mirror of
https://github.com/Smaug123/AdventOfCode2022
synced 2025-10-10 03:58:41 +00:00
Day 16 (#26)
This commit is contained in:
Patrick Stevens
GitHub
15
.github/workflows/dotnet.yaml
vendored
15
.github/workflows/dotnet.yaml
vendored
@@ -33,8 +33,17 @@ jobs:
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run: dotnet build --no-restore --configuration ${{matrix.config}}
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- name: Test
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run: dotnet test --no-build --verbosity normal --configuration ${{matrix.config}}
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- name: Run app
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run: dotnet run --project AdventOfCode2022.App/AdventOfCode2022.App.fsproj --no-build --configuration ${{matrix.config}}
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run-app:
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runs-on: ubuntu-latest
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steps:
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- uses: actions/checkout@v3
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- name: Setup .NET
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uses: actions/setup-dotnet@v3
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with:
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dotnet-version: 7.0.x
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- name: Run app
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run: dotnet run --project AdventOfCode2022.App/AdventOfCode2022.App.fsproj --configuration Release
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check-format:
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runs-on: ubuntu-latest
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@@ -67,7 +76,7 @@ jobs:
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name: Run link checker
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all-required-checks-complete:
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needs: [check-format, build, shellcheck, linkcheck]
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needs: [check-format, build, shellcheck, linkcheck, run-app]
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runs-on: ubuntu-latest
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steps:
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- run: echo "All required checks complete."
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@@ -25,6 +25,7 @@
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<EmbeddedResource Include="..\AdventOfCode2022.Test\Inputs\Day13.txt" />
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<EmbeddedResource Include="..\AdventOfCode2022.Test\Inputs\Day14.txt" />
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<EmbeddedResource Include="..\AdventOfCode2022.Test\Inputs\Day15.txt" />
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<EmbeddedResource Include="..\AdventOfCode2022.Test\Inputs\Day16.txt" />
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</ItemGroup>
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<ItemGroup>
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@@ -2,5 +2,5 @@ namespace AdventOfCode2022.App
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[<RequireQualifiedAccess>]
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module Inputs =
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let days = Array.init 15 (fun day -> Assembly.readResource $"Day%i{day + 1}.txt")
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let days = Array.init 16 (fun day -> Assembly.readResource $"Day%i{day + 1}.txt")
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let inline day (i : int) = days.[i - 1]
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@@ -57,6 +57,22 @@ type Benchmark11To15 () =
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[<GlobalCleanup>]
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member _.Cleanup () = Run.shouldWrite <- true
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type Benchmark16To20 () =
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[<GlobalSetup>]
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member _.Setup () = Run.shouldWrite <- false
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[<Params(16)>]
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member val Day = 0 with get, set
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[<Params(false, true)>]
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member val IsPartOne = false with get, set
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[<Benchmark>]
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member this.Benchmark () : unit =
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Run.allRuns.[this.Day - 1] (not this.IsPartOne) (Inputs.day this.Day)
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[<GlobalCleanup>]
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member _.Cleanup () = Run.shouldWrite <- true
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module Program =
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@@ -72,6 +88,7 @@ module Program =
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let _summary = BenchmarkRunner.Run<Benchmark1To5> config
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let _summary = BenchmarkRunner.Run<Benchmark6To10> config
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let _summary = BenchmarkRunner.Run<Benchmark11To15> config
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let _summary = BenchmarkRunner.Run<Benchmark16To20> config
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0
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| _ ->
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@@ -218,6 +218,20 @@ module Run =
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if shouldWrite then
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printfn "%i" output
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let day16 (partTwo : bool) (input : string) =
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let day16 = input.Split '\n'
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if not partTwo then
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let output = Day16.part1 day16
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if shouldWrite then
