#782988 (C#) No.5007 Steiner Space Travel

提出ソース

結果

問題	No.5007 Steiner Space Travel
ユーザー	g4np0n
提出日時	2022-07-30 15:29:11
言語	C# (.NET 8.0.203)
結果	AC
実行時間	143 ms / 1,000 ms
コード長	20,908 bytes
コンパイル時間	8,128 ms
実行使用メモリ	175,404 KB
スコア	6,519,191
最終ジャッジ日時	2022-07-30 15:29:25
合計ジャッジ時間	13,949 ms
ジャッジサーバーID （参考情報）	judge13 / judge15
	純コード判定しない問題か言語

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	125 ms 38,792 KB
testcase_01	AC	126 ms 38,836 KB
testcase_02	AC	127 ms 39,316 KB
testcase_03	AC	131 ms 41,212 KB
testcase_04	AC	128 ms 38,752 KB
testcase_05	AC	129 ms 38,992 KB
testcase_06	AC	131 ms 39,580 KB
testcase_07	AC	129 ms 39,300 KB
testcase_08	AC	136 ms 38,984 KB
testcase_09	AC	141 ms 38,936 KB
testcase_10	AC	128 ms 39,100 KB
testcase_11	AC	133 ms 39,256 KB
testcase_12	AC	129 ms 39,528 KB
testcase_13	AC	124 ms 38,396 KB
testcase_14	AC	125 ms 38,876 KB
testcase_15	AC	130 ms 39,352 KB
testcase_16	AC	129 ms 38,880 KB
testcase_17	AC	128 ms 38,940 KB
testcase_18	AC	131 ms 39,028 KB
testcase_19	AC	127 ms 38,784 KB
testcase_20	AC	143 ms 38,896 KB
testcase_21	AC	134 ms 38,892 KB
testcase_22	AC	125 ms 38,996 KB
testcase_23	AC	124 ms 39,256 KB
testcase_24	AC	125 ms 39,056 KB
testcase_25	AC	126 ms 38,688 KB
testcase_26	AC	127 ms 38,344 KB
testcase_27	AC	128 ms 38,888 KB
testcase_28	AC	128 ms 39,408 KB
testcase_29	AC	125 ms 175,404 KB

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コンパイルメッセージ

  Determining projects to restore...
  Restored /home/judge/data/code/main.csproj (in 121 ms).
.NET 向け Microsoft (R) Build Engine バージョン 17.0.0-preview-21470-01+cb055d28f
Copyright (C) Microsoft Corporation.All rights reserved.

  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

raw source code

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using static System.Math;

partial class Program
{
    static int[] dx = new int[] { 1, 0, -1, 0, 1, -1, -1, 1 };
    static int[] dy = new int[] { 0, 1, 0, -1, 1, 1, -1, -1 };
    const long mod = 1000000007;
    //const long mod = 998244353;
    static Random rnd = new Random();

    public void Solve()
    {
        var (N, M) = io.GetMulti<int, int>();
        var A = 5;
        var planets = io.GetIntArray(N).Select((e, id) => new Pos(e[0], e[1], id)).ToArray();

        var stations = new Pos[M];
        for (int i = 0; i < M; i++)
        {
            stations[i] = new Pos(rnd.Next(0, 1001), rnd.Next(0, 1001), N + i);
        }

        var G = (long.MaxValue / 3).Repeat(N + M, N + M);
        var dijkstra = new Dijkstra(N);
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
            {
                if (i == j) continue;
                G[i][j] = A * A * planets[i].Length(planets[j]);
                dijkstra.AddEdge(i, j, A * A * planets[i].Length(planets[j]));
            }
        }
        var len = new long[N][];
        var path = new int[N][][];
        for (int i = 0; i < N; i++)
        {
            len[i] = dijkstra.GetDist(i);
            path[i] = new int[N][];
            for (int j = 0; j < N; j++) path[i][j] = dijkstra.GetPath(j);
        }

        var now = 0;
        var visited = new bool[N];
        visited[0] = true;
        var visitedCnt = 1;
        var ans = new List<Pos>();
        ans.Add(planets[0]);
        long S = 0;
        while (visitedCnt != N)
        {
            var next = -1;
            var min = long.MaxValue;
            for (int i = 0; i < N; i++)
            {
                if (visited[i]) continue;
                if (min.Chmin(len[now][i])) next = i;
            }
            S += min;
            ans.AddRange(path[now][next].Select(e=>planets[e]));
            visited[next] = true;
            visitedCnt++;
            now = next;
        }
        ans.AddRange(path[now][0].Select(e=>planets[e]));
        S += len[now][0];

