Year 2015 Day 13 Part 1

README.md

@@ -132,7 +132,13 @@ solution.
 
     New Parser Effect stack and DLists
 
+  - [Day 13](src/Years/Y2015/Day13.md)
+
+    Naive ring buffer and `parameters` blocks[^2]
+
 ## References
 
 [^1]: Idris 2 Manual:
     [Views and the "with" rule](https://idris2.readthedocs.io/en/latest/tutorial/views.html#views-and-the-with-rule)
+
+[^2]: <https://idris2.readthedocs.io/en/latest/tutorial/modules.html#parameterised-blocks-parameters-blocks>

src/SUMMARY.md

@@ -34,3 +34,4 @@
   - [Day 10 - Digits View](Years/Y2015/Day10.md)
   - [Day 11 - Refinement Types](Years/Y2015/Day11.md)
   - [Day 12 - Custom Parser Effect and DLists](Years/Y2015/Day12.md)
+  - [Day 13 - Naive Ring Buffer and parameters blocks](Years/Y2015/Day13.md)

src/Years/Y2015.md

@@ -19,6 +19,7 @@ import Years.Y2015.Day9
 import Years.Y2015.Day10
 import Years.Y2015.Day11
 import Years.Y2015.Day12
+import Years.Y2015.Day13
 ```
 
 # Days
@@ -101,6 +102,12 @@ y2015 = MkYear 2015 [
   , day12
 ```
 
