結果

問題 No.1115 二つの数列 / Two Sequences
ユーザー 👑 terry_u16terry_u16
提出日時 2020-07-17 22:40:46
言語 C#(csc)
(csc 3.9.0)
結果
AC  
実行時間 166 ms / 2,000 ms
コード長 23,596 bytes
コンパイル時間 4,317 ms
コンパイル使用メモリ 123,756 KB
実行使用メモリ 42,228 KB
最終ジャッジ日時 2023-08-20 02:21:38
合計ジャッジ時間 9,275 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge15
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 77 ms
22,572 KB
testcase_01 AC 64 ms
21,700 KB
testcase_02 AC 63 ms
21,664 KB
testcase_03 AC 152 ms
41,004 KB
testcase_04 AC 163 ms
40,228 KB
testcase_05 AC 152 ms
41,052 KB
testcase_06 AC 145 ms
38,308 KB
testcase_07 AC 165 ms
42,112 KB
testcase_08 AC 76 ms
22,392 KB
testcase_09 AC 119 ms
29,240 KB
testcase_10 AC 161 ms
40,284 KB
testcase_11 AC 64 ms
21,604 KB
testcase_12 AC 165 ms
42,228 KB
testcase_13 AC 166 ms
40,248 KB
testcase_14 AC 164 ms
42,200 KB
testcase_15 AC 63 ms
23,696 KB
testcase_16 AC 63 ms
21,712 KB
testcase_17 AC 63 ms
19,660 KB
testcase_18 AC 64 ms
21,700 KB
testcase_19 AC 64 ms
21,664 KB
testcase_20 AC 64 ms
21,824 KB
testcase_21 AC 63 ms
21,608 KB
testcase_22 AC 64 ms
21,632 KB
testcase_23 AC 78 ms
24,796 KB
testcase_24 AC 102 ms
27,448 KB
testcase_25 AC 143 ms
38,064 KB
testcase_26 AC 87 ms
23,264 KB
testcase_27 AC 110 ms
28,332 KB
testcase_28 AC 123 ms
29,480 KB
testcase_29 AC 147 ms
38,316 KB
testcase_30 AC 161 ms
41,824 KB
testcase_31 AC 91 ms
23,800 KB
testcase_32 AC 85 ms
22,864 KB
testcase_33 AC 152 ms
39,148 KB
testcase_34 AC 65 ms
21,676 KB
testcase_35 AC 64 ms
21,676 KB
testcase_36 AC 65 ms
23,684 KB
testcase_37 AC 64 ms
21,652 KB
testcase_38 AC 64 ms
21,828 KB
testcase_39 AC 64 ms
21,636 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
Microsoft (R) Visual C# Compiler version 3.9.0-6.21124.20 (db94f4cc)
Copyright (C) Microsoft Corporation. All rights reserved.

ソースコード

diff # 

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using YukicoderContest257.Extensions;
using YukicoderContest257.Numerics;
using YukicoderContest257.Questions;

namespace YukicoderContest257.Questions
{
    public class QuestionC : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var n = inputStream.ReadInt();
            var a = new Queue<int>(inputStream.ReadIntArray().Select(i => i - 1));
            var b = inputStream.ReadIntArray().Select(i => i - 1).ToArray();

            var bit = new BinaryIndexedTree(n);

            var indexOfB = new int[n];
            for (int i = 0; i < b.Length; i++)
            {
                indexOfB[b[i]] = i;
            }

            long count = 0;
            foreach (var ai in a)
            {
                var index = indexOfB[ai];
                count += bit.Sum((index + 1)..);
                bit[index]++;
            }

            yield return count;
        }

        public class BinaryIndexedTree
        {
            long[] _data;
            public int Length { get; }

            public BinaryIndexedTree(int length)
            {
                _data = new long[length + 1];   // 内部的には1-indexedにする
                Length = length;
            }

            public BinaryIndexedTree(IEnumerable<long> data, int length) : this(length)
            {
                var count = 0;
                foreach (var n in data)
                {
                    AddAt(count++, n);
                }
            }

            public BinaryIndexedTree(ICollection<long> collection) : this(collection, collection.Count) { }

            public long this[Index index]
            {
                get => Sum(index..(index.GetOffset(Length) + 1));
                set
                {
                    if (value < 0)
                    {
                        throw new ArgumentOutOfRangeException(nameof(value), $"{nameof(value)}は0以上の値である必要があります。");
                    }
                    AddAt(index, value - this[index]);
                }
            }

