#946791 (C#) No.2616 中央番目の中央値

• 問題: No.2616 中央番目の中央値
• ユーザー: tobisatis
• 提出日時: 2024-01-26 23:13:21
• 言語: C# (.NET 8.0.203)
• 結果: AC
• 実行時間: 1,344 ms / 2,000 ms
• コード長: 8,283 bytes
• コンパイル時間: 9,155 ms
• コンパイル使用メモリ: 158,892 KB
• 実行使用メモリ: 223,048 KB
• 最終ジャッジ日時: 2024-01-26 23:14:07
• 合計ジャッジ時間: 33,763 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	78 ms; 33,060 KB
testcase_01	AC	78 ms; 33,060 KB
testcase_02	AC	78 ms; 33,060 KB
testcase_03	AC	77 ms; 33,060 KB
testcase_04	AC	77 ms; 33,060 KB
testcase_05	AC	78 ms; 33,060 KB
testcase_06	AC	77 ms; 33,060 KB
testcase_07	AC	83 ms; 33,060 KB
testcase_08	AC	77 ms; 33,060 KB
testcase_09	AC	76 ms; 33,060 KB
testcase_10	AC	79 ms; 33,060 KB
testcase_11	AC	79 ms; 33,060 KB
testcase_12	AC	82 ms; 33,188 KB
testcase_13	AC	91 ms; 33,700 KB
testcase_14	AC	99 ms; 33,956 KB
testcase_15	AC	123 ms; 35,108 KB
testcase_16	AC	154 ms; 36,388 KB
testcase_17	AC	196 ms; 37,028 KB
testcase_18	AC	266 ms; 41,380 KB
testcase_19	AC	469 ms; 47,580 KB
testcase_20	AC	464 ms; 47,580 KB
testcase_21	AC	891 ms; 55,972 KB
testcase_22	AC	1,323 ms; 71,428 KB
testcase_23	AC	1,344 ms; 71,628 KB
testcase_24	AC	1,045 ms; 71,632 KB
testcase_25	AC	1,048 ms; 71,632 KB
testcase_26	AC	1,325 ms; 71,632 KB
testcase_27	AC	1,323 ms; 71,632 KB
testcase_28	AC	1,326 ms; 71,632 KB
testcase_29	AC	1,303 ms; 71,884 KB
testcase_30	AC	1,337 ms; 71,628 KB
testcase_31	AC	1,304 ms; 71,628 KB
testcase_32	AC	1,303 ms; 71,628 KB
testcase_33	AC	1,336 ms; 71,628 KB
testcase_34	AC	1,338 ms; 71,628 KB
testcase_35	AC	1,330 ms; 71,628 KB
testcase_36	AC	1,314 ms; 223,048 KB

コンパイルメッセージ

  復元対象のプロジェクトを決定しています...
  /home/judge/data/code/main.csproj を復元しました (101 ms)。
MSBuild のバージョン 17.7.3+8ec440e68 (.NET)
  main -> /home/judge/data/code/bin/Release/net7.0/main.dll
  main -> /home/judge/data/code/bin/Release/net7.0/publish/

ソースコード

namespace AtCoder;

#nullable enable

using System.Numerics;
using System.Text;

readonly record struct ModInt :
    IEqualityOperators<ModInt, ModInt, bool>,
    IAdditiveIdentity<ModInt, ModInt>,
    IAdditionOperators<ModInt, ModInt, ModInt>,
    IUnaryNegationOperators<ModInt, ModInt>,
    ISubtractionOperators<ModInt, ModInt, ModInt>,
    IMultiplicativeIdentity<ModInt, ModInt>,
    IMultiplyOperators<ModInt, ModInt, ModInt>,
    IDivisionOperators<ModInt, ModInt, ModInt>
{
    int V { get; init; }
    public const int Mod = 998244353;
    public ModInt(long value)
    {
        var v = value % Mod;
        if (v < 0) v += Mod;
        V = (int)v;
    }
    ModInt(int value) { V = value; }

