#783137 (C#) No.5007 Steiner Space Travel

• 問題: No.5007 Steiner Space Travel
• ユーザー: inani_waon
• 提出日時: 2022-07-30 16:37:34
• 言語: C# (.NET 8.0.203)
• 結果: AC
• 実行時間: 995 ms / 1,000 ms
• コード長: 8,779 bytes
• コンパイル時間: 7,093 ms
• 実行使用メモリ: 172,584 KB
• スコア: 7,831,346
• 最終ジャッジ日時: 2022-07-30 16:38:16
• 合計ジャッジ時間: 39,536 ms
• ジャッジサーバーID （参考情報）: judge13 / judge15

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	993 ms; 31,688 KB
testcase_01	AC	993 ms; 29,568 KB
testcase_02	AC	993 ms; 29,908 KB
testcase_03	AC	995 ms; 31,840 KB
testcase_04	AC	993 ms; 29,808 KB
testcase_05	AC	993 ms; 31,740 KB
testcase_06	AC	994 ms; 31,780 KB
testcase_07	AC	994 ms; 30,028 KB
testcase_08	AC	993 ms; 31,536 KB
testcase_09	AC	992 ms; 31,612 KB
testcase_10	AC	992 ms; 31,832 KB
testcase_11	AC	995 ms; 33,716 KB
testcase_12	AC	994 ms; 31,704 KB
testcase_13	AC	995 ms; 31,296 KB
testcase_14	AC	995 ms; 31,924 KB
testcase_15	AC	994 ms; 33,584 KB
testcase_16	AC	993 ms; 33,872 KB
testcase_17	AC	992 ms; 31,620 KB
testcase_18	AC	995 ms; 33,388 KB
testcase_19	AC	993 ms; 31,676 KB
testcase_20	AC	994 ms; 32,160 KB
testcase_21	AC	994 ms; 31,512 KB
testcase_22	AC	993 ms; 31,776 KB
testcase_23	AC	995 ms; 31,564 KB
testcase_24	AC	994 ms; 32,064 KB
testcase_25	AC	994 ms; 31,844 KB
testcase_26	AC	993 ms; 32,008 KB
testcase_27	AC	993 ms; 31,764 KB
testcase_28	AC	993 ms; 31,828 KB
testcase_29	AC	994 ms; 172,584 KB

コンパイルメッセージ

  Determining projects to restore...
  Restored /home/judge/data/code/main.csproj (in 114 ms).
.NET 向け Microsoft (R) Build Engine バージョン 17.0.0-preview-21470-01+cb055d28f
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  プレビュー版の .NET を使用しています。https://aka.ms/dotnet-core-preview をご覧ください
  main -> /home/judge/data/code/bin/Release/net6.0/main.dll
  main -> /home/judge/data/code/bin/Release/net6.0/publish/

ソースコード

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;

class Yukico5007
{
    static void Main(string[] args)
    {
        var sw = Stopwatch.StartNew();
        var nums = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var N = nums[0];
        var M = nums[1];

        var planets = new List<(int y, int x)>();
        for (int i = 0; i < N; i++)
        {
            nums = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            planets.Add((nums[0], nums[1]));
        }

        var directCosts = new double[(N + 1) * (N + 1)];
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
            {
                if (i == j) continue;
                var cost = Math.Sqrt(Math.Abs(planets[i].y - planets[j].y) * Math.Abs(planets[i].y - planets[j].y) +
                                     Math.Abs(planets[i].x - planets[j].x) * Math.Abs(planets[i].x - planets[j].x));
                directCosts[i * (N + 1) + j] = cost;
            }
        }
        for (int i = 0; i < N; i++)
        {
            directCosts[(N + 1) * N + i] = directCosts[0 * (N + 1) + i];
            directCosts[(N + 1) * i + N] = directCosts[i * (N + 1) + 0];
        }

        var inputs = new Inputs(sw, planets, directCosts, null);
        var solver = new Solver();
        var command = solver.GetCommand(inputs);
        command.Print();
    }
}

class Inputs
{
    /// <summary>惑星の座標</summary>
    public List<(int y, int x)> Planets;

