結果

問題 No.981 一般冪乗根
ユーザー keymoonkeymoon
提出日時 2020-01-24 00:00:51
言語 C#(csc)
(csc 3.9.0)
結果
RE  
実行時間 -
コード長 6,476 bytes
コンパイル時間 1,090 ms
コンパイル使用メモリ 117,404 KB
実行使用メモリ 30,908 KB
最終ジャッジ日時 2024-10-09 13:54:06
合計ジャッジ時間 40,832 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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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 RE -
testcase_01 RE -
testcase_02 RE -
testcase_03 RE -
testcase_04 RE -
testcase_05 RE -
testcase_06 RE -
testcase_07 RE -
testcase_08 RE -
testcase_09 RE -
testcase_10 RE -
testcase_11 RE -
testcase_12 RE -
testcase_13 RE -
testcase_14 RE -
testcase_15 RE -
testcase_16 RE -
testcase_17 RE -
testcase_18 RE -
testcase_19 RE -
testcase_20 RE -
testcase_21 RE -
testcase_22 RE -
testcase_23 RE -
testcase_24 RE -
testcase_25 RE -
testcase_26 RE -
testcase_27 RE -
testcase_28 RE -
evil_60bit1.txt RE -
evil_60bit2.txt RE -
evil_60bit3.txt RE -
evil_hack RE -
evil_hard_random RE -
evil_hard_safeprime.txt RE -
evil_hard_tonelli0 RE -
evil_hard_tonelli1 RE -
evil_hard_tonelli2 RE -
evil_hard_tonelli3 RE -
evil_sefeprime1.txt RE -
evil_sefeprime2.txt RE -
evil_sefeprime3.txt RE -
evil_tonelli1.txt RE -
evil_tonelli2.txt RE -
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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.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    public static void Main()
    {
        Action abort = () => { Console.WriteLine(-1); Environment.Exit(0); };

        var line = Console.ReadLine();
        Assert(!Regex.IsMatch(line, @"^\d+ \d+  \d+$"));
        
        var pka = line.Split().Select(int.Parse).ToArray();
        var p = pka[0];
        var k = pka[1];
        var a = pka[2];

        Assert(2 <= k && k <= 1000);
        Assert(2 <= p && p <= 1000000007);
        Assert(1 <= a && a < p);

        ModInt.Mod = p;

        //有限体Z/pZの原始根rを一つ求め、
        var g = GetPrimitiveRoot(p);
        //そのgについてのaの指数を求める。
        var aIndex = Log(a, g);
        //これによって、Z/(p-1)Z上でのa/kを求める問題に帰着できる 解けません とりあえず出します

        if (aIndex % k == 0)
        {
            Console.WriteLine(Power(g, aIndex / k));
            return;
        }

        //ここで、aを生成元とする有限体Z/pZ上の巡回群を考える。
        //その位数orderは、
        var order = (p - 1) / GCD(aIndex, p - 1);

        //ここで、有限体Z/pZ上でのX^k=aは、(a^x)^k=aより、巡回群Z/orderZ上においてのkx=1と対応する。
        //そのため、これを満たすxが存在すれば、Z/pZ上でのa^xが答え。

        //巡回群Z/orderZにおいて、kの逆元が存在するための条件は k|order であり、これは必要十分。
        if (GCD(k, order) != 1) abort();
        //x=1/k
        var x = GetInverse(k, order);

        Console.WriteLine(Power(a, x));
    }

    static int GetPrimitiveRoot(long m)
    {
        var subgroupOrders = new List<long>();
        var order = m - 1;
        if ((order & 1) == 0)
        {
            while ((order & 1) == 0) order >>= 1;
            subgroupOrders.Add((m - 1) / 2);
        }
        for (long i = 3; i * i <= order; i += 2)
            if (order % i == 0)
            {
                while (order % i == 0) order /= i;
                subgroupOrders.Add((m - 1) / i);
            }
        if (order != 1) subgroupOrders.Add((m - 1) / order);