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printfn "%i" output
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else
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let output = Day16.part2 day16
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if shouldWrite then
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printfn "%i" output
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let allRuns =
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[|
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day1
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@@ -235,4 +249,5 @@ module Run =
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day13
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day14
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day15
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day16
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|]
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@@ -23,6 +23,7 @@
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<Compile Include="Day13.fs" />
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<Compile Include="Day14.fs" />
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<Compile Include="Day15.fs" />
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<Compile Include="Day16.fs" />
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<EmbeddedResource Include="Inputs\Day1.txt" />
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<EmbeddedResource Include="Inputs\Day2.txt" />
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<EmbeddedResource Include="Inputs\Day3.txt" />
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@@ -38,6 +39,7 @@
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<EmbeddedResource Include="Inputs\Day13.txt" />
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<EmbeddedResource Include="Inputs\Day14.txt" />
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<EmbeddedResource Include="Inputs\Day15.txt" />
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<EmbeddedResource Include="Inputs\Day16.txt" />
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</ItemGroup>
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<ItemGroup>
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49
AdventOfCode2022.Test/Day16.fs
Normal file
49
AdventOfCode2022.Test/Day16.fs
Normal file
@@ -0,0 +1,49 @@
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namespace AdventOfCode2022.Test
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open NUnit.Framework
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open FsUnitTyped
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open AdventOfCode2022
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[<TestFixture>]
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module TestDay16 =
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let input =
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"""Valve AA has flow rate=0; tunnels lead to valves DD, II, BB
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Valve BB has flow rate=13; tunnels lead to valves CC, AA
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Valve CC has flow rate=2; tunnels lead to valves DD, BB
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Valve DD has flow rate=20; tunnels lead to valves CC, AA, EE
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Valve EE has flow rate=3; tunnels lead to valves FF, DD
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Valve FF has flow rate=0; tunnels lead to valves EE, GG
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Valve GG has flow rate=0; tunnels lead to valves FF, HH
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Valve HH has flow rate=22; tunnel leads to valve GG
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Valve II has flow rate=0; tunnels lead to valves AA, JJ
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Valve JJ has flow rate=21; tunnel leads to valve II
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"""
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[<Test>]
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let ``seq behaviour`` () =
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Day16.ofSeq [ 1 ; 2 ; 3 ; 16 ]
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|> Day16.toSeq
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|> List.ofSeq
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|> shouldEqual [ 1 ; 2 ; 3 ; 16 ]
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[<Test>]
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let ``Part 1, given`` () =
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Day16.part1 (input.Split '\n') |> shouldEqual 1651
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[<Test>]
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let ``Part 1`` () =
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let input = Assembly.readResource "Day16.txt"
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Day16.part1 (input.Split '\n') |> shouldEqual 1751
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[<Test>]
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let ``Part 2, given`` () =
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Day16.part2 (input.Split '\n') |> shouldEqual 1707
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[<Test>]
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let ``Part 2`` () =
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let input = Assembly.readResource "Day16.txt"
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Day16.part2 (input.Split '\n') |> shouldEqual 2207
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60
AdventOfCode2022.Test/Inputs/Day16.txt
Normal file
60
AdventOfCode2022.Test/Inputs/Day16.txt
Normal file
@@ -0,0 +1,60 @@
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Valve QP has flow rate=0; tunnels lead to valves IS, DG
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Valve MC has flow rate=0; tunnels lead to valves XX, QQ
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Valve OT has flow rate=7; tunnels lead to valves OE, BL, DJ, JS, LS
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Valve CZ has flow rate=0; tunnels lead to valves IC, ZL