    /// <summary>他の惑星を経由せずに直接飛ぶコスト(αは考慮しない)</summary>
    public double[] DirectCosts;
    /// <summary>他の惑星を経由して飛ぶ最小コスト(αは考慮しない)</summary>
    public double[] RouteCosts;

    public Stopwatch Sw;
    public const int N = 100;
    public const int NP1 = 101;
    public const int M = 8;
    public const int A = 5;
    public const int AA = 25;

    public Inputs(Stopwatch sw, List<(int y, int x)> planets, double[] directCosts, double[] routeCosts)
    {
        Sw = sw;
        Planets = planets;
        DirectCosts = directCosts;
        RouteCosts = routeCosts;
    }
}

class Outputs
{
    public List<(int y, int x)> Stations = new();
    public List<(int t, int r)> Route = new();

    public void Print()
    {
        foreach (var pos in Stations)
        {
            Console.WriteLine($"{pos.y} {pos.x}");
        }
        Console.WriteLine(Route.Count);
        foreach (var via in Route)
        {
            Console.WriteLine($"{via.t} {via.r + 1}");
        }
    }
}

class Solver
{
    public Outputs GetCommand(Inputs inputs)
    {
        var defaultRoute = Enumerable.Range(0, Inputs.N).Append(0).ToArray();
        var twoOpt = new TwoOpt(Inputs.NP1, inputs.DirectCosts, defaultRoute, new Random(1728), inputs.Sw);
        twoOpt.Exec();

        var res = new Outputs();
        foreach (var i in twoOpt.IdxByOrders)
        {
            res.Route.Add((1, i));
        }
        res = AddStations(inputs, res, twoOpt.IdxByOrders);
        return res;
    }

    Outputs AddStations(Inputs inputs, Outputs outputs, int[] order)
    {
        while (outputs.Stations.Count < 8)
        {
            var maxCost = double.MinValue;
            var maxCostIndex = -1;  // (i - 1) -> i

            for (int i = 1; i < outputs.Route.Count; i++)
            {
                var bf = outputs.Route[i - 1];
                var af = outputs.Route[i];
                if (af.t == 2 || af.t == 2) continue;
                double cost;
                if (bf.t == 1 && af.t == 1)
                {
                    cost = inputs.DirectCosts[bf.r * Inputs.NP1 + af.r] * Inputs.AA;
                }
                else
                {
                    var rate = (bf.t == 2 && af.t == 2) ? 1 : Inputs.A;
                    var bfPos = bf.t == 1 ? inputs.Planets[bf.r] : outputs.Stations[bf.r];
                    var afPos = af.t == 1 ? inputs.Planets[af.r] : outputs.Stations[af.r];
                    cost = Math.Sqrt(Math.Abs(bfPos.y - afPos.y) * Math.Abs(bfPos.y - afPos.y) +
                                     Math.Abs(bfPos.x - afPos.x) * Math.Abs(bfPos.x - afPos.x)) * rate;
                }
                if (cost > maxCost)
                {
                    maxCostIndex = i;
                    maxCost = cost;
                }
            }

            var bf2 = outputs.Route[maxCostIndex - 1];
            var af2 = outputs.Route[maxCostIndex];
            var bfPos2 = bf2.t == 1 ? inputs.Planets[bf2.r] : outputs.Stations[bf2.r];
            var afPos2 = af2.t == 1 ? inputs.Planets[af2.r] : outputs.Stations[af2.r];
            var y = (bfPos2.y + afPos2.y) / 2;
            var x = (bfPos2.x + afPos2.x) / 2;

            outputs.Stations.Add((y, x));
            //outputs.Route.Insert(maxCostIndex, (2, outputs.Stations.Count - 1));

            outputs = GetNextRoute(inputs, outputs, order);
        }
        return outputs;
    }

