結果

問題 No.3030 ミラー・ラビン素数判定法のテスト
ユーザー fairy_lettucefairy_lettuce
提出日時 2020-07-28 01:04:22
言語 C#(csc)
(csc 3.9.0)
結果
AC  
実行時間 3,541 ms / 9,973 ms
コード長 11,262 bytes
コンパイル時間 1,214 ms
コンパイル使用メモリ 112,896 KB
実行使用メモリ 22,528 KB
最終ジャッジ日時 2024-11-16 23:27:16
合計ジャッジ時間 11,578 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 27 ms
18,176 KB
testcase_01 AC 27 ms
18,176 KB
testcase_02 AC 27 ms
18,432 KB
testcase_03 AC 32 ms
18,688 KB
testcase_04 AC 1,954 ms
22,524 KB
testcase_05 AC 1,882 ms
22,400 KB
testcase_06 AC 758 ms
22,396 KB
testcase_07 AC 746 ms
22,528 KB
testcase_08 AC 747 ms
22,400 KB
testcase_09 AC 3,541 ms
22,260 KB
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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.IO;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Diagnostics;

namespace FertiLib.Contest.A
{
	static class Program
	{
		public static void Solve(Scanner cin)
		{
			int n = cin.ReadInt();
			var x = cin.ReadValueArray<ulong>(n);
			for (int i = 0; i < n; i++)
			{
				string ans = $"{x[i]} ";
				bool ok = Factorizer.IsPrime(x[i]);
				if (ok) ans += "1";
				else ans += "0";
				Console.WriteLine(ans);
			}
		}

		public static void Main(string[] args)
		{
			var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
			Console.SetOut(sw);
			var cin = new Scanner();
			Solve(cin);
			Console.Out.Flush();
		}

		public static void YESNO(bool condition) => Console.WriteLine(condition ? "YES" : "NO");
		public static void YesNo(bool condition) => Console.WriteLine(condition ? "Yes" : "No");
		public static void yesno(bool condition) => Console.WriteLine(condition ? "yes" : "no");

		public static bool Chmax<T>(ref T a, T b) where T : IComparable<T>
		{
			if (a.CompareTo(b) >= 0) return false;
			a = b;
			return true;
		}
		public static bool Chmin<T>(ref T a, T b) where T : IComparable<T>
		{
			if (a.CompareTo(b) <= 0) return false;
			a = b;
			return true;
		}
	}

	public static class Factorizer
	{
		// http://miller-rabin.appspot.com/
		static readonly ulong[] baseSingle = { 126401071349994536 };                 // <= 291,831
		static readonly ulong[] baseDouble = { 336781006125, 9639812373923155 };     // <= 1,050,535,501
		static readonly ulong[] baseQuad = { 2, 2570940, 211991001, 3749873356 };    // <= 47,636,622,961,201
		static readonly ulong[] baseBig = { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 };

		/// <summary>
		/// Factorizes n.
		/// </summary>
		/// <param name="n">The number to factorize.</param>
		/// <returns>Dictionary that has prime factors in Key, the number of each factor in Value.</returns>
		public static SortedDictionary<ulong, int> Factorize(ulong n)
		{
			var ret = new SortedDictionary<ulong, int>();
			var que = new Queue<ulong>();
			que.Enqueue(n);
			while (que.Count > 0)
			{
				var now = que.Dequeue();
				if (now == 1) continue;
				if (IsPrime(now))
				{
					if (ret.ContainsKey(now)) ret[now]++;
					else ret.Add(now, 1);
					continue;
				}

				ulong f = FindFactor(now);
				que.Enqueue(f);
				que.Enqueue(now / f);
			}

			return ret;
		}

		/// <summary>
		/// Tests if n is prime or not using Miller-Rabin Algorithm. Complexity: O(log^2 n)
		/// </summary>
		/// <param name="n">The number to test.</param>
		/// <returns>True if prime, False otherwise.</returns>
		public static bool IsPrime(ulong n)
		{
			if (n == 1) return false;
			if (n == 2) return true;

