Architeuthis

Luckily I noticed the numbers produced in every iteration were incredibly repetitive, so I assigned a separate accumulator to each one, and every iteration I only kept the unique numbers and updated the corresponding accumulators with how many times they had appeared, and finally I summed the accumulators.

The most unique numbers in one iteration were 3777, the 75 step execution was basically instant.

edit: other unhinged attempts included building a cache with how many pebbles resulted from a number after x steps that I would start using after reaching the halfway point, so every time I found a cached number I would replace that branch with the final count according to the remaining steps, but I couldn't think of a way to actually track how many pebbles result downstream from a specific pebble, but at least it got me thinking about tracking something along each pebble.

// F# as usual
// fst and snd are tuple deconstruction helpers

[<TailCall>]
let rec blink (idx:int) (maxIdx:int) (pebbles : (int64*int64) list) =
    if idx = maxIdx
    then pebbles |> List.sumBy snd
    else
        pebbles
        // Expand array
        |> List.collect (fun (pebbleId, pebbleCount) -> 
            let fpb = float pebbleId
            let digitCount = Math.Ceiling(Math.Log(fpb + 1.0,10))      
            match pebbleId with
            | 0L -> [ 1L, pebbleCount ]
            | x when digitCount % 2.0 = 0.0 -> 
                let factor = Math.Pow(10,digitCount/2.0)
                let right = fpb % factor
                let left = (fpb - right) / factor
                [int64 left, pebbleCount; int64 right,pebbleCount]   
            | x -> [ x * 2024L, pebbleCount ])
        // Compress array
        |> List.groupBy fst
        |> List.map (fun (pebbleId, pebbleGroup) -> pebbleId, pebbleGroup |> List.sumBy snd)
        |> blink (idx+1) maxIdx


"./input.example"
|> Common.parse
|> List.map (fun pebble -> pebble,1L)
|> blink 0 25 
|> Global.shouldBe 55312L

"./input.actual"
|> Common.parse
|> List.map (fun pebble -> pebble,1L)
|> blink 0 75 
|> printfn "Pebble count after 75 blinks is %d" 

(* F# - file reading code and other boilerplate omited *)

let mapAllTrails (matrix : int array2d) =
    let rowCount = matrix |> Array2D.length1
    let colCount = matrix |> Array2D.length2

    let rec search (current:int*int) (visited: HashSet<int*int>) (path: (int*int) list) : (int*int) list list= 
        let (row,col) = current
        let currentValue = matrix.[row,col]

        // Remove to solve for 10-2
        visited.Add (row,col) |> ignore

        // If on a 9 return the complete path
        if currentValue = 9 then [List.append path [row,col] ]
        // Otherwise filter for eligible neihboring cells and continue search
        else                    
            [ row-1, col;row, col-1; row, col+1; row+1,col]
            |> List.filter (fun (r,c) -> 
                not (visited.Contains(r,c))
                && r >= 0 && c>=0 && r < rowCount && c < colCount
                && matrix.[r,c]-currentValue = 1 )
            |> List.collect (fun next ->
                [row,col] 
                |> List.append path  
                |> search next visited)

    // Find starting cells, i.e. contain 0
    matrix
    |> Global.matrixIndices
    |> Seq.filter (fun (row,col) -> matrix.[row,col] = 0)
    // Find all trails starting from those cells and flatten the result
    |> Seq.collect (fun trailhead -> search trailhead (HashSet<int*int>()) [])
    

"./input.example"
|> Common.parse 
|> mapAllTrails
|> Seq.length
|> Global.shouldBe 81

"./input.actual"
|> Common.parse 
|> mapAllTrails
|> Seq.length
|> printfn "The sum total of trail rankings is %d"

// F#
let isLegit ((total: int64), (calibration : int64 array)) = 

    let rec search (index : int) (acc: int64) =
        let currentValue = calibration.[index]
        
        [Add; Times; Concat] // operators - remove 'Concat' to solve for 7-1
        |> List.exists (fun op -> // List.exists returns true the first time the lambda returns true, so search stops at first true
                match op with // update accumulator
                | Add -> acc + currentValue
                | Times -> acc * currentValue
                | Concat -> int64 (sprintf "%d%d" acc currentValue)
                |> function // stop search on current accumulator value (state) exceeding total, or being just right
                | state when state > total -> false
                | state when state = total && index < (calibration.Length-1) -> false // this was the problem
                | state when state = total && index = (calibration.Length-1) -> true
                | state -> // stop if index exceeds input length, or continue search
                    if index+1 = calibration.Length
                    then false
                    else search (index+1) state
        )
     
    // start search from second element using the first as current sum
    search 1 calibration.[0]

EDIT: total && index < (calibration.Length-1) -> false -- i.e. stop if you reach the total before using all numbers, well, also stops you from checking the next operator, So, removing it worked.

Rubber ducking innocent people on the internets works, who knew.

So ideally 1|2, 2|3, 3|4 -> 1|2|3|4 -> 1|2, 2|3, 3|4, 1|3, 1|4, 2|4

Except I forgot the last part and just returned the branch elements pairwise in sequence, which is just the original rules, which I noticed accidentally after the fact since I was getting correct results, because apparently it was completely unnecessary and I was just overthinking myself into several corners at the same time.

let comparerFactory (ruleset: (int*int) list) :int -> int -> int = 
    let leftIndex = 
        ruleset 
        |> List.groupBy fst 
        |> List.map (fun (key,grp)-> key, grp |> List.map snd)
        |> Map.ofList

    fun page1 page2 -> 
        match (leftIndex  |> Map.tryFind page1) with
        | Some afterSet when afterSet |> List.contains page2 -> -1
        | _ -> 1

The memoization pattern is for caching an index of rules grouped by the before page, so I can sort according to where each part of the comparison appears. I started out with having a second index where the key was the 'after' page of the rule which I would check if the page didn't appear on the left side of any rule, but it turned out I could just return the opposite case, so again unnecessary.

Would have been pretty useful too if 4-2 turned out to be about finding longer patterns, instead of smaller and in half the directions.

let rec isXmas (row:int) (col:int) (dir:int) (depth:int) (arr: char array2d) : bool =
    let value = arr.[row,col]
    if depth = 3
    then value = 'S'
    else if  [|'X';'M';'A';'S'|].[depth] = value
    then
        let (nextRow, nextCol) =
            match dir with
            | 1 -> row + 1, col - 1
            | 2 -> row + 1, col
            | 3 -> row + 1, col + 1
            | 4 -> row, col - 1
            | 6 -> row, col + 1
            | 7 -> row - 1, col - 1
            | 8 -> row - 1, col
            | 9 -> row - 1, col + 1
            | _ -> failwith $"{dir} isn't a numpad direction." 

        let rowCount = arr |> Array2D.length1
        let colCount = arr |> Array2D.length2
       
        if nextRow >= 0 && nextRow < rowCount && nextCol >= 0 && nextCol < colCount
        then isXmas nextRow nextCol dir (depth+1) arr
        else false
    else false

Then you run this for every appropriately pruned 'X' times every direction and count the trues.