    Outputs GetNextRoute(Inputs inputs, Outputs outputs, int[] order)
    {
        var res = new Outputs();
        res.Stations = new List<(int y, int x)>(outputs.Stations);
        res.Route.Add((1, 0));
        for (int i = 1; i < order.Length; i++)
        {
            var bfPlanet = order[i - 1];
            var directCost = inputs.DirectCosts[bfPlanet * Inputs.NP1 + order[i]] * inputs.DirectCosts[bfPlanet * Inputs.NP1 + order[i]] * Inputs.AA;   // 直接

            var bestT = 1;
            var bestR = -1;
            var bestCost = directCost;

            var bfPos = inputs.Planets[bfPlanet];
            var afPos = inputs.Planets[order[i]];
            for (int j = 0; j < res.Stations.Count; j++)
            {
                var ctPos = res.Stations[j];
                var cost1 = Math.Sqrt(Math.Abs(bfPos.y - ctPos.y) * Math.Abs(bfPos.y - ctPos.y) +
                                      Math.Abs(bfPos.x - ctPos.x) * Math.Abs(bfPos.x - ctPos.x));
                var cost2 = Math.Sqrt(Math.Abs(afPos.y - ctPos.y) * Math.Abs(afPos.y - ctPos.y) +
                                      Math.Abs(afPos.x - ctPos.x) * Math.Abs(afPos.x - ctPos.x));
                cost1 = cost1 * cost1 * Inputs.A;
                cost2 = cost2 * cost2 * Inputs.A;
                if (cost1 + cost2 < bestCost)
                {
                    bestT = 2;
                    bestR = j;
                    bestCost = cost1 + cost2;
                }
            }
            
            if (bestR != -1)
            {
                res.Route.Add((bestT, bestR));
            }
            res.Route.Add((1, order[i]));
        }
        return res;
    }
}

public class TwoOpt
{
    public readonly int NodeCount;
    public readonly int NodeCount2;
    public readonly double[] Costs;
    /// <summary>idx番目に経由する点がvalue番目の要素</summary>
    public readonly int[] IdxByOrders;

    Random _random;
    System.Diagnostics.Stopwatch _sw;

    public TwoOpt(int n, double[] costs, int[] defaultOrder, Random random, System.Diagnostics.Stopwatch sw)
    {
        NodeCount = n;
        NodeCount2 = defaultOrder.Length;
        Costs = costs;
        IdxByOrders = new int[NodeCount2];
        Array.Copy(defaultOrder, IdxByOrders, NodeCount2);
        _random = random;
        _sw = sw;
    }

    public void Exec()
    {
        //var cnt = 0;
        var costsSpan = new Span<double>(Costs);
        while (_sw.ElapsedMilliseconds < 950)
        {
            for (int i = 0; i < 100; i++)
            {
                // 先頭、末尾は交換しない
                var from1order = _random.Next(NodeCount2 - 4);
                var from2order = _random.Next(from1order + 3, NodeCount2);

                var from1 = IdxByOrders[from1order];
                var from2 = IdxByOrders[from2order];
                var to1 = IdxByOrders[from1order + 1];
                var to2 = IdxByOrders[from2order - 1];

                // コスト計算
                var oldRouteCost = costsSpan[from1 * NodeCount + to1] + costsSpan[from2 * NodeCount + to2];
                var newRouteCost = costsSpan[from1 * NodeCount + to2] + costsSpan[from2 * NodeCount + to1];

                // 改善されていれば更新
                if (newRouteCost < oldRouteCost) Swap(from1order, from2order);
            }
            //cnt++;
        }
    }

    /// <summary>
    /// 2点の接続を交換する
    /// </summary>
    /// <param name="from1order">点1のOrder順</param>
    /// <param name="from2order">点2のOrder順</param>
    public void Swap(int from1order, int from2order)
    {
        Array.Reverse(IdxByOrders, from1order + 1, from2order - from1order - 1);
    }
}