        TSP(ans);
        Console.Clear();

        for (int i = 0; i < M; i++) io.Print($"{0} {0}");
        Console.WriteLine(ans.Count);
        for (int i = 0; i < ans.Count; i++) Console.WriteLine($"{1} {ans[i].id + 1}");
    }

    long Score(long length)
    {
        return (long)Round(1000000000 / (1000 + Sqrt(length)));
    }

    long Length((int x, int y) a, (int x, int y) b) => (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);

    class Dijkstra
    {
        public Dijkstra(int V)
        {
            this.V = V;
            G = new List<(int to, long dist)>[V];
            for (int i = 0; i < V; i++)
            {
                G[i] = new List<(int to, long dist)>();
            }
            from = new int[this.V];
        }
        long _INF = long.MaxValue;
        int V;
        List<(int to, long dist)>[] G;
        int[] from;

        /// <summary>
        /// 無向辺を追加します。
        /// </summary>
        public void AddEdge(int u, int v, long dist)
        {
            G[u].Add((v, dist));
            G[v].Add((u, dist));
        }

        /// <summary>
        /// 有向辺を追加します。
        /// </summary>
        public void AddDirectedEdge(int from, int to, long dist)
        {
            G[from].Add((to, dist));
        }

        /// <summary>
        /// 各頂点への最短経路長を求めます。
        /// 計算量はO((E+V)logV)です。
        /// </summary>
        public long[] GetDist(int s)
        {
            var dist = new long[V];
            dist.AsSpan().Fill(_INF);
            from = new int[V];
            from.AsSpan().Fill(-1);
            var pq = new PriorityQueue<int>();
            dist[s] = 0;
            pq.Enqueue(0, s);
            while (pq.Count > 0)
            {
                var (d, v) = pq.Dequeue();
                if (dist[v] != d) continue;
                foreach (var edge in G[v])
                {
                    var alt = d + edge.dist;
                    if (alt >= dist[edge.to]) continue;
                    dist[edge.to] = alt;
                    from[edge.to] = v;
                    pq.Enqueue(alt, edge.to);
                }
            }
            for (int i = 0; i < V; i++) if (dist[i] == _INF) dist[i] = -1;
            return dist;
        }

        public int[] GetPath(int t)
        {
            var now = t;
            var ls = new List<int>();
            while (from[t] != -1)
            {
                ls.Add(t);
                t = from[t];
            }
            ls.Reverse();
            return ls.ToArray();
        }
    }

    class PriorityQueue<T>
    {
        /// <summary>
        /// 空の優先度付きキューを生成します。
        /// </summary>
        public PriorityQueue()
        {
            _keys = new List<long>();
            _elements = new List<T>();
        }
        List<long> _keys;
        List<T> _elements;

        /// <summary>
        /// 優先度付きキューに要素を追加します。
        /// 計算量は O(log(要素数)) です。
        /// </summary>
        public void Enqueue(long key, T elem)
        {
            var n = _elements.Count;
            _keys.Add(key);
            _elements.Add(elem);
            while (n != 0)
            {
                var i = (n - 1) / 2;
                if (_keys[n] < _keys[i])
                {
                    (_keys[n], _keys[i]) = (_keys[i], _keys[n]);
                    (_elements[n], _elements[i]) = (_elements[i], _elements[n]);
                }
                n = i;
            }
        }