			ulong d = n - 1;
			int s = 0;
			while (d % 2 == 0)
			{
				d /= 2;
				s++;
			}

			ulong[] bases;
			if (n < 291831) bases = baseSingle;
			else if (n < 1050535501) bases = baseDouble;
			else if (n < 47636622961201) bases = baseQuad;
			else bases = baseBig;

			foreach (var e in bases)
			{
				if (!MillerRabinTest(e, d, n, s)) return false;
			}
			return true;
		}

		private static bool MillerRabinTest(ulong e, ulong d, ulong n, long s)
		{
			ulong pow = ModPow(e, d, n);
			if (pow == 1) return true;
			for (int i = 0; i < s; i++)
			{
				if (pow == n - 1) return true;
				pow = ModPow(pow, 2, n);
			}
			return false;
		}

		private static ulong ModPow(ulong a, ulong p, ulong mod)
		{
			if (mod <= int.MaxValue)
			{
				a %= mod;
				ulong ret = 1;
				for (ulong i = 1; i <= p; i *= 2)
				{
					if (p / i % 2 == 1)
					{
						ret *= a;
						ret %= mod;
					}

					a *= a;
					a %= mod;
				}
				return ret;
			}
			else
			{
				BigInteger retbig = 1;
				BigInteger abig = a % mod;
				for (ulong i = 1; i <= p; i *= 2)
				{
					if (p / i % 2 == 1)
					{
						retbig *= abig;
						retbig %= mod;
					}

					abig *= abig;
					abig %= mod;
				}
				return (ulong)retbig;
			}
		}

		/// <summary>
		/// Finds a factor of n by Pollard's ρ algorithm. Complexity: O(n^(1/4))
		/// </summary>
		/// <param name="n">The number to get a factor.</param>
		/// <returns>A prime factor of n.</returns>
		public static ulong FindFactor(ulong n)
		{
			if (n % 2 == 0) return 2;
			ulong i = 0;
			while (true)
			{
				i++;
				ulong x = i;
				ulong y = Next(i, n);
				while (true)
				{
					ulong g = GCD(x - y, n);
					if (g >= n) break;
					if (1 < g) return g;
					x = Next(x, n);
					y = Next(y, n);
					y = Next(y, n);
				}
			}
		}

		private static ulong Next(ulong x, ulong mod)
		{
			BigInteger tmp = x;
			tmp *= tmp;
			tmp++;
			tmp %= mod;
			return (ulong)tmp;
		}

		private static ulong GCD(ulong a, ulong b)
		{
			//a = Math.Abs(a);
			//b = Math.Abs(b);
			while (a > 0)
			{
				b %= a;
				var x = a;
				a = b;
				b = x;
			}
			return b;
		}
	}

	static class Util
	{
		public static string Join<T>(this IEnumerable<T> x, string separator = "") => string.Join(separator, x);
	}

	class Scanner
	{
		string[] s;
		int i;

		char[] separator = new char[] { ' ' };

		public Scanner()
		{
			s = new string[0];
			i = 0;
		}

		public string Read() => ReadString();

		public string ReadString()
		{
			if (i < s.Length) return s[i++];
			string st = Console.ReadLine();
			while (st == "") st = Console.ReadLine();
			s = st.Split(separator, StringSplitOptions.RemoveEmptyEntries);
			if (s.Length == 0) return ReadString();
			i = 0;
			return s[i++];
		}

		public string[] ReadStringArray(int N)
		{
			string[] Array = new string[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadString();
			}
			return Array;
		}

		public int ReadInt()
		{
			return int.Parse(ReadString());
		}

		public int[] ReadIntArray(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadInt() + add;
			}
			return Array;
		}