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Valve GI has flow rate=0; tunnels lead to valves OM, GF
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Valve YB has flow rate=0; tunnels lead to valves DQ, MX
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Valve EJ has flow rate=0; tunnels lead to valves GB, ES
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Valve IS has flow rate=19; tunnels lead to valves AS, OB, QP
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Valve WI has flow rate=21; tunnels lead to valves SS, AK
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Valve JS has flow rate=0; tunnels lead to valves OT, HV
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Valve UR has flow rate=0; tunnels lead to valves OM, ZI
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Valve UC has flow rate=0; tunnels lead to valves QX, NG
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Valve BL has flow rate=0; tunnels lead to valves YW, OT
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Valve AK has flow rate=0; tunnels lead to valves WI, AL
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Valve QQ has flow rate=16; tunnels lead to valves MC, WH, MS, IY
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Valve PW has flow rate=0; tunnels lead to valves ZL, EK
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Valve AS has flow rate=0; tunnels lead to valves IS, MS
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Valve ZL has flow rate=9; tunnels lead to valves CD, QX, PW, CZ, PQ
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Valve OB has flow rate=0; tunnels lead to valves HS, IS
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Valve OE has flow rate=0; tunnels lead to valves IC, OT
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Valve AL has flow rate=0; tunnels lead to valves VX, AK
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Valve AM has flow rate=0; tunnels lead to valves OM, YW
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Valve QX has flow rate=0; tunnels lead to valves UC, ZL
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Valve DJ has flow rate=0; tunnels lead to valves OT, ST
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Valve ZI has flow rate=0; tunnels lead to valves VX, UR
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Valve PQ has flow rate=0; tunnels lead to valves ZL, YW
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Valve OM has flow rate=22; tunnels lead to valves GI, AM, EK, UR
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Valve NG has flow rate=13; tunnels lead to valves UC, HS, GF
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Valve AA has flow rate=0; tunnels lead to valves UJ, ES, JP, HY, ST
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Valve HY has flow rate=0; tunnels lead to valves GZ, AA
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Valve MS has flow rate=0; tunnels lead to valves AS, QQ
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Valve JK has flow rate=0; tunnels lead to valves YW, GB
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Valve JP has flow rate=0; tunnels lead to valves AA, PF
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Valve ST has flow rate=0; tunnels lead to valves AA, DJ
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Valve CD has flow rate=0; tunnels lead to valves SS, ZL
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Valve ES has flow rate=0; tunnels lead to valves EJ, AA
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Valve PF has flow rate=0; tunnels lead to valves JP, HV
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Valve RL has flow rate=0; tunnels lead to valves GB, IC
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Valve IY has flow rate=0; tunnels lead to valves QQ, SN
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Valve UJ has flow rate=0; tunnels lead to valves IC, AA
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Valve HS has flow rate=0; tunnels lead to valves NG, OB
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Valve WH has flow rate=0; tunnels lead to valves QQ, MX
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Valve YA has flow rate=0; tunnels lead to valves GB, HV
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Valve SN has flow rate=0; tunnels lead to valves IY, DG
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Valve GF has flow rate=0; tunnels lead to valves GI, NG
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Valve YW has flow rate=8; tunnels lead to valves GZ, JK, BL, PQ, AM
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Valve DG has flow rate=17; tunnels lead to valves QP, SN
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Valve MX has flow rate=11; tunnels lead to valves WH, YB
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Valve DQ has flow rate=0; tunnels lead to valves YB, HV
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Valve SS has flow rate=0; tunnels lead to valves CD, WI
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Valve HV has flow rate=4; tunnels lead to valves YA, DQ, TO, JS, PF
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Valve GB has flow rate=6; tunnels lead to valves LS, RL, JK, EJ, YA
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Valve EK has flow rate=0; tunnels lead to valves OM, PW
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Valve LS has flow rate=0; tunnels lead to valves GB, OT
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Valve IC has flow rate=5; tunnels lead to valves CZ, OE, UJ, TO, RL
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Valve XX has flow rate=0; tunnels lead to valves MC, FM
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Valve VX has flow rate=25; tunnels lead to valves ZI, AL
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Valve GZ has flow rate=0; tunnels lead to valves HY, YW
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Valve FM has flow rate=20; tunnel leads to valve XX
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Valve TO has flow rate=0; tunnels lead to valves IC, HV
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@@ -25,6 +25,11 @@
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<Compile Include="Day13.fs" />
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<Compile Include="Day14.fs" />
