b) -> [(a, b)] +neighbours4 (x,y) = [(x+1,y),(x,y+1),(x-1,y),(x,y-1)] + +-- | Returns the 8 points orthogonally or diagonally adjacent to the given point. +neighbours8 :: (Enum a, Enum b, Eq a, Eq b, Num a, Num b) => (a, b) -> [(a, b)] +neighbours8 (x,y) = [(x+p,y+q) | p <- [-1..1], q <- [-1..1], p /= 0 || q /= 0] + +-- | Returns the 6 points orthogonally adjacent to the given point in 3D space. +neighbours6 :: (Num a, Num b, Num c) => (a, b, c) -> [(a, b, c)] +neighbours6 (x,y,z) = [(x+1,y,z),(x,y+1,z),(x,y,z+1),(x-1,y,z),(x,y-1,z),(x,y,z-1)] + +-- | Returns the 26 points orthogonally or diagonally adjacent to the given point in 3D space. +neighbours26 :: (Enum a, Enum b, Enum c, Eq a, Eq b, Eq c, Num a, Num b, Num c) => (a, b, c) -> [(a, b, c)] +neighbours26 (x,y,z) = [(x+p,y+q,z+r) | p <- [-1..1], q <- [-1..1], r <- [-1..1], p /= 0 || q /= 0 || r /= 0] + +-- | Returns the Taxicab/Manhattan distance between two points in 2D space. +taxicab2 :: Num a => (a, a) -> (a, a) -> a +taxicab2 (a,b) (c,d) = abs (a-c) + abs (b-d) + +-- | Returns the Taxicab/Manhattan distance between two points in 3D space. +taxicab3 :: Num a => (a, a, a) -> (a, a, a) -> a +taxicab3 (a,b,c) (d,e,f) = abs (a-d) + abs (b-e) + abs (c-f) + +enumerateBase :: (Num y, Num x, Enum y, Enum x) => String -> [((x, y), Char)] +enumerateBase s = + let ss = lines s + ys = zipWith (\n l -> map (n,) l) [0..] ss + xs = map (zipWith (\x (y,c) -> ((x,y),c)) [0..]) ys + in concat xs + +-- $cat2 +-- The following functions operate on a grid of characters as a string with a newline after each row (as seen in several Advent of Code puzzle inputs). + +-- | Converts a grid to a list of triples @(x,y,c)@ representing xy coordinates and the character at that location. +enumerate :: (Num y, Num x, Enum y, Enum x) => String -> [(x, y, Char)] +enumerate = map (\((x,y),c) -> (x,y,c)) . enumerateBase + +-- | Enumerates a grid along with reading the characters (usually as integers). +enumerateRead :: (Read c, Num y, Num x, Enum y, Enum x) => String -> [(x, y, c)] +enumerateRead = map (\((x,y),c) -> (x,y,read [c])) . enumerateBase + +-- | Enumerates a grid and stores it in a @HashMap@ where points are mapped to the character at that location. +enumerateHM :: (Num x, Num y, Enum x, Enum y, Hashable x, Hashable y) => String -> HM.HashMap (x, y) Char +enumerateHM = HM.fromList . enumerateBase + +-- | Enumerates a grid and stores it in a @HashMap@ along with reading the characters (usually as integers). +enumerateReadHM :: (Num x, Num y, Enum x, Enum y, Hashable x, Hashable y, Read c) => String -> HM.HashMap (x, y) c +enumerateReadHM = HM.fromList . map (\((x,y),c) -> ((x,y),read [c])) . enumerateBase + +-- | Returns a list of points on a grid for which a certain condition is met. +enumerateFilter :: (Num y, Num x, Enum y, Enum x) => (Char -> Bool) -> String -> [(x, y)] +enumerateFilter f = map fst . filter (f . snd) . enumerateBase + +-- | Returns a set of points on a grid for which a certain condition is met. +enumerateFilterSet :: (Ord x, Ord y, Num y, Num x, Enum y, Enum x) => (Char -> Bool) -> String -> S.Set (x, y) +enumerateFilterSet f = S.fromList . enumerateFilter f + +floodFill' :: Ord a => (a -> [a]) -> S.Set a -> S.Set a -> S.Set a -> S.Set a +floodFill' neighbours finished frontier blocks + | S.null frontier = finished + | otherwise = floodFill' neighbours (S.union frontier finished) newfrontier blocks + where + newfrontier = S.filter (\n -> n `S.notMember` finished || n `S.notMember` frontier || n `S.notMember` blocks) $ S.unions $ S.map (S.fromList . neighbours) frontier + +floodFillWith' :: Ord a => (a -> a -> Bool) -> (a -> [a]) -> S.Set a -> S.Set a -> S.Set a +floodFillWith' cond neighbours finished frontier + | S.null frontier = finished + | otherwise = floodFillWith' cond neighbours (S.union frontier finished) newfrontier + where + newfrontier = S.filter (\n -> n `S.notMember` finished || n `S.notMember` frontier) $ S.unions $ S.map (S.fromList . (\c -> filter (cond c) $ neighbours c)) frontier + +-- | Applies a flood fill algorithm given a function to generate a point's neighbours, a starting set of points, and a set of points to avoid. Returns a set of all points covered. +floodFill :: Ord a + => (a -> [a]) -- ^ Neighbour function + -> S.Set a -- ^ Initial set of points + -> S.Set a -- ^ Set of points to avoid + -> S.Set a +floodFill neighbours = floodFill' neighbours S.empty + +-- | Applies a flood fill algorithm given a function to generate a point's neighbours, a condition that filters out points generated by said function, and a starting set of points. Returns a set of all points covered. +-- The condition is of the form @a -> a -> Bool@, which returns @True@ if the second point is a valid neighbour of the first point and @False@ otherwise. +floodFillWith :: Ord a + => (a -> a -> Bool) -- ^ Condition + -> (a -> [a]) -- ^ Neighbour function + -> S.Set a -- ^ Initial set of points + -> S.Set a +floodFillWith cond neighbours = floodFillWith' cond neighbours S.empty + +-- | Generates a list of all possible lists of length n by taking elements from the provided list of length l. +-- Relative order is maintained, and the length of the returned list is \(_{n}C_{l}\). +choose :: (Num n, Eq n) => n -> [a] -> [[a]] +choose n (x:xs) = map (x:) (choose (n-1) xs) ++ choose n xs +choose 0 _ = [[]] +choose _ [] = [] + +-- | Generates a list of all possible lists of length n by taking elements from the provided list of length l. +-- The length of the returned list is \(_{n}P_{l}\). +permute :: (Num n, Eq n) => n -> [a] -> [[a]] +permute n = concatMap permutations . choose n + +-- | Gets the nth element of an infinite list, assuming that each element in the list can be generated using the previous element, for example, a list generated with @iterate@. +extrapolate :: (Integral b, Ord a) => b -> [a] -> a +extrapolate n ls = let (o,p) = helper 0 S.empty ls in ls `genericIndex` (((n-o) `mod` p) + o) + where + helper k finished (l:ls') + | S.null matches = helper (k+1) (S.insert (k,l) finished) ls' + | otherwise = let o = fst $ S.elemAt 0 matches in (o,k-o) + where matches = S.filter ((==l) . snd) finished + +-- | Generates a range with @[x..y]@, but reverses the list instead of returning an empty range if x > y. +range :: (Ord a, Enum a) => a -> a -> [a] +range x y = if y < x then [x,pred x..y] else [x..y] + +-- | Takes (a,b) and (c,d) as arguments and returns the intersection of the ranges [a..b] and [c..d] as another pair if it is not empty. +rangeIntersect :: Ord b => (b, b) -> (b, b) -> Maybe (b, b) +rangeIntersect (a,b) (c,d) + | b < c || a > d = Nothing + | otherwise = Just (max a c, min b d) + +-- | Converts a list of booleans (parsed as a binary number) to an integer. +binToDec :: Num a => [Bool] -> a binToDec = sum . zipWith (*) (map (2^) [0..]) . map (fromIntegral . fromEnum) . reverse