        /// <summary>
        /// 頂点要素を返し、削除します。
        /// 計算量は O(log(要素数)) です。
        /// </summary>
        public (long key, T value) Dequeue()
        {
            var t = Peek();
            Pop();
            return t;
        }

        void Pop()
        {
            var n = _elements.Count - 1;
            _elements[0] = _elements[n];
            _elements.RemoveAt(n);
            _keys[0] = _keys[n];
            _keys.RemoveAt(n);
            for (int i = 0, j; (j = 2 * i + 1) < n;)
            {
                //左の子と右の子で右の子の方が優先度が高いなら右の子を処理したい
                if ((j != n - 1) && _keys[j] > _keys[j + 1]) j++;
                //親より子が優先度が高いなら親子を入れ替える
                if (_keys[i] > _keys[j])
                {
                    (_keys[i], _keys[j]) = (_keys[j], _keys[i]);
                    (_elements[i], _elements[j]) = (_elements[j], _elements[i]);
                }
                i = j;
            }
        }


        /// <summary>
        /// 頂点要素を返します。
        /// 計算量は O(1) です。
        /// </summary>
        public (long key, T value) Peek() => (_keys[0], _elements[0]);

        /// <summary>
        /// 優先度付きキューに格納されている要素の数を返します。
        /// 計算量は O(1) です。
        /// </summary>
        public int Count => _elements.Count;

        /// <summary>
        /// 要素が存在するかを返します。
        /// </summary>
        /// <returns></returns>
        public bool Any() => _elements.Any();
    }

    struct Pos
    {
        public long x;
        public long y;
        public int id;
        public Pos(long _x, long _y, int _id)
        {
            x = _x;
            y = _y;
            id = _id;
        }

        public long Length(Pos pos) => (pos.x - x) * (pos.x - x) + (pos.y - y) * (pos.y - y);
        override public string ToString() => $"{x} {y}";
    }

    void TSP(List<Pos> pos)
    {
        var cnt = 0;
        var ccnt = 0;
        while (cnt < 100000)
        {
            cnt++;
            var a = rnd.Next(pos.Count);
            var b = rnd.Next(pos.Count);
            if (a == b) continue;
            if (a > b) (a, b) = (b, a);
            var ap = pos[a];
            var bp = pos[b];
            var cp = pos[(b + 1) % pos.Count];
            var dp = pos[a + 1];
            var diff = (ap.Length(dp) + bp.Length(cp) - ap.Length(bp) - cp.Length(dp));
            if (diff > 0)
            {
                ccnt++;
                var (x, y) = (a + 1, b);
                while (x < y)
                {
                    (pos[x], pos[y]) = (pos[y], pos[x]);
                    x++; y--;
                }
            }
        }
    }

    IO io = new IO();
    static void Main()
    {
        Console.SetIn(new StreamReader(Console.OpenStandardInput(8192)));
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var program = new Program();
        //var t = new Thread(program.Solve, 134217728);
        //t.Start();
        //t.Join();
        program.Solve();
        Console.Out.Flush();
        Console.Read();
    }
}


//------------------------------------------------------------------------------------------------------------------

public static class Ex
{
    public static bool IsNullOrEmpty(this string s) { return string.IsNullOrEmpty(s); }
    public static void yesno(this bool b) => Console.WriteLine(b ? "yes" : "no");
    public static void YesNo(this bool b) => Console.WriteLine(b ? "Yes" : "No");
    public static void YESNO(this bool b) => Console.WriteLine(b ? "YES" : "NO");
    public static void Yes() => Console.WriteLine("Yes");
    public static void YES() => Console.WriteLine("YES");
    public static void No() => Console.WriteLine("No");
    public static void NO() => Console.WriteLine("NO");
    public static void M1() => Console.WriteLine("-1");
    public static void TakahashiAoki(this bool b) => Console.WriteLine(b ? "Takahashi" : "Aoki");