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<Compile Include="Day15.fs" />
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<Compile Include="Day16.fs" />
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</ItemGroup>
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<ItemGroup>
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<PackageReference Include="FSharp.Collections.ParallelSeq" Version="1.2.0" />
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</ItemGroup>
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|
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</Project>
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@@ -61,17 +61,6 @@ module Day15 =
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let inline manhattan (p1 : Coordinate) (p2 : Coordinate) : int = abs (p1.X - p2.X) + abs (p1.Y - p2.Y)
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let inline cantorBijection (x : int) (y : int) : int64 =
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let sum = x + y
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let major =
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if sum % 2 = 0 then
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int64 (sum / 2) * int64 (sum + 1)
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else
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int64 sum * int64 ((sum + 1) / 2)
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major + int64 y
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let inline couldBeBeacon
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(sensors : ResizeArray<Coordinate>)
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(closestManhattans : int[])
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@@ -163,14 +152,14 @@ module Day15 =
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let mutable xIndex = 0
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while answer = -1L && xIndex < sensorXCoords.Length - 1 do
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while answer <> 1L && xIndex < sensorXCoords.Length - 1 do
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let xMin = sensorXCoords.[xIndex]
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xIndex <- xIndex + 1
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let xMax = sensorXCoords.[xIndex]
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let mutable yIndex = 0
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|
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while answer = -1L && yIndex < sensorYCoords.Length - 1 do
|
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while answer <> 1L && yIndex < sensorYCoords.Length - 1 do
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let yMin = sensorYCoords.[yIndex]
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yIndex <- yIndex + 1
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let yMax = sensorYCoords.[yIndex]
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@@ -195,6 +184,42 @@ module Day15 =
|
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else
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plusXPlusYConstraint <- min plusXPlusYConstraint (-manhattan + sensor.X + sensor.Y - 1)
|
||||
|
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let yMax =
|
||||
if
|
||||
plusXPlusYConstraint <> Int32.MaxValue
|
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&& plusXMinusYConstraint <> Int32.MaxValue
|
||||
then
|
||||
min ((plusXPlusYConstraint - plusXMinusYConstraint) / 2) yMax
|
||||
else
|
||||
yMax
|
||||
|
||||
let xMax =
|
||||
if
|
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plusXPlusYConstraint <> Int32.MaxValue
|
||||
&& minusXPlusYConstraint <> Int32.MaxValue
|
||||
then
|
||||
min ((plusXPlusYConstraint - minusXPlusYConstraint) / 2) xMax
|
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else
|
||||
xMax
|
||||
|
||||
let xMin =
|
||||
if
|
||||
minusXMinusYConstraint <> Int32.MaxValue
|
||||
&& minusXPlusYConstraint <> Int32.MaxValue
|
||||
then
|
||||
max xMin (-(minusXMinusYConstraint + minusXPlusYConstraint) / 2)
|
||||
else
|
||||
xMin
|
||||
|
||||
let yMin =
|
||||
if
|
||||
minusXMinusYConstraint <> Int32.MaxValue
|
||||
&& plusXMinusYConstraint <> Int32.MaxValue
|
||||
then
|
||||
max yMin (-(minusXMinusYConstraint + plusXMinusYConstraint) / 2)
|
||||
else
|
||||
yMin
|
||||
|
||||
// (fst constraints).{x, y} <= (snd constraints), and also xMin <= x <= xMax and
|
||||
// yMin <= y <= yMax.
|
||||
let mutable falsified = false
|
||||
@@ -221,32 +246,6 @@ module Day15 =
|
||||
falsified <- true
|
||||
|
||||
if not falsified then
|
||||
// The most likely way for there to be no slack is if equality holds throughout both conjugate pairs
|
||||
// of constraints.
|
||||
// (It's also possible for there to be no slack by having one of the "x <= 33" constraints binding.
|
||||
// See below for the treatment of this case.)
|
||||
if
|
||||
minusXMinusYConstraint = -plusXPlusYConstraint
|
||||
&& plusXMinusYConstraint = -minusXPlusYConstraint
|
||||
then
|
||||
let y = (plusXPlusYConstraint - plusXMinusYConstraint) / 2
|
||||
let x = (plusXPlusYConstraint - minusXPlusYConstraint) / 2
|
||||
|
||||
if xMin <= x && x <= xMax && yMin <= y && y <= yMax then
|
||||
answer <- int64 x * 4000000L + int64 y
|
||||
|
||||
if answer = -1L then
|
||||
// In fact one of the xMax/xMin or yMax/yMin constraints binds.
|
||||
let mutable xIndex = 0
|
||||
|
||||
while answer = -1 && xIndex < sensorXCoords.Length do
|
||||
xIndex <- xIndex + 1
|
||||
// Try with this x.
|
||||
let _x = sensorXCoords.Length
|
||||
|
||||
for _sensor in sensors do
|
||||
// Construct the necessary inequalities, then solve them.
|
||||
failwith "I couldn't be bothered to implement this"
|
||||
|
||||
answer <- int64 xMax * 4000000L + int64 yMax
|
||||
|
||||
answer
|
||||
|
||||
429
AdventOfCode2022/Day16.fs
Normal file
429
AdventOfCode2022/Day16.fs
Normal file
@@ -0,0 +1,429 @@
|
||||
namespace AdventOfCode2022
|
||||
|
||||
open System
|
||||
open FSharp.Collections.ParallelSeq
|
||||
|
||||
#if DEBUG
|
||||
open Checked
|
||||
#else
|
||||
#nowarn "9"
|
||||
#endif
|
||||
|
||||
|
||||
[<RequireQualifiedAccess>]
|
||||
module Day16 =
|
||||
|
||||
type Node = int
|
||||
|
||||
/// Returns the nodes, and also the "AA" node.
