#797829 (C#) No.2074 Product is Square ?

• 問題: No.2074 Product is Square ?
• ユーザー: KumaTachiRen
• 提出日時: 2022-09-16 21:39:52
• 言語: C# (.NET 8.0.404)
• 結果: TLE
• 実行時間: -
• コード長: 9,013 bytes
• コンパイル時間: 16,541 ms
• コンパイル使用メモリ: 170,796 KB
• 実行使用メモリ: 59,296 KB
• 最終ジャッジ日時: 2024-12-21 18:43:23
• 合計ジャッジ時間: 114,216 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

ファイルパターン	結果
sample	AC * 1
other	AC * 1 TLE * 32

コンパイルメッセージ

  復元対象のプロジェクトを決定しています...
  /home/judge/data/code/main.csproj を復元しました (88 ms)。
MSBuild のバージョン 17.9.6+a4ecab324 (.NET)
  main -> /home/judge/data/code/bin/Release/net8.0/main.dll
  main -> /home/judge/data/code/bin/Release/net8.0/publish/

ソースコード

using System.Diagnostics;
using System;
using System.Linq;
using System.Numerics;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Text;
using static Functions;

using N = System.Int64;

static class Program
{
    static public void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}

public class Solver
{
    public void Solve()
    {
        int t = ri;
        var ans = new string[t];
        for (int q = 0; q < t; q++)
        {
            int n = ri;
            var d = new Dictionary<long, int>();
            for (int i = 0; i < n; i++)
            {
                var f = PrimeFactoring(rl);
                foreach (var k in f.Keys)
                {
                    if (d.ContainsKey(k)) d[k] ^= (int)(f[k] & 1);
                    else d.Add(k, (int)(f[k] & 1));
                }
            }
            bool ok = true;
            foreach (var p in d.Keys) ok &= d[p] == 0;
            ans[q] = ok ? "Yes" : "No";
        }
        WriteJoin("\n", ans);
    }

    bool IsPrimeMR(long n)
    {
        if ((n & 1) == 0) return n == 2;
        long s = 0, d = n - 1;
        while ((d & 1) == 0)
        {
            s++;
            d >>= 1;
        }
        var aarr = new long[] { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 };
        foreach (var a in aarr)
        {
            long p = 1;
            long x = a;
            var c = d;
            while (c > 0)
            {
                if ((c & 1) == 1) p *= x;
                x = x * x % n;
                c >>= 1;
            }
            if (p == 1) continue;
            bool no = true;
            for (int i = 0; i < s; i++)
            {
                p = p * p % n;
                if (p == n - 1)
                {
                    no = false;
                    break;
                }
            }
            if (no) return false;
        }
        return true;
    }
    long FindFactorRho(long n)
    {
        long m = 1;
        while (m * m * m * m * m * m * m * m < n) m++;
        for (int c = 1; c < 100; c++)
        {
            long x = 0, y = 2, ys = 0, r = 1, q = 1, g = 1;
            while (g == 1)
            {
                x = y;
                for (int i = 0; i < r; i++) y = (y * y + c) % n;
                long k = 0;
                while (k < r && g == 1)
                {
                    ys = y;
                    for (int i = 0; i < m && i < r - k; i++)
                    {
                        y = (y * y + c) % n;
                        q = q * Math.Abs(x - y) % n;
                    }
                    g = Gcd(q, n);
                    k += m;
                }
                r <<= 1;
            }
            if (g == n)
            {
                g = 1;
                while (g == 1)
                {
                    ys = (ys * ys + c) % n;
                    g = Gcd(Math.Abs(x - ys), n);
                }
            }
            if (g < n)
            {
                if (IsPrimeMR(g)) return g;
                else if (IsPrimeMR(n / g)) return n / g;
                return FindFactorRho(g);
            }
        }
        return 1;
    }
    SortedDictionary<long, long> PrimeFactoring(long n)
    {
        long i = 2;
        var ret = new SortedDictionary<long, long>();
        while (i * i <= n)
        {
            long k = 0;
            while (n % i == 0)
            {
                n /= i;
                k++;
            }
            if (k > 0) ret.Add(i, k);
            i += 1 + (i & 1);
            if (i == 101 && n >= (1 << 20))
            {
                while (n > 1)
                {
                    if (IsPrimeMR(n))
                    {
                        ret.Add(n, 1);
                        n = 1;
                    }
                    else
                    {
                        long j = FindFactorRho(n);
                        k = 0;
                        while (n % j == 0)
                        {
                            n /= j;
                            k++;
                        }
                        ret.Add(j, k);
                    }
                }
            }
        }
        if (n > 1) ret.Add(n, 1);
        return ret;
    }