            /// <summary>
            /// BITの<c>index</c>番目の要素に<c>n</c>を加算します。
            /// </summary>
            /// <param name="index">加算するインデックス（0-indexed）</param>
            /// <param name="value">加算する数</param>
            public void AddAt(Index index, long value)
            {
                var i = index.GetOffset(Length);
                unchecked
                {
                    if ((uint)i >= (uint)Length)
                    {
                        throw new ArgumentOutOfRangeException(nameof(index));
                    }
                }

                i++;  // 1-indexedにする

                while (i <= Length)
                {
                    _data[i] += value;
                    i += i & -i;    // LSBの加算
                }
            }

            /// <summary>
            /// [0, <c>end</c>)の部分和を返します。
            /// </summary>
            /// <param name="end">部分和を求める半開区間の終了インデックス</param>
            /// <returns>区間の部分和</returns>
            public long Sum(Index end)
            {
                var i = end.GetOffset(Length);  // 0-indexedの半開区間＝1-indexedの閉区間なので+1は不要
                unchecked
                {
                    if ((uint)i >= (uint)_data.Length)
                    {
                        throw new ArgumentOutOfRangeException(nameof(end));
                    }
                }

                long sum = 0;
                while (i > 0)
                {
                    sum += _data[i];
                    i -= i & -i;    // LSBの減算
                }
                return sum;
            }

            /// <summary>
            /// <c>range</c>の部分和を返します。
            /// </summary>
            /// <param name="range">部分和を求める半開区間</param>
            /// <returns>区間の部分和</returns>
            public long Sum(Range range) => Sum(range.End) - Sum(range.Start);

            /// <summary>
            /// [<c>start</c>, <c>end</c>)の部分和を返します。
            /// </summary>
            /// <param name="start">部分和を求める半開区間の開始インデックス</param>
            /// <param name="end">部分和を求める半開区間の終了インデックス</param>
            /// <returns>区間の部分和</returns>
            public long Sum(int start, int end) => Sum(end) - Sum(start);

            /// <summary>
            /// [0, <c>index</c>)の部分和が<c>sum</c>未満になる最大の<c>index</c>を返します。
            /// BIT上の各要素は0以上の数である必要があります。
            /// </summary>
            /// <param name="sum"></param>
            /// <returns></returns>
            public int GetLowerBound(long sum)
            {
                int index = 0;
                for (int offset = GetMostSignificantBitOf(Length); offset > 0; offset >>= 1)
                {
                    if (index + offset < _data.Length && _data[index + offset] < sum)
                    {
                        index += offset;
                        sum -= _data[index];
                    }
                }

                return index;

                int GetMostSignificantBitOf(int n)
                {
                    int k = 1;
                    while ((k << 1) <= n)
                    {
                        k <<= 1;
                    };
                    return k;
                }
            }
        }

    }
}

namespace YukicoderContest257
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionC();
            var answers = question.Solve(Console.In);

            var writer = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(writer);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
            Console.Out.Flush();
        }
    }
}

#region Base Class

namespace YukicoderContest257.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }
}

#endregion

#region Algorithm

namespace YukicoderContest257.Numerics
{
    public static class NumericalAlgorithms
    {
        public static long Gcd(long a, long b)
        {
            if (a < b)
            {
                (a, b) = (b, a);
            }

            var result = b switch
            {
                0 => a,
                long n when n > 0 => Gcd(b, a % b),
                _ => throw new ArgumentOutOfRangeException($"{nameof(a)}, {nameof(b)}は0以上の整数である必要があります。")
            };

            return result;
        }

        public static long Lcm(long a, long b)
        {
            if (a < 0 || b < 0)
            {
                throw new ArgumentOutOfRangeException($"{nameof(a)}, {nameof(b)}は0以上の整数である必要があります。");
            }

            return a / Gcd(a, b) * b;
        }

        public static long Factorial(int n)
        {
            if (n < 0)
            {
                throw new ArgumentOutOfRangeException(nameof(n), $"{n}は0以上の整数でなければなりません。");
            }

            long result = 1;
            for (int i = 2; i <= n; i++)
            {
                result *= i;
            }
            return result;
        }

        public static long Permutation(int n, int r)
        {
            CheckNR(n, r);
            long result = 1;
            for (int i = 0; i < r; i++)
            {
                result *= n - i;
            }
            return result;
        }

        public static long Combination(int n, int r)
        {
            CheckNR(n, r);
            r = Math.Min(r, n - r);