|
||||
let parse (lines : string seq) : Map<Node, int * Node Set> * Node =
|
||||
let allNodes =
|
||||
lines
|
||||
|> Seq.filter (not << String.IsNullOrEmpty)
|
||||
|> Seq.mapi (fun i line ->
|
||||
let split = line.Split "tunne" |> Array.last |> (fun s -> s.Trim ())
|
||||
let split = split.Split(' ').[4..] |> Array.map (fun s -> s.Trim ',') |> Set.ofArray
|
||||
line.[6..7], (i, (Int32.Parse line.[line.IndexOf '=' + 1 .. line.IndexOf ';' - 1], split))
|
||||
)
|
||||
|> Map.ofSeq
|
||||
|
||||
let result =
|
||||
allNodes
|
||||
|> Map.toSeq
|
||||
|> Seq.map (fun (key, (node, (weight, outbound))) ->
|
||||
node, (weight, (Set.map (fun x -> fst (Map.find x allNodes)) outbound))
|
||||
)
|
||||
|> Map.ofSeq
|
||||
|
||||
result, fst allNodes.["AA"]
|
||||
|
||||
let inline tryMax< ^a when ^a : comparison> (s : seq<'a>) : 'a option =
|
||||
use enum = s.GetEnumerator ()
|
||||
|
||||
if not (enum.MoveNext ()) then
|
||||
None
|
||||
else
|
||||
let mutable answer = enum.Current
|
||||
|
||||
while enum.MoveNext () do
|
||||
answer <- max answer enum.Current
|
||||
|
||||
Some answer
|
||||
|
||||
let tryMin (s : seq<'a>) : 'a option =
|
||||
use enum = s.GetEnumerator ()
|
||||
|
||||
if not (enum.MoveNext ()) then
|
||||
None
|
||||
else
|
||||
let mutable answer = enum.Current
|
||||
|
||||
while enum.MoveNext () do
|
||||
answer <- min answer enum.Current
|
||||
|
||||
Some answer
|
||||
|
||||
let getShortestPathLength (valves : Map<_, _>) : Node -> Node -> int =
|
||||
let rec go (seenSoFar : Node Set) (v1 : Node) (v2 : Node) =
|
||||
let v2Neighbours = snd valves.[v2]
|
||||
|
||||
if v1 = v2 then
|
||||
Some 0
|
||||
elif Set.contains v1 v2Neighbours then
|
||||
Some 1
|
||||
elif Set.contains v2 seenSoFar then
|
||||
None
|
||||
else
|
||||
v2Neighbours
|
||||
|> Seq.choose (go (Set.add v2 seenSoFar) v1)
|
||||
|> tryMin
|
||||
|> Option.map ((+) 1)
|
||||
|
||||
fun v1 v2 -> go Set.empty v1 v2 |> Option.get
|
||||
|
||||
|
||||
type NodeSet = int64
|
||||
|
||||
let inline setNode (set : NodeSet) (nodeId : int) : NodeSet = set ||| (1L <<< nodeId)
|
||||
let inline getNode (set : NodeSet) (nodeId : int) : bool = set &&& (1L <<< nodeId) <> 0
|
||||
let ofSeq (nodes : Node seq) : NodeSet = (0L, nodes) ||> Seq.fold setNode
|
||||
|
||||
let toSeq (nodes : NodeSet) : Node seq =
|
||||
seq {
|
||||
let mutable nodes = nodes
|
||||
let mutable count = 0
|
||||
|
||||
while nodes > 0 do
|
||||
if nodes % 2L = 1L then
|
||||
yield count
|
||||
|
||||
nodes <- nodes >>> 1
|
||||
count <- count + 1
|
||||
}
|
||||
|
||||
let count (nodes : NodeSet) : int =
|
||||
let mutable nodes = nodes
|
||||
let mutable ans = 0
|
||||
|
||||
while nodes > 0 do
|
||||
if nodes % 2L = 1L then
|
||||
ans <- ans + 1
|
||||
|
||||
nodes <- nodes >>> 1
|
||||
|
||||
ans
|
||||
|
||||
|
||||
let first (nodes : NodeSet) : int =
|
||||
