Advent of Code 2023 6

advent2023-6.fs

open System
  
let input = """Time:      7  15   30
Distance:  9  40  200""" |> (fun s -> s.Split('\n', StringSplitOptions.RemoveEmptyEntries))

type Race =
    { time : int64
      distance : int64 }

let splitInts (s: string) = s.Split([|' '|], StringSplitOptions.RemoveEmptyEntries) |> Array.map int

let parseRaces (input: string array) =
    let times = input[0].Substring(6) |> splitInts
    let distances = input.[1].Substring(9) |> splitInts
    Array.zip times distances |> Array.map (fun (t, d) -> { time = t; distance = d })

let parseRace (input: string array) =
    let time =
        input[0].Substring(6)
        |> fun x -> x.Split([|' '|], StringSplitOptions.RemoveEmptyEntries)
        |> String.Concat
        |> int64
    let distances =
        input.[1].Substring(9)
        |> fun x -> x.Split([|' '|], StringSplitOptions.RemoveEmptyEntries)
        |> String.Concat
        |> int64

    { time = time
      distance = distances }

let amountOfWinCombos race =
    let T = race.time
    let D = race.distance
    // amount of win combos are actually all integers values of X which satisfy the following equation:
    // x^2 - T * x + D < 0
    // where T - time, D - distance
    let sqrtDiscriminant = T * T - 4L * D |> float |> sqrt
    let x1 = (float T + sqrtDiscriminant) / 2.
    let x2 = (float T - sqrtDiscriminant) / 2.
    
    // we need to exclude roots of the equation, and floor/ceil won't work if roots of the equation are integers
    let x1Floor =
        if x1 = int x1 then int64 x1 - 1L
                       else floor x1 |> int64
    let x2Ceil =
        if x2 = int x2 then int64 x2 + 1L
                       else ceil x2 |> int64
    x1Floor - x2Ceil + 1L

let part1 =
    parseRaces input
    |> Seq.map amountOfWinCombos
    |> Seq.reduce (*) // 288
    
let part2 =
    parseRace input
    |> amountOfWinCombos // 71503