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool Chmax(ref this int a, int b)
    {
        if (a < b) { a = b; return true; }
        else return false;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool Chmin(ref this int a, int b)
    {
        if (a > b) { a = b; return true; }
        else return false;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool Chmax(ref this long a, long b)
    {
        if (a < b) { a = b; return true; }
        else return false;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool Chmin(ref this long a, long b)
    {
        if (a > b) { a = b; return true; }
        else return false;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool Chmin<T>(ref this long a, long b)
    {
        if (a > b) { a = b; return true; }
        else return false;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool Chmax<T>(ref this T a, T b) where T : struct, IComparable<T>
    {
        if (b.CompareTo(a) > 0) { a = b; return true; }
        else return false;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool Chmin<T>(ref this T a, T b) where T : struct, IComparable<T>
    {
        if (b.CompareTo(a) < 0) { a = b; return true; }
        else return false;
    }

    /// <summary>
    /// constraintを満たす最小のインデックスを返します。
    /// </summary>
    /// <param name="constraint">T key が満たすべき制約</param>
    /// <returns>制約を満たす最小のインデックス(0-indexed)</returns>
    public static int LowerBound<T>(this IList<T> ls, Func<T, bool> constraint)
    {
        var ng = -1;
        var ok = ls.Count;
        while (ok - ng > 1)
        {
            var mid = (ok + ng) / 2;
            if (constraint(ls[mid])) ok = mid;
            else ng = mid;
        }
        return ok;

    }

    public static void Swap(this IList<int> arr, int a, int b) => (arr[a], arr[b]) = (arr[b], arr[a]);

    public static long[] GetCum(this IList<long> ls)
    {
        var res = new long[ls.Count + 1];
        for (int i = 0; i < ls.Count; i++) res[i + 1] = res[i] + ls[i];
        return res;
    }

    public static T[] GetCum<T>(this IList<T> ls, bool fromLeft, T gen, Func<T, T, T> func)
    {
        var res = new T[ls.Count + 1];
        res.AsSpan().Fill(gen);
        if (fromLeft)
        {
            for (int i = 0; i < ls.Count; i++) res[i + 1] = func(res[i], ls[i]);
        }
        else
        {
            for (int i = ls.Count; i > 0; i--) res[i - 1] = func(res[i], ls[i - 1]);
        }
        return res;
    }

    public static T[] Repeat<T>(this T element, int N)
    {
        var res = new T[N];
        res.AsSpan().Fill(element);
        return res;
    }

    public static T[][] Repeat<T>(this T element, int H, int W)
    {
        var res = new T[H][];
        for (int i = 0; i < H; i++)
        {
            res[i] = new T[W];
            res[i].AsSpan().Fill(element);
        }
        return res;
    }

    public static T[][][] Repeat<T>(this T element, int H, int W, int R)
    {
        var res = new T[H][][];
        for (int i = 0; i < H; i++)
        {
            res[i] = new T[W][];
            for (int j = 0; j < W; j++)
            {
                res[i][j] = new T[R];
                res[i][j].AsSpan().Fill(element);
            }
        }
        return res;
    }

}

class IO
{
    public string GetStr() => Console.ReadLine().Trim();
    public char GetChar() => Console.ReadLine().Trim()[0];
    public int GetInt() => int.Parse(Console.ReadLine().Trim());
    public long GetLong() => long.Parse(Console.ReadLine().Trim());
    public double GetDouble() => double.Parse(Console.ReadLine().Trim());
    public decimal GetDecimal() => decimal.Parse(Console.ReadLine().Trim());
    public string[] GetStrArray() => Console.ReadLine().Trim().Split(' ');
    public string[][] GetStrArray(int N)
    {
        var res = new string[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ');
        return res;
    }
    public int[] GetIntArray() => Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
    public int[][] GetIntArray(int N)
    {
        var res = new int[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
        return res;
    }
    public long[] GetLongArray() => Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
    public long[][] GetLongArray(int N)
    {
        var res = new long[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
        return res;
    }
    public decimal[] GetDecimalArray() => Console.ReadLine().Trim().Split(' ').Select(decimal.Parse).ToArray();
    public decimal[][] GetDecimalArray(int N)
    {
        var res = new decimal[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(decimal.Parse).ToArray();
        return res;
    }
    public char[] GetCharArray() => Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray();
    public double[] GetDoubleArray() => Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray();
    public double[][] GetDoubleArray(int N)
    {
        var res = new double[N][];
        for (int i = 0; i < N; i++) res[i] = Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray();
        return res;
    }
    public char[][] GetGrid(int H)
    {
        var res = new char[H][];
        for (int i = 0; i < H; i++) res[i] = Console.ReadLine().Trim().ToCharArray();
        return res;
    }