let mutable nodes = nodes
|
||||
let mutable count = 0
|
||||
let mutable ans = 0
|
||||
let mutable keepGoing = true
|
||||
|
||||
while keepGoing && nodes > 0 do
|
||||
if nodes % 2L = 1L then
|
||||
ans <- count
|
||||
keepGoing <- false
|
||||
|
||||
nodes <- nodes >>> 1
|
||||
count <- count + 1
|
||||
|
||||
ans
|
||||
|
||||
let part1 (lines : string seq) : int =
|
||||
let valves, aaNode = parse lines
|
||||
let allTaps = valves |> Map.filter (fun _ (x, _) -> x > 0) |> Map.keys |> ofSeq
|
||||
|
||||
let getShortestPathLength = getShortestPathLength valves
|
||||
|
||||
#if DEBUG
|
||||
let pathWeights = Arr2D.zeroCreate<int> valves.Count valves.Count
|
||||
#else
|
||||
let pathWeightsStorage = Array.zeroCreate (valves.Count * valves.Count)
|
||||
use ptr = fixed pathWeightsStorage
|
||||
let pathWeights = Arr2D.zeroCreate<int> ptr valves.Count valves.Count
|
||||
#endif
|
||||
for v1 in toSeq allTaps do
|
||||
for v2 in toSeq allTaps do
|
||||
let length = getShortestPathLength v1 v2
|
||||
Arr2D.set pathWeights v1 v2 length
|
||||
|
||||
let rec go
|
||||
(timeRemainingOnCurrentPath : int)
|
||||
(headingTo : Node)
|
||||
(alreadyOn : NodeSet)
|
||||
(currentWeight : int)
|
||||
(remaining : int)
|
||||
=
|
||||
if remaining <= 0 then
|
||||
currentWeight
|
||||
elif timeRemainingOnCurrentPath > 0 then
|
||||
go (timeRemainingOnCurrentPath - 1) headingTo alreadyOn currentWeight (remaining - 1)
|
||||
else
|
||||
|
||||
let alreadyOn = setNode alreadyOn headingTo
|
||||
|
||||
let mutable allTaps = allTaps &&& (~~~alreadyOn)
|
||||
let mutable count = 0
|
||||
let mutable max = ValueNone
|
||||
|
||||
while allTaps > 0 do
|
||||
if allTaps % 2L = 1 then
|
||||
let addToWeight = fst valves.[headingTo] * (remaining - 1)
|
||||
|
||||
let candidate =
|
||||
go
|
||||
(Arr2D.get pathWeights count headingTo)
|
||||
count
|
||||
alreadyOn
|
||||
(currentWeight + addToWeight)
|
||||
(remaining - 1)
|
||||
|
||||
match max with
|
||||
| ValueNone -> max <- ValueSome candidate
|
||||
| ValueSome existingMax ->
|
||||
if existingMax < candidate then
|
||||
max <- ValueSome candidate
|
||||
|
||||
allTaps <- allTaps >>> 1
|
||||
count <- count + 1
|
||||
|
||||
match max with
|
||||
| ValueSome v -> v
|
||||
| ValueNone -> currentWeight + (remaining - 1) * (fst valves.[headingTo])
|
||||
|
||||
let mutable startChoices = allTaps
|
||||
let mutable start = 0
|
||||
let mutable maxValue = Int32.MinValue
|
||||
|
||||
while startChoices > 0 do
|
||||
if startChoices % 2L = 1L then
|
||||
let distance = getShortestPathLength aaNode start
|
||||
// By inspecting the graph, I can see that AA is screened off from the rest
|
||||
// of the graph by the set of valves with distance at most 3 from it.
|
||||
// Assume that we're going to turn them on when we pass through - this isn't
|
||||
// actually fully general, but it is enough.