            // See https://stackoverflow.com/questions/1838368/calculating-the-amount-of-combinations
            long result = 1;
            for (int i = 1; i <= r; i++)
            {
                result *= n--;
                result /= i;
            }
            return result;
        }

        public static long CombinationWithRepetition(int n, int r) => Combination(n + r - 1, r);

        public static IEnumerable<(int prime, int count)> PrimeFactorization(int n)
        {
            if (n <= 1)
            {
                throw new ArgumentOutOfRangeException(nameof(n), $"{n}は2以上の整数でなければなりません。");
            }

            var dictionary = new Dictionary<int, int>();
            for (int i = 2; i * i <= n; i++)
            {
                while (n % i == 0)
                {
                    if (dictionary.ContainsKey(i))
                    {
                        dictionary[i]++;
                    }
                    else
                    {
                        dictionary[i] = 1;
                    }

                    n /= i;
                }
            }

            if (n > 1)
            {
                dictionary[n] = 1;
            }

            return dictionary.Select(p => (p.Key, p.Value));
        }

        private static void CheckNR(int n, int r)
        {
            if (n <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(n), $"{nameof(n)}は正の整数でなければなりません。");
            }
            if (r < 0)
            {
                throw new ArgumentOutOfRangeException(nameof(r), $"{nameof(r)}は0以上の整数でなければなりません。");
            }
            if (n < r)
            {
                throw new ArgumentOutOfRangeException($"{nameof(n)},{nameof(r)}", $"{nameof(r)}は{nameof(n)}以下でなければなりません。");
            }
        }
    }

    public readonly struct Modular : IEquatable<Modular>, IComparable<Modular>
    {
        private const int DefaultMod = 1000000007;
        public int Value { get; }
        public static int Mod { get; set; } = DefaultMod;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public Modular(long value)
        {
            if (unchecked((ulong)value) < unchecked((ulong)Mod))
            {
                Value = (int)value;
            }
            else
            {
                Value = (int)(value % Mod);
                if (Value < 0)
                {
                    Value += Mod;
                }
            }
        }

        private Modular(int value) => Value = value;
        public static Modular Zero => new Modular(0);
        public static Modular One => new Modular(1);

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static Modular operator +(Modular a, Modular b)
        {
            var result = a.Value + b.Value;
            if (result >= Mod)
            {
                result -= Mod;    // 剰余演算を避ける
            }
            return new Modular(result);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static Modular operator -(Modular a, Modular b)
        {
            var result = a.Value - b.Value;
            if (result < 0)
            {
                result += Mod;    // 剰余演算を避ける
            }
            return new Modular(result);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static Modular operator *(Modular a, Modular b) => new Modular((long)a.Value * b.Value);

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static Modular operator /(Modular a, Modular b) => a * Pow(b.Value, Mod - 2);

        // 需要は不明だけど一応
        public static bool operator ==(Modular left, Modular right) => left.Equals(right);
        public static bool operator !=(Modular left, Modular right) => !(left == right);
        public static bool operator <(Modular left, Modular right) => left.CompareTo(right) < 0;
        public static bool operator <=(Modular left, Modular right) => left.CompareTo(right) <= 0;
        public static bool operator >(Modular left, Modular right) => left.CompareTo(right) > 0;
        public static bool operator >=(Modular left, Modular right) => left.CompareTo(right) >= 0;

        public static implicit operator Modular(long a) => new Modular(a);
        public static explicit operator int(Modular a) => a.Value;
        public static explicit operator long(Modular a) => a.Value;

        public static Modular Pow(int a, int n)
        {
            switch (n)
            {
                case 0:
                    return Modular.One;
                case 1:
                    return a;
                case int m when m >= 0: // ジャンプテーブル化はできなくなる
                    var p = Pow(a, m >> 1);             // m / 2
                    return p * p * Pow(a, m & 0x01);    // m % 2
                default:
                    throw new ArgumentOutOfRangeException(nameof(n), $"べき指数{nameof(n)}は0以上の整数でなければなりません。");
            }
        }

        private static List<int> _factorialCache;
        private static List<int> FactorialCache => _factorialCache ??= new List<int>() { 1 };
        private static int[] FactorialInverseCache { get; set; }
        const int defaultMaxFactorial = 1000000;

        public static Modular Factorial(int n)
        {
            if (n < 0)
            {
                throw new ArgumentOutOfRangeException(nameof(n), $"{nameof(n)}は0以上の整数でなければなりません。");
            }

            for (int i = FactorialCache.Count; i <= n; i++)  // Countが1（0!までキャッシュ済み）のとき1!～n!まで計算
            {
                FactorialCache.Add((int)((long)FactorialCache[i - 1] * i % Mod));
            }
            return new Modular(FactorialCache[n]);
        }

        public static Modular Permutation(int n, int r)
        {
            CheckNR(n, r);
            return Factorial(n) / Factorial(n - r);
        }