    const long inf = (long)1 << 60;
    int ri { get { return (int)sc.Integer(); } }
    long rl { get { return sc.Integer(); } }
    double rd { get { return sc.Double(); } }
    string rs { get { return sc.Scan(); } }
    public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());

    void WriteJoin<T>(string s, T[] t) { Console.WriteLine(string.Join(s, t)); }
    void WriteJoin<T>(string s, List<T> t) { Console.WriteLine(string.Join(s, t)); }
    void Write<T>(T t) { Console.WriteLine(t.ToString()); }
    void Debug<T>(T t) { Console.WriteLine(t.ToString()); Console.Out.Flush(); }
    void YN(bool t) { Console.WriteLine(t ? "YES" : "NO"); }
    void Yn(bool t) { Console.WriteLine(t ? "Yes" : "No"); }
    void yn(bool t) { Console.WriteLine(t ? "yes" : "no"); }
}

public static class Functions
{
    public static int Popcount(long x)
    {
        x = x - ((x >> 1) & 0x5555555555555555);
        x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333);
        x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f;
        x = x + (x >> 8);
        x = x + (x >> 16);
        x = x + (x >> 32);
        return (int)(x & 0x0000007f);
    }
    public static int Ctz(long x)
    {
        if (x == 0) return -1;
        return Popcount((x & -x) - 1);
    }
    public static int SafeMod(int x, int m)
    {
        int r = x % m;
        return r < 0 ? r + m : r;
    }
    public static long SafeMod(long x, long m)
    {
        long r = x % m;
        return r < 0 ? r + m : r;
    }
    public static long Floor(long a, long b) => a >= 0 ? a / b : (a + 1) / b - 1;
    public static long Ceil(long a, long b) => a > 0 ? (a - 1) / b + 1 : a / b;
    public static int Gcd(int a, int b) => b == 0 ? a : Gcd(b, a % b);
    public static long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b);
    public static void Swap(ref int x, ref int y) { x ^= y; y ^= x; x ^= y; }
    public static void Swap(ref long x, ref long y) { x ^= y; y ^= x; x ^= y; }
    public static void Swap<T>(ref T x, ref T y) { T t = y; y = x; x = t; }
    public static void Chmin(ref int x, int y) => x = Math.Min(x, y);
    public static void Chmin(ref long x, long y) => x = Math.Min(x, y);
    public static void Chmin(ref double x, double y) => x = Math.Min(x, y);
    public static void Chmax(ref int x, int y) => x = Math.Max(x, y);
    public static void Chmax(ref long x, long y) => x = Math.Max(x, y);
    public static void Chmax(ref double x, double y) => x = Math.Max(x, y);
    public static int LowerBound<T, S>(in List<T> list, S val, Func<T, S, int> comp)
    {
        if (list.Count == 0) return -1;
        if (comp(list.Last(), val) <= 0) return list.Count;
        int l = 0, r = list.Count;
        while (l < r)
        {
            int x = (l + r) / 2;
            if (comp(list[x], val) < 0) l = x + 1;
            else r = x;
        }
        return l;
    }
    public static int UpperBound<T, S>(in List<T> list, S val, Func<T, S, int> comp)
    {
        if (list.Count == 0) return 0;
        if (comp(list.Last(), val) < 0) return list.Count;
        int l = 0, r = list.Count;
        while (l < r)
        {
            int x = (l + r) / 2;
            if (comp(list[x], val) <= 0) l = x + 1;
            else r = x;
        }
        return l;
    }
}


public class StreamScanner
{
    public StreamScanner(Stream stream) { str = stream; }
    private readonly Stream str;
    private readonly byte[] buf = new byte[1024];
    private int len, ptr;
    public bool isEof = false;
    public bool IsEndOfStream { get { return isEof; } }
    private byte read()
    {
        if (isEof) throw new EndOfStreamException();
        if (ptr >= len)
        {
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; }
        }
        return buf[ptr++];
    }
    public char Char()
    {
        byte b = 0;
        do b = read();
        while (b < 33 || 126 < b);
        return (char)b;
    }
    public string Scan()
    {
        var sb = new StringBuilder();
        for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
        return sb.ToString();
    }
    public long Integer()
    {
        long ret = 0; byte b = 0; var ng = false;
        do b = read();
        while (b != '-' && (b < '0' || '9' < b));
        if (b == '-') { ng = true; b = read(); }
        for (; true; b = read())
        {
            if (b < '0' || '9' < b) return ng ? -ret : ret;
            else ret = ret * 10 + b - '0';
        }
    }
    public double Double() { return double.Parse(Scan()); }
}