|
||||
if distance <= 3 then
|
||||
let candidate = go distance start 0 0 30
|
||||
maxValue <- max maxValue candidate
|
||||
|
||||
startChoices <- startChoices >>> 1
|
||||
start <- start + 1
|
||||
|
||||
maxValue
|
||||
|
||||
let part2 (lines : string seq) : int =
|
||||
let valves, aaNode = parse lines
|
||||
let valvesIndexed = valves |> Map.values |> Array.ofSeq
|
||||
|
||||
let allTaps = valves |> Map.filter (fun _ (x, _) -> x > 0) |> Map.keys |> ofSeq
|
||||
|
||||
let getShortestPathLength = getShortestPathLength valves
|
||||
|
||||
#if DEBUG
|
||||
let pathWeights = Arr2D.zeroCreate<int> valves.Count valves.Count
|
||||
#else
|
||||
let pathWeightsStorage = Array.zeroCreate (valves.Count * valves.Count)
|
||||
use ptr = fixed pathWeightsStorage
|
||||
let pathWeights = Arr2D.zeroCreate<int> ptr valves.Count valves.Count
|
||||
#endif
|
||||
|
||||
for v1 in toSeq allTaps do
|
||||
for v2 in toSeq allTaps do
|
||||
let length = getShortestPathLength v1 v2
|
||||
Arr2D.set pathWeights v1 v2 length
|
||||
|
||||
let rec go
|
||||
(journey1 : int)
|
||||
(journey2 : int)
|
||||
(headingTo1 : Node)
|
||||
(headingTo2 : Node)
|
||||
(alreadyOn : NodeSet)
|
||||
(currentWeight : int)
|
||||
(remaining : int)
|
||||
=
|
||||
if remaining <= 0 then
|
||||
currentWeight
|
||||
elif journey1 > 0 && journey2 > 0 then
|
||||
go (journey1 - 1) (journey2 - 1) headingTo1 headingTo2 alreadyOn currentWeight (remaining - 1)
|
||||
elif journey1 = 0 && journey2 > 0 then
|
||||
|
||||
let addToWeight =
|
||||
if getNode alreadyOn headingTo1 then
|
||||
0
|
||||
else
|
||||
(remaining - 1) * (fst valvesIndexed.[headingTo1])
|
||||
|
||||
let newWeight = addToWeight + currentWeight
|
||||
|
||||
let alreadyOn = setNode alreadyOn headingTo1
|
||||
|
||||
let mutable allTaps = allTaps &&& ~~~alreadyOn
|
||||
let mutable node = 0
|
||||
let mutable max = ValueNone
|
||||
|
||||
while allTaps > 0L do
|
||||
// Strictly speaking we might be able to overtake the other one
|
||||
// who is heading for their node, but it so happens that the
|
||||
// test cases don't care about that.
|
||||
if allTaps % 2L = 1L && node <> headingTo2 then
|
||||
let next =
|
||||
go
|
||||
(Arr2D.get pathWeights node headingTo1)
|
||||
(journey2 - 1)
|
||||
node
|
||||
headingTo2
|
||||
alreadyOn
|
||||
newWeight
|
||||
(remaining - 1)
|
||||
|
||||
match max with
|
||||
| ValueNone -> max <- ValueSome next
|
||||
| ValueSome existingMax ->
|
||||
if next > existingMax then
|
||||
max <- ValueSome next
|
||||
|
||||
allTaps <- allTaps >>> 1
|
||||
node <- node + 1
|
||||
|
||||
match max with
|
||||
| ValueSome v -> v
|
||||
| ValueNone -> go 1000000 (journey2 - 1) headingTo1 headingTo2 alreadyOn newWeight (remaining - 1)
|
||||
|
||||
elif journey2 = 0 && journey1 > 0 then
|
||||
let addToWeight =
|
||||
if getNode alreadyOn headingTo2 then
|
||||
0
|
||||
else
|
||||
fst valvesIndexed.[headingTo2] * (remaining - 1)
|
||||
|
||||
let newWeight = addToWeight + currentWeight
|
||||
|
||||
let alreadyOn = setNode alreadyOn headingTo2
|
||||
|
||||
let mutable allTaps = allTaps &&& ~~~alreadyOn
|
||||
let mutable node = 0
|
||||
let mutable max = ValueNone
|
||||
|
||||
while allTaps > 0L do
|
||||
// Strictly speaking we might be able to overtake the other one
|
||||
// who is heading for their node, but it so happens that the
|
||||
// test cases don't care about that.
