#403516 (C#(csc)) No.577 Prime Powerful Numbers

• 問題: No.577 Prime Powerful Numbers
• ユーザー: mban
• 提出日時: 2019-12-01 04:47:34
• 言語: C#(csc) (csc 3.9.0)
• 結果: WA
• 実行時間: -
• コード長: 6,587 bytes
• コンパイル時間: 908 ms
• コンパイル使用メモリ: 114,700 KB
• 実行使用メモリ: 51,216 KB
• 最終ジャッジ日時: 2024-11-21 04:12:31
• 合計ジャッジ時間: 18,261 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	56 ms; 32,004 KB
testcase_01	WA	-
testcase_02	AC	27 ms; 32,136 KB
testcase_03	TLE	-
testcase_04	AC	43 ms; 32,260 KB
testcase_05	TLE	-
testcase_06	TLE	-
testcase_07	TLE	-
testcase_08	TLE	-
testcase_09	AC	1,987 ms; 25,316 KB
testcase_10	AC	26 ms; 48,912 KB

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

using System;
using System.Text;
using CompLib.Mathematics;

public class Program
{
    public void Solve()
    {
        var sc = new Scanner();
        int q = sc.NextInt();
        var sb = new StringBuilder();
        for (int i = 0; i < q; i++)
        {
            sb.AppendLine(Query(sc.NextLong()));
        }

        Console.Write(sb.ToString());
    }

    string Query(long n)
    {
        // Goldbach's conjecture
        // n <= 10^18では真
        if (n % 2 == 0)
        {
            return n == 2 ? "No" : "Yes";
        }

        // nは奇数
        // p,qが奇素数ならnは偶数になるはず
        // どちらかは2
        // 対称性より p = 2とする

        if (n < 5) return "No";

        for (long pa = 2; pa < n; pa *= 2)
        {
            long qb = n - pa;
            if (PrimalityTest.IsPrime(qb))
            {
                return "Yes";
            }

            for (long b = 2; b <= 60; b++)
            {
                long min = 0;
                long max = (long) Math.Pow(long.MaxValue, (double) 1 / b);
                while (max - min > 1)
                {
                    long med = (max + min) / 2;
                    if (Pow(med, b) <= qb)
                    {
                        min = med;
                    }
                    else
                    {
                        max = med;
                    }
                }

                if (min < 2) break;
                if (Pow(min, b) == qb && PrimalityTest.IsPrime(min))
                {
                    return "Yes";
                }
            }
        }

        return "No";
    }

    public long Pow(long a, long b)
    {
        if (b == 0) return 1;
        long res = Pow(a * a, b / 2);
        if (b % 2 == 1) res *= a;
        return res;
    }

    public static void Main(string[] args)
    {
        new Program().Solve();
    }
}

namespace CompLib.Mathematics
{
    using System;

    public static class PrimalityTest
    {
        private static Random Random = new Random();

        /// <summary>
        /// Miller-Rabin素数判定法を用いてnが素数か判定 O(k log^2 n)
        /// </summary>
        /// <param name="n"></param>
        /// <param name="k"></param>
        /// <returns></returns>
        public static bool IsPrime(long n, int k = 60)
        {
            if (n < 2) return false;
            if (n == 2) return true;
            if (n % 2 == 0) return false;

            if (n < 10000)
            {
                for (int i = 3; i * i <= n; i++)
                {
                    if (n % i == 0)
                    {
                        return false;
                    }
                }

                return true;
            }

            if (!StrongFermatTest(2, n))
            {
                return false;
            }

            for (int i = 0; i < k; i++)
            {
                if (!StrongFermatTest(NextLong(2, n), n))
                {
                    return false;
                }
            }

            return true;
        }

        public static bool StrongFermatTest(long a, long n)
        {
            long t = n - 1;
            long t2 = t;
            while (t % 2 == 0)
            {
                t /= 2;
                if (Pow(a, t, n) == t2)
                {
                    return true;
                }
            }

            return Pow(a, t, n) == 1;
        }

        private static long Pow(long x, long y, long mod)
        {
            x %= mod;
            long result = 1;
            while (y > 0)
            {
                if (y % 2 == 1)
                {
                    result = Multiplication(result, x, mod);
                }

                x = Multiplication(x, x, mod);
                y /= 2;
            }

            return result;
        }

        private static long Multiplication(long a, long b, long mod)
        {
            if (mod < int.MaxValue)
            {
                return (a * b) % mod;
            }

            long result = 0;
            while (b > 0)
            {
                if (b % 2 == 1)
                {
                    result += a;
                    result %= mod;
                }

                a *= 2;
                a %= mod;
                b /= 2;
            }

            return result;
        }

        private static long NextLong(long min, long max)
        {
            long d = max - min;
            long result = Random.Next();
            result <<= 31;
            result += Random.Next();
            result %= d;
            return result + min;
        }
    }
}

class Scanner
{
    public Scanner()
    {
        _pos = 0;
        _line = new string[0];
    }

    const char Separator = ' ';
    private int _pos;
    private string[] _line;

    #region スペース区切りで取得

    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = Console.ReadLine().Split(Separator);
            _pos = 0;
        }

        return _line[_pos++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }

    #endregion

    #region 型変換

    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }

    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }

    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }

    #endregion

    #region 配列取得

    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = Console.ReadLine().Split(Separator);

        _pos = _line.Length;
        return _line;
    }

    public int[] IntArray()
    {
        return ToIntArray(Array());
    }

    public long[] LongArray()
    {
        return ToLongArray(Array());
    }

    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }

    #endregion
}