    public List<int>[] GetUnweightedAdjanceyList(int V, int E, bool isDirected, bool isNode_0indexed)
    {
        var ls = new List<int>[V];
        for (int i = 0; i < V; i++) ls[i] = new List<int>();
        for (int i = 0; i < E; i++)
        {
            var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            if (isNode_0indexed == false) { input[0]--; input[1]--; }
            ls[input[0]].Add(input[1]);
            if (isDirected == false) ls[input[1]].Add(input[0]);
        }
        return ls;
    }

    public List<(int to, long dist)>[] GetWeightedAdjacencyList(int V, int E, bool isDirected, bool isNode_0indexed)
    {
        var ls = new List<(int to, long dist)>[V];
        for (int i = 0; i < V; i++) ls[i] = new List<(int to, long dist)>();
        for (int i = 0; i < E; i++)
        {
            var hoge = Console.ReadLine().Split(' ');
            var a = int.Parse(hoge[0]);
            var b = int.Parse(hoge[1]);
            var c = long.Parse(hoge[2]);
            if (isNode_0indexed == false) { a--; b--; }
            ls[a].Add((b, c));
            if (isDirected == false) ls[b].Add((a, c));
        }
        return ls;
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                       : eq<T, long>() ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, decimal>() ? ct<T, decimal>(decimal.Parse(s))
                       : eq<T, char>() ? ct<T, char>(s[0])
                       : ct<T, string>(s);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    void Multi<T>(out T a) => a = cv<T>(GetStr());
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    void Multi<T, U>(out T a, out U b)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    void Multi<T, U, V>(out T a, out U b, out V c)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    {
        var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public (T, U) GetMulti<T, U>()
    {
        var ar = Console.ReadLine().Split(' ');
        return (cv<T>(ar[0]), cv<U>(ar[1]));
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public (T, U, V) GetMulti<T, U, V>()
    {
        var ar = Console.ReadLine().Split(' ');
        return (cv<T>(ar[0]), cv<U>(ar[1]), cv<V>(ar[2]));
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public (T, U, V, W) GetMulti<T, U, V, W>()
    {
        var ar = Console.ReadLine().Split(' ');
        return (cv<T>(ar[0]), cv<U>(ar[1]), cv<V>(ar[2]), cv<W>(ar[3]));
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public (T, U, V, W, X) GetMulti<T, U, V, W, X>()
    {
        var ar = Console.ReadLine().Split(' ');
        return (cv<T>(ar[0]), cv<U>(ar[1]), cv<V>(ar[2]), cv<W>(ar[3]), cv<X>(ar[4]));
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public (T, U, V, W, X, Y) GetMulti<T, U, V, W, X, Y>()
    {
        var ar = Console.ReadLine().Split(' ');
        return (cv<T>(ar[0]), cv<U>(ar[1]), cv<V>(ar[2]), cv<W>(ar[3]), cv<X>(ar[4]), cv<Y>(ar[5]));
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public void Print() => Console.WriteLine();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public void Print<T>(T t) => Console.WriteLine(t);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public void Print<T>(string separator, IList<T> ls) => Console.WriteLine(string.Join(separator, ls));
    public void Debug<T>(IList<T> ls)
    {
        Console.Error.WriteLine();
        Console.Error.WriteLine("[" + string.Join(",", ls) + "]");
    }
    public void Debug<T>(IList<IList<T>> ls)
    {
        Console.Error.WriteLine();
        foreach (var l in ls)
        {
            Console.Error.WriteLine("[" + string.Join(",", l) + "]");
        }
        Console.Error.WriteLine();
    }
}

yukicoder

結果

テストケース

コンパイルメッセージ

ソースコード