    public static implicit operator ModInt(long v) => new(v);
    public static implicit operator int(ModInt modInt) => modInt.V;
    public static ModInt operator +(ModInt a, ModInt b)
    {
        var v = a.V + b.V;
        if (v >= Mod) v -= Mod;
        return new(v);
    }
    public static ModInt operator -(ModInt a) => new(a.V == 0 ? 0 : Mod - a.V);
    public static ModInt operator -(ModInt a, ModInt b)
    {
        var v = a.V - b.V;
        if (v < 0) v += Mod;
        return new(v);
    }
    public static ModInt operator *(ModInt a, ModInt b) => new((int)((long)a.V * b.V % Mod));
    public static ModInt operator /(ModInt a, ModInt b)
    {
        if (b == 0) throw new DivideByZeroException();
        var (d, x, _) = ExtendedGcd(b.V, Mod);
        if (d > 1) throw new DivideByZeroException();
        return x * a.V;
    }

    public ModInt Power(long p)
    {
        if (p < 0) return (MultiplicativeIdentity / V).Power(-p);
        long res = 1;
        long k = V;
        while (p > 0)
        {
            if ((p & 1) > 0) res = res * k % Mod;
            k = k * k % Mod;
            p >>= 1;
        }
        return res;
    }

    static (long d, long x, long y) ExtendedGcd(long a, long b)
    {
        if (b == 0) return (a, 1, 0);
        var (d, x, y) = ExtendedGcd(b, a % b);
        return (d, y, x - a / b * y);
    }

    public static ModInt AdditiveIdentity => new(0);
    public static ModInt MultiplicativeIdentity => new(1);

    public override string ToString() => V.ToString();
}

static class FactorialExtensions
{
    static ModInt[] fac = Array.Empty<ModInt>();
    static ModInt[] inv = Array.Empty<ModInt>();
    const uint Capacity = 1 << 24;
    
    static void Resize(uint n)
    {
        if (n < fac.Length) return;
        var s = 1;
        while (s < n && s < Capacity) s <<= 1;
        fac = new ModInt[s + 1];
        fac[0] = 1;
        for (var i = 1; i <= s; i++) fac[i] = fac[i - 1] * i;
        inv = new ModInt[s + 1];
        inv[s] = fac[0] / fac[s];
        for (var i = s; i > 0; i--) inv[i - 1] = inv[i] * i;
    }

    public static ModInt Factorial(this int n) { Resize((uint)Math.Abs(n)); return n < 0 ? inv[-n] : fac[n]; }

    public static ModInt C(this int n, int r)
    {
        if (r < 0 || n < r) return 0;
        if (n <= Capacity) return Factorial(n) * Factorial(r - n) * Factorial(-r);
        if (n - r < r) return C(n, n - r);
        var res = fac[0];
        for (var i = n; i > n - r; i--) res *= i;
        return res * Factorial(-r);
    }
    public static ModInt P(this int n, int r) => C(n, r) * Factorial(-r);
    public static ModInt H(this int n, int r) => C(n + r - 1, r);
}

abstract class SegmentTree<TMonoid>
{
    public interface IOperator
    {
        TMonoid IdentityElement { get; }
        TMonoid Operation(TMonoid x, TMonoid y);
    }

    public interface IBinarySearchOperator { bool F(TMonoid value); }

    public class Body<TOperator> where TOperator : struct, IOperator
    {
        public int BaseSize { get; init; }
        protected int Height { get; init; }
        protected TOperator Op { get; init; }
        protected TMonoid[] Values { get; init; }

        public Body(TMonoid[] initial, TOperator op = default)
        {
            Op = op;
            (BaseSize, Height) = (1, 0);
            while (BaseSize < initial.Length) (BaseSize, Height) = (BaseSize << 1, Height + 1);
            var size = BaseSize << 1;
            Values = new TMonoid[size];
            for (var i = 0; i < size; i++) Values[i] = op.IdentityElement;
            for (var i = 0; i < initial.Length; i++) Values[i + BaseSize] = initial[i];
            for (var i = BaseSize - 1; i > 0; i--) Update(i);
        }