+## [Day 13](Y2015/Day13.md)
+
+```idris
+  , day13
+```
+
 ```idris
   ]
 ```

src/Years/Y2015/Day13.md

@@ -0,0 +1,241 @@
+# [Year 2015 Day 13](https://adventofcode.com/2015/day/13)
+
+This day exhibits a naive, `Vect` based implementation of a ring buffer, as well
+as our first introduction to `parameters` blocks.
+
+```idris hide
+module Years.Y2015.Day13
+
+import Data.Primitives.Interpolation
+
+import Control.Eff
+
+import Runner
+```
+
+```idris
+import Data.String
+import Data.List1
+import Data.List.Lazy
+import Data.Vect
+import Data.Maybe
+import Data.SortedMap.Dependent
+import Decidable.Equality
+
+import Util
+
+%default total
+```
+
+## Parsing and Data Structures
+
+```idris
+Name : Type
+Name = String
+
+Happiness : Type
+Happiness = Integer
+```
+
+Describe a change in happiness from a change in seating arrangement as data
+structure, indexed by the name of the individual whose happiness it describes,
+and provide some projections.
+
+```idris
+data Change : (changee : Name) -> Type where
+  NextTo : (changee : Name) -> (other : Name) -> (amount : Happiness)
+    -> Change (changee)
+
+(.changee) : Change changee -> Name
+(.changee) (NextTo changee _ _) = changee
+
+(.other) : Change changee -> Name
+(.other) (NextTo _ other _) = other
+
+(.amount) : Change changee -> Happiness
+(.amount) (NextTo _ _ amount) = amount
+```
+
+Collect the list of changes provided as input into a structure that encodes our
+assumptions at the type level.
+
+The changes are stored in a in a dependent map, with the name of the individual
+as the key, and lists of potential changes to their happiness as the values.
+
+This problem is a bit nicer to express in terms of a collection of known size,
+and we don't want to be constantly converting the keys list to a `Vect`, so we
+instead store it in `Changes` as a `Vect`. We don't want to accidentally store
+the wrong thing here, so we store an auto-implicit proof of equality,
+`keys_prf`, proving that the `names` list is exactly the list of keys in
+`change_map` converted to a Vect with `fromList`.
+
+It will also make things a bit nicer if we can assume that our `names` list is
+non-empty, after all it really doesn't make sense to talk about seating
+arrangements at a table with 0 people at it, so we store an auto-implict
+`nonempty` proof establishing that the length of `change_map`'s keys list, and
+thus `names`, is at least 1.
+
+```idris
+record Changes where
+  constructor MkChanges
+  change_map : SortedDMap Name (\n => List (Change n))
+  names : Vect (length (keys change_map)) Name
+  {auto keys_prf : names = fromList (keys change_map)}
+  {auto nonempty : IsSucc (length (keys change_map))}
+```
+
+Our usual pattern-matching based parsing of one element of the input, returning
+a dependent pair of the name of the individual this record describes, and the
+change described by that record.
+
+```idris
+parseChange : Has (Except String) fs => String -> Eff fs (name ** Change name)
+parseChange str = do
+  changee ::: [_, direction, amount, _, _, _, _, _, _, other] 
+    <- pure $ split (== ' ') str
+    | _ => throw "Invalid input string \{str}"
+  amount <- note "Invalid amount \{amount} in \{str}" $ parseInteger amount
+  amount : Happiness <-
+    case direction of
+      "gain" => pure amount
+      "lose" => pure $ negate amount
+      x      => throw "Invalid direction \{x} in \{str}" 
+  let other = pack . filter (/= '.') . unpack $ other
+  pure (_ ** (changee `NextTo` other) amount)
+```
+
+Parse the entire list of changes in the input, collecting them into a dependent
+map as we go along, and performing the checks needed for Idris to be satisfied
+that the conditions encoded by the auto-implict proofs in `Changes` are met.
+
+```idris
+parseChanges : Has (Except String) fs =>
+  List String -> Eff fs Changes
+parseChanges strs = do
+  changes <- traverse parseChange strs
+  let change_map = insertChanges changes empty
+  case isItSucc (length (keys change_map)) of
+    Yes prf => pure $ MkChanges change_map (fromList (keys change_map))
+    No contra => throw "Empty table, not very interesting"
+  where
+    insertChanges : List (name ** Change name) 
+      -> (acc : SortedDMap Name (\n => List (Change n)))
+      -> SortedDMap Name (\n => List (Change n))
+    insertChanges [] acc = acc
+    insertChanges ((name ** change) :: xs) acc = 
+      case lookupPrecise name acc of
+        Nothing => insertChanges xs (insert name [change] acc)
+        Just ys => insertChanges xs (insert name (change :: ys) acc)
+```
+
+## Solver functions
+
+All of these functions are about to take the same first argument,
+`(cs : Changes)`. This is a really common occurrence, especially when dealing
+with dependent proof types, so Idris has syntax sugar to avoid repeating your
+self in theses situations, `parameters` blocks[^1].
+
+A `parameters` block adds the provided arguments to the start of every top level
+signature contained within it, in this case, making the first argument of all of
+these functions have type `(cs : Changes)`. The arguments to the `parameters`
+blocks are also added to the front of the arguments list, using the names
+provided in the signature.
+
+`parameters` blocks also provide another fun bit of functionality that makes
+code within them more concise, within a `parameters` block, the parameters are
+implicitly passed as arguments to calls to functions in the same block.
+
+```idris
+parameters (cs : Changes)
+```
+
+Calculate the happiness change for a given person in a seating arrangement, use
+`finS` and `unfinS` to get the indexes of the parties seated to either side of
+us, and look them up in our map, adding the amount of change described by them
+together.
+
+Notice how `cs` appears neither in the arguments list, nor the type signature,
+yet we can still refer to it as if it was included at the start of both.
+
+```idris
+  happinessFor :
+    (arrangement : Vect (length (keys cs.change_map)) Name)
+    -> (idx : Fin (length (keys cs.change_map)))
+    -> Happiness
+  happinessFor arrangement idx = 
+    let name = idx `index` arrangement
+    in case name `lookupPrecise` cs.change_map of
+      Nothing => 0
+      Just changes => 
+        let name_right = (finS idx) `index` arrangement
+            change_right = 
+              fromMaybe 0 . map (.amount) . find ((== name_right) . (.other)) $ 
+                changes
+            name_left = (unfinS idx) `index` arrangement
+            change_left = 
+              fromMaybe 0 . map (.amount) . find ((== name_left) . (.other)) $ 
+                changes
+        in change_right + change_left
+```
+
+Calculate the overall happiness change for a given arrangement by mapping our
+`happinessFor` function over a list of all possible indexes to the `arrangement`
+vect, and summing the results.
+
+Notice how the `cs` parameter is implicitly passed to `happinessFor`, as we are
+inside the same `parameters` block as it.
+
+```idris
+  happinessChange :
+    (arrangement : Vect (length (keys cs.change_map)) Name)
+    -> Happiness
+  happinessChange arrangement = 
+    let idxes = List.allFins (length (keys cs.change_map))
+        changes = map (happinessFor arrangement) idxes
+    in sum changes
+```
+
+Find the arrangement with the maximum total change in happiness by mapping
+`happinessChange` over a list of all the possible permutations of our seed
+arrangement described by `names`, and using `maxBy` to identify the largest
+positive change in overall happiness.
+
+```idris
+  maxHappiness : Has (Except String) fs =>   
+    Eff fs (Happiness, Vect (length (keys cs.change_map)) Name)
+  maxHappiness =
+    let arrangements = permutations cs.names
+        changes = map happinessChange arrangements
+        pairs = zip changes arrangements
+    in case pairs of
+      [] => throw "No arrangements"
+      (x :: xs) => pure $ maxBy (compare `on` fst) x xs
+```
+
+## Part Functions
+
+### Part 1
+
+Parse our input and feed it into our `maxHappiness` function.
+
+Notice how, since we are outside the `parameters` block, we have to provide the
+`cs` argument to `maxHappiness` explicitly.
+
+```idris
+part1 : Eff (PartEff String) (Happiness, ())
+part1 = do
+  input <- map lines $ askAt "input"
+  changes <- parseChanges input
+  (max, arrangement) <- maxHappiness changes
+  pure (max, ())
+```
+
+```idris hide
+public export
+day13 : Day
+day13 = First 13 part1
+```
+
+## References
+
+[^1]: <https://idris2.readthedocs.io/en/latest/tutorial/modules.html#parameterised-blocks-parameters-blocks>