|
||||
if allTaps % 2L = 1L && node <> headingTo1 then
|
||||
let next =
|
||||
go
|
||||
(journey1 - 1)
|
||||
(Arr2D.get pathWeights node headingTo2)
|
||||
headingTo1
|
||||
node
|
||||
alreadyOn
|
||||
newWeight
|
||||
(remaining - 1)
|
||||
|
||||
match max with
|
||||
| ValueNone -> max <- ValueSome next
|
||||
| ValueSome existingMax ->
|
||||
if next > existingMax then
|
||||
max <- ValueSome next
|
||||
|
||||
allTaps <- allTaps >>> 1
|
||||
node <- node + 1
|
||||
|
||||
match max with
|
||||
| ValueSome v -> v
|
||||
| ValueNone -> go (journey1 - 1) 1000000 headingTo1 headingTo2 alreadyOn newWeight (remaining - 1)
|
||||
|
||||
else
|
||||
// Both reached destination at same time
|
||||
let addToWeight1 =
|
||||
if getNode alreadyOn headingTo1 then
|
||||
0
|
||||
else
|
||||
(remaining - 1) * fst valvesIndexed.[headingTo1]
|
||||
|
||||
let addToWeight2 =
|
||||
if getNode alreadyOn headingTo2 then
|
||||
0
|
||||
else
|
||||
(remaining - 1) * fst valvesIndexed.[headingTo2]
|
||||
|
||||
let newWeight =
|
||||
if headingTo1 <> headingTo2 then
|
||||
addToWeight1 + addToWeight2 + currentWeight
|
||||
else
|
||||
addToWeight1 + currentWeight
|
||||
|
||||
let alreadyOn = setNode (setNode alreadyOn headingTo1) headingTo2
|
||||
|
||||
let nextChoices = allTaps &&& ~~~alreadyOn
|
||||
|
||||
if count nextChoices >= 2 then
|
||||
let mutable maxVal = Int32.MinValue
|
||||
|
||||
let mutable next1 = nextChoices
|
||||
let mutable count1 = 0
|
||||
|
||||
while next1 > 0 do
|
||||
if next1 % 2L = 1 then
|
||||
let mutable next2 = nextChoices
|
||||
let mutable count2 = 0
|
||||
|
||||
while next2 > 0 do
|
||||
// It's never correct for both to try and turn on the same node.
|
||||
if next2 % 2L = 1 && next1 <> next2 then
|
||||
let candidate =
|
||||
go
|
||||
(Arr2D.get pathWeights count1 headingTo1)
|
||||
(Arr2D.get pathWeights count2 headingTo2)
|
||||
count1
|
||||
count2
|
||||
alreadyOn
|
||||
newWeight
|
||||
(remaining - 1)
|
||||
|
||||
maxVal <- max maxVal candidate
|
||||
|
||||
next2 <- next2 >>> 1
|
||||
count2 <- count2 + 1
|
||||
|
||||
next1 <- next1 >>> 1
|
||||
count1 <- count1 + 1
|
||||
|
||||
maxVal
|
||||
|
||||
elif nextChoices = 0 then
|
||||
0
|
||||
else
|
||||
// nextChoices.Count = 1
|
||||
let next = first nextChoices
|
||||
go 100000 (Arr2D.get pathWeights next headingTo2) next next alreadyOn newWeight (remaining - 1)
|
||||
|
||||
let startChoices =
|
||||
allTaps
|
||||
|> toSeq
|
||||
|> Seq.map (fun startNode -> startNode, getShortestPathLength aaNode startNode)
|
||||
|> Map.ofSeq
|
||||
|
||||
let maxVal = ref Int32.MinValue
|
||||
|
||||
Seq.allPairs startChoices startChoices
|
||||
|> Seq.filter (fun (KeyValue (n1, distance1), KeyValue (n2, distance2)) ->
|
||||
// By inspecting the graph, I can see that AA is screened off from the rest
|
||||
// of the graph by the set of valves with distance at most 3 from it.
|
||||
// Assume that we're going to turn them on when we pass through - this isn't
|
||||
// actually fully general, but it is enough.
|
||||
n1 < n2 && distance1 <= 3 && distance2 <= 3
|
||||
)
|
||||
|> PSeq.map (fun (KeyValue (start1, distance1), KeyValue (start2, distance2)) ->
|
||||
go distance1 distance2 start1 start2 0 0 26
|
||||
)
|
||||
|> PSeq.iter (fun s ->
|
||||
lock
|
||||
maxVal
|
||||
(fun () ->
|
||||
if s > maxVal.Value then
|
||||
maxVal.Value <- s
|
||||
)
|
||||
)
|
||||
|
||||
maxVal.Value
|
||||
Reference in New Issue
Block a user