#312316 (C#(csc)) No.308 素数は通れません

• 問題: No.308 素数は通れません
• ユーザー: AreTrash
• 提出日時: 2019-01-24 00:55:06
• 言語: C#(csc) (csc 3.9.0)
• 結果: AC
• 実行時間: 43 ms / 1,000 ms
• コード長: 5,311 bytes
• コンパイル時間: 1,110 ms
• コンパイル使用メモリ: 114,476 KB
• 実行使用メモリ: 19,584 KB
• 最終ジャッジ日時: 2024-09-16 04:33:22
• 合計ジャッジ時間: 7,985 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

ファイルパターン	結果
other	AC * 107

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.IO;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

namespace No308
{
    public class Program
    {
        void Solve(StreamScanner ss, StreamWriter sw)
        {
            //---------------------------------
            var N = ss.Next(BigInteger.Parse);

            if (N < 100)
            {
                sw.WriteLine(BruteForce((int)N));
                return;
            }

            if (N % 8 != 1)
            {
                sw.WriteLine(8);
                return;
            }

            sw.WriteLine(MillerRabin.IsPrime(N - 8) ? 14 : 8);
            //---------------------------------
        }

        int BruteForce(int n)
        {
            for (var w = 1; w <= n; w++)
            {
                var uf = new UnionFind(n + 1);
                for (var i = 1; i <= n; i++)
                {
                    if (MillerRabin.IsPrime(i)) continue;
                    if (i + 1 <= n && i % w != 0 && !MillerRabin.IsPrime(i + 1)) uf.Unite(i, i + 1);
                    if (i + w <= n && !MillerRabin.IsPrime(i + w)) uf.Unite(i, i + w);
                }
                if (uf.IsSameSet(1, n)) return w;
            }
            return -1;
        }

        static void Main()
        {
            var ss = new StreamScanner(new StreamReader(Console.OpenStandardInput()));
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            new Program().Solve(ss, sw);
            sw.Flush();
        }
    }

    public static class MillerRabin
    {
        const int RandomTestCount = 30;

        static readonly BigInteger[] BasePrimes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,};
        static readonly BigInteger[] WitnessRanges =
        {
            2047,
            1373653,
            25326001,
            118670087467, //3215031751が例外
            2152302898747,
            3474749660383,
            341550071728321,
            341550071728321,
            3825123056546413051,
            3825123056546413051,
            3825123056546413051,
            BigInteger.Parse("318665857834031151167461"),
            BigInteger.Parse("3317044064679887385961981"),
        };

        public static bool IsPrime(BigInteger n)
        {
            if (n < 2 || n == 3215031751) return false;
            if (n < 42) return BasePrimes.Contains(n);
            if (BasePrimes.Any(p => n % p == 0)) return false;

            var d = n - 1;
            while ((d & 1) == 0) d >>= 1;

            for (var i = 0; i < BasePrimes.Length; i++)
            {
                if (!MillerRabinTest(n, d, BasePrimes[i])) return false;
                if (n < WitnessRanges[i]) return true;
            }

            //n > 3.3e24
            var random = new Random();
            for (var i = 0; i < RandomTestCount; i++)
            {
                if (!MillerRabinTest(n, d, random.Next(1, int.MaxValue))) return false;
            }
            return true;
        }

        static bool MillerRabinTest(BigInteger n, BigInteger d, BigInteger a)
        {
            a = BigInteger.ModPow(a, d, n);
            if (a == 1 || a == n - 1) return true;

            while ((d <<= 1) < n - 1)
            {
                a = a * a % n;
                if (a == n - 1) return true;
            }

            return false;
        }
    }

    public class UnionFind
    {
        readonly int[] p;

        public UnionFind(int n)
        {
            p = new int[n];
            for (var i = 0; i < n; i++) p[i] = -1;
        }

        public int Root(int x)
        {
            return p[x] < 0 ? x : (p[x] = Root(p[x]));
        }

        public bool IsSameSet(int x, int y)
        {
            return Root(x) == Root(y);
        }

        public bool Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);
            if (x == y) return false;

            if (p[x] > p[y])
            {
                var t = x;
                x = y;
                y = t;
            }

            p[x] += p[y];
            p[y] = x;
            return true;
        }

        public int Size(int x)
        {
            return -p[Root(x)];
        }
    }

    public class StreamScanner
    {
        static readonly char[] Sep = {' '};
        readonly Queue<string> buffer = new Queue<string>();
        readonly TextReader textReader;

        public StreamScanner(TextReader textReader)
        {
            this.textReader = textReader;
        }

        public T Next<T>(Func<string, T> parser)
        {
            if (buffer.Count != 0) return parser(buffer.Dequeue());
            var nextStrings = textReader.ReadLine().Split(Sep, StringSplitOptions.RemoveEmptyEntries);
            foreach (var nextString in nextStrings) buffer.Enqueue(nextString);
            return Next(parser);
        }

        public T[] Next<T>(Func<string, T> parser, int x)
        {
            var ret = new T[x];
            for (var i = 0; i < x; ++i) ret[i] = Next(parser);
            return ret;
        }

        public T[][] Next<T>(Func<string, T> parser, int x, int y)
        {
            var ret = new T[y][];
            for (var i = 0; i < y; ++i) ret[i] = Next(parser, x);
            return ret;
        }
    }
}