        for (int g = 2; g < m; g++)
        {
            if (subgroupOrders.Any(x => Power(g, x) == 1)) continue;
            return g;
        }
        throw new Exception();
    }

    static int Log(ModInt a, ModInt b)
    {
        const int PACKET_SIZE = 65536;
        ModInt current = 1;
        Dictionary<ModInt, int> babySteps = new Dictionary<ModInt, int>();
        for (int i = 0; i < PACKET_SIZE; i++)
        {
            if (babySteps.ContainsKey(current))
            {
                if (babySteps.ContainsKey(a)) return babySteps[a];
                else return -1;
            }
            babySteps.Add(current, i);
            current *= b;
        }
        ModInt singleGiantStep = current;
        current = 1;
        for (int i = 0; i < ModInt.Mod; i += PACKET_SIZE)
        {
            var babyStep = a / current;
            if (babySteps.ContainsKey(babyStep)) return i + babySteps[babyStep];
            current *= singleGiantStep;
        }
        return -1;
    }

    static ModInt Power(ModInt n, long m)
    {
        ModInt pow = n;
        ModInt res = 1;
        while (m > 0)
        {
            if ((m & 1) == 1) res *= pow;
            pow *= pow;
            m >>= 1;
        }
        return res;
    }

    static void Assert(bool cond)
    {
        if (!cond) throw new Exception();
    }


    static long GCD(long a, long b)
    {
        while (true)
        {
            if (b == 0) return a;
            a %= b;
            if (a == 0) return b;
            b %= a;
        }
    }

    static long GetInverse(long a, long MOD)
    {
        long div, p = MOD, x1 = 1, y1 = 0, x2 = 0, y2 = 1;
        while (true)
        {
            if (p == 1) return x2 + MOD; div = a / p; x1 -= x2 * div; y1 -= y2 * div; a %= p;
            if (a == 1) return x1 + MOD; div = p / a; x2 -= x1 * div; y2 -= y1 * div; p %= a;
        }
    }
}



struct ModInt
{
    public static int Mod
    {
        get
        {
            return Mod;
        }
        set
        {
            MOD = value;
            POSITIVIZER = (long)MOD << 31;
        }
    }
    static int MOD = 1000000007;
    static long POSITIVIZER = ((long)MOD) << 31;
        long Data;
    public ModInt(long data) { if ((Data = data % MOD) < 0) Data += MOD; }
    public static implicit operator long(ModInt modInt) => modInt.Data;
    public static implicit operator ModInt(long val) => new ModInt(val);
    public static ModInt operator +(ModInt a, int b) => new ModInt() { Data = (a.Data + b + POSITIVIZER) % MOD };
    public static ModInt operator +(ModInt a, long b) => new ModInt(a.Data + b);
    public static ModInt operator +(ModInt a, ModInt b) { long res = a.Data + b.Data; return new ModInt() { Data = res >= MOD ? res - MOD : res }; }
    public static ModInt operator -(ModInt a, int b) => new ModInt() { Data = (a.Data - b + POSITIVIZER) % MOD };
    public static ModInt operator -(ModInt a, long b) => new ModInt(a.Data - b);
    public static ModInt operator -(ModInt a, ModInt b) { long res = a.Data - b.Data; return new ModInt() { Data = res < 0 ? res + MOD : res }; }
    public static ModInt operator *(ModInt a, int b) => new ModInt(a.Data * b);
    public static ModInt operator *(ModInt a, long b) => a * new ModInt(b);
    public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % MOD };
    public static ModInt operator /(ModInt a, ModInt b) => new ModInt() { Data = a.Data * GetInverse(b) % MOD };
    public override string ToString() => Data.ToString();
    static long GetInverse(long a)
    {
        long div, p = MOD, x1 = 1, y1 = 0, x2 = 0, y2 = 1;
        while (true)
        {
            if (p == 1) return x2 + MOD; div = a / p; x1 -= x2 * div; y1 -= y2 * div; a %= p;
            if (a == 1) return x1 + MOD; div = p / a; x2 -= x1 * div; y2 -= y1 * div; p %= a;
        }
    }
}
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