        public static Modular Combination(int n, int r)
        {
            CheckNR(n, r);
            r = Math.Min(r, n - r);
            try
            {
                return new Modular(FactorialCache[n]) * new Modular(FactorialInverseCache[r]) * new Modular(FactorialInverseCache[n - r]);
            }
            catch (Exception ex) when (ex is NullReferenceException || ex is ArgumentOutOfRangeException)
            {
                throw new InvalidOperationException($"{nameof(Combination)}を呼び出す前に{nameof(InitializeCombinationTable)}により前計算を行う必要があります。", ex);
            }
        }

        public static void InitializeCombinationTable(int max = defaultMaxFactorial)
        {
            Factorial(max);
            FactorialInverseCache = new int[max + 1];

            var fInv = (Modular.One / Factorial(max)).Value;
            FactorialInverseCache[max] = fInv;
            for (int i = max - 1; i >= 0; i--)
            {
                fInv = (int)((long)fInv * (i + 1) % Mod);
                FactorialInverseCache[i] = fInv;
            }
        }

        public static Modular CombinationWithRepetition(int n, int r) => Combination(n + r - 1, r);

        private static void CheckNR(int n, int r)
        {
            if (n < 0)
            {
                throw new ArgumentOutOfRangeException(nameof(n), $"{nameof(n)}は0以上の整数でなければなりません。");
            }
            if (r < 0)
            {
                throw new ArgumentOutOfRangeException(nameof(r), $"{nameof(r)}は0以上の整数でなければなりません。");
            }
            if (n < r)
            {
                throw new ArgumentOutOfRangeException($"{nameof(n)},{nameof(r)}", $"{nameof(r)}は{nameof(n)}以下でなければなりません。");
            }
        }

        public override string ToString() => Value.ToString();
        public override bool Equals(object obj) => obj is Modular m ? Equals(m) : false;
        public bool Equals([System.Diagnostics.CodeAnalysis.AllowNull] Modular other) => Value == other.Value;
        public int CompareTo([System.Diagnostics.CodeAnalysis.AllowNull] Modular other) => Value.CompareTo(other.Value);
        public override int GetHashCode() => Value.GetHashCode();
    }

    public interface ISemigroup<TSet> where TSet : ISemigroup<TSet>
    {
        public TSet Multiply(TSet other);
        public static TSet operator *(ISemigroup<TSet> a, TSet b) => a.Multiply(b);
    }

    public interface IMonoid<TSet> : ISemigroup<TSet> where TSet : IMonoid<TSet>, new()
    {
        public TSet Identity { get; }
    }

    public interface IGroup<TSet> : IMonoid<TSet> where TSet : IGroup<TSet>, new()
    {
        public TSet Invert();
        public static TSet operator ~(IGroup<TSet> a) => a.Invert();
    }

}

#endregion

#region Extensions

namespace YukicoderContest257.Extensions
{
    public static class StringExtensions
    {
        public static string Join<T>(this IEnumerable<T> source) => string.Concat(source);
        public static string Join<T>(this IEnumerable<T> source, char separator) => string.Join(separator, source);
        public static string Join<T>(this IEnumerable<T> source, string separator) => string.Join(separator, source);
    }

    public static class TextReaderExtensions
    {
        public static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        public static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        public static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        public static string ReadString(this TextReader reader) => reader.ReadLine();

        public static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        public static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        public static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        public static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);

        // Supports primitive type only.
        public static T1 ReadValue<T1>(this TextReader reader) => (T1)Convert.ChangeType(reader.ReadLine(), typeof(T1));

        public static (T1, T2) ReadValue<T1, T2>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            return (v1, v2);
        }

        public static (T1, T2, T3) ReadValue<T1, T2, T3>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            return (v1, v2, v3);
        }

        public static (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
            return (v1, v2, v3, v4);
        }

        public static (T1, T2, T3, T4, T5) ReadValue<T1, T2, T3, T4, T5>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
            var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
            return (v1, v2, v3, v4, v5);
        }

        public static (T1, T2, T3, T4, T5, T6) ReadValue<T1, T2, T3, T4, T5, T6>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
            var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
            var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
            return (v1, v2, v3, v4, v5, v6);
        }

        public static (T1, T2, T3, T4, T5, T6, T7) ReadValue<T1, T2, T3, T4, T5, T6, T7>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
            var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
            var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
            var v7 = (T7)Convert.ChangeType(inputs[6], typeof(T7));
            return (v1, v2, v3, v4, v5, v6, v7);
        }

        public static (T1, T2, T3, T4, T5, T6, T7, T8) ReadValue<T1, T2, T3, T4, T5, T6, T7, T8>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
            var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
            var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
            var v7 = (T7)Convert.ChangeType(inputs[6], typeof(T7));
            var v8 = (T8)Convert.ChangeType(inputs[7], typeof(T8));
            return (v1, v2, v3, v4, v5, v6, v7, v8);
        }
    }
}

#endregion
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