		public long ReadLong()
		{
			return long.Parse(ReadString());
		}

		public long[] ReadLongArray(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadLong() + add;
			}
			return Array;
		}

		public double ReadDouble()
		{
			return double.Parse(ReadString());
		}

		public double[] ReadDoubleArray(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = ReadDouble() + add;
			}
			return Array;
		}

		public T1 ReadValue<T1>() => (T1)Convert.ChangeType(ReadString(), typeof(T1));

		public (T1, T2) ReadValue<T1, T2>()
		{
			var inputs = ReadStringArray(2);
			var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
			var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
			return (v1, v2);
		}

		public (T1, T2, T3) ReadValue<T1, T2, T3>()
		{
			var inputs = ReadStringArray(3);
			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 (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>()
		{
			var inputs = ReadStringArray(4);
			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 (T1, T2, T3, T4, T5) ReadValue<T1, T2, T3, T4, T5>()
		{
			var inputs = ReadStringArray(5);
			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 (T1, T2, T3, T4, T5, T6) ReadValue<T1, T2, T3, T4, T5, T6>()
		{
			var inputs = ReadStringArray(6);
			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 (T1, T2, T3, T4, T5, T6, T7) ReadValue<T1, T2, T3, T4, T5, T6, T7>()
		{
			var inputs = ReadStringArray(7);
			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 T1[] ReadValueArray<T1>(int N)
		{
			var v1 = new T1[N];
			for (int i = 0; i < N; i++)
			{
				v1[i] = ReadValue<T1>();
			}
			return v1;
		}

		public (T1[], T2[]) ReadValueArray<T1, T2>(int N)
		{
			var (v1, v2) = (new T1[N], new T2[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2) = ReadValue<T1, T2>();
				v1[i] = t1;
				v2[i] = t2;
			}
			return (v1, v2);
		}

		public (T1[], T2[], T3[]) ReadValueArray<T1, T2, T3>(int N)
		{
			var (v1, v2, v3) = (new T1[N], new T2[N], new T3[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3) = ReadValue<T1, T2, T3>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
			}
			return (v1, v2, v3);
		}

		public (T1[], T2[], T3[], T4[]) ReadValueArray<T1, T2, T3, T4>(int N)
		{
			var (v1, v2, v3, v4) = (new T1[N], new T2[N], new T3[N], new T4[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4) = ReadValue<T1, T2, T3, T4>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
			}
			return (v1, v2, v3, v4);
		}

		public (T1[], T2[], T3[], T4[], T5[]) ReadValueArray<T1, T2, T3, T4, T5>(int N)
		{
			var (v1, v2, v3, v4, v5) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4, t5) = ReadValue<T1, T2, T3, T4, T5>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
				v5[i] = t5;
			}
			return (v1, v2, v3, v4, v5);
		}

		public (T1[], T2[], T3[], T4[], T5[], T6[]) ReadValueArray<T1, T2, T3, T4, T5, T6>(int N)
		{
			var (v1, v2, v3, v4, v5, v6) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4, t5, t6) = ReadValue<T1, T2, T3, T4, T5, T6>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
				v5[i] = t5;
				v6[i] = t6;
			}
			return (v1, v2, v3, v4, v5, v6);
		}

		public (T1[], T2[], T3[], T4[], T5[], T6[], T7[]) ReadValueArray<T1, T2, T3, T4, T5, T6, T7>(int N)
		{
			var (v1, v2, v3, v4, v5, v6, v7) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N], new T7[N]);
			for (int i = 0; i < N; i++)
			{
				var (t1, t2, t3, t4, t5, t6, t7) = ReadValue<T1, T2, T3, T4, T5, T6, T7>();
				v1[i] = t1;
				v2[i] = t2;
				v3[i] = t3;
				v4[i] = t4;
				v5[i] = t5;
				v6[i] = t6;
				v7[i] = t7;
			}
			return (v1, v2, v3, v4, v5, v6, v7);
		}
	}
}
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