        public TMonoid Product(int l, int r)
        {
            (l, r) = (l + BaseSize, r + BaseSize);
            var (resL, resR) = (Op.IdentityElement, Op.IdentityElement);
            while (l < r)
            {
                if ((l & 1) == 1) resL = Op.Operation(resL, Values[l++]);
                if ((r & 1) == 1) resR = Op.Operation(Values[--r], resR);
                (l, r) = (l >> 1, r >> 1);
            }
            return Op.Operation(resL, resR);
        }

        public void Set(int index, TMonoid value)
        {
            var j = index + BaseSize;
            Values[j] = value;
            for (var i = 1; i <= Height; i++) Update(j >> i);
        }

        // the result might be greater than n
        public int MinIndex<TMinIndexOperator>(TMinIndexOperator op = default) where TMinIndexOperator : struct, IBinarySearchOperator
        {
            if (!op.F(Values[1])) return BaseSize + 1;
            var product = Op.IdentityElement;
            var (res, w, i) = (0, BaseSize, 1);
            while (w > 0)
            {
                var p = Op.Operation(product, Values[i]);
                if (!op.F(p))
                {
                    res += w;
                    i++;
                    product = p;
                }
                w >>= 1;
                i <<= 1;
            }
            return res + 1;
        }

        protected void Update(int k) { Values[k] = Op.Operation(Values[k << 1], Values[(k << 1) + 1]); }
    }
}

struct Op : SegmentTree<int>.IOperator
{
    public int IdentityElement => 0;
    public int Operation(int x, int y) => x + y;
}

static class Extensions
{
    public static T[] Repeat<T>(this int time, Func<T> F) => Enumerable.Range(0, time).Select(_ => F()).ToArray();
}

class AtCoder
{
    object? Solve()
    {
        var n = Int();
        var q = new int[n];
        for (var i = 0; i < n; i++)
        {
            var x = Int() - 1;
            q[x] = i;
        }
        var t0 = new SegmentTree<int>.Body<Op>(n.Repeat(() => 0));
        var t1 = new SegmentTree<int>.Body<Op>(n.Repeat(() => 1));
        ModInt ans = 0;
        for (var i = 0; i < n; i++)
        {
            var k = q[i];
            ModInt bns = 1;
            for (var j = 0; j < 2; j++)
            {
                var x = t0.Product(0, k);
                var y = t1.Product(k + 1, n);
                var s = x + y;
                bns *= s.Factorial() / (x.Factorial() * y.Factorial());
                (t0, t1) = (t1, t0);
            }
            ans += bns;
            t0.Set(k, 1);
            t1.Set(k, 0);
        }
        return ans;
    }

    public static void Main() => new AtCoder().Run();
    public void Run()
    {
        var res = Solve();
        if (res != null)
        {
            if (res is bool yes) res = yes ? "Yes" : "No";
            sw.WriteLine(res);
        }
        sw.Flush();
    }

    string[] input = Array.Empty<string>();
    int iter = 0;
    readonly StreamWriter sw = new(Console.OpenStandardOutput()) { AutoFlush = false };

    #pragma warning disable IDE0051
    string String()
    {
        while (iter >= input.Length) (input, iter) = (Console.ReadLine()!.Split(' '), 0);
        return input[iter++];
    }
    T Input<T>() where T : IParsable<T> => T.Parse(String(), null);
    int Int() => Input<int>();
    void Out(object? x, string? separator = null)
    {
        separator ??= Environment.NewLine;
        if (x is System.Collections.IEnumerable obj and not string)
        {
            var firstLine = true;
            foreach (var item in obj)
            {
                if (!firstLine) sw.Write(separator);
                firstLine = false;
                sw.Write(item);
            }
        }
        else sw.Write(x);
        sw.WriteLine();
    }
    #pragma warning restore IDE0051
}