結果
| 問題 | No.2074 Product is Square ? |
| コンテスト | |
| ユーザー |
 KumaTachiRen
|
| 提出日時 | 2022-09-17 23:33:11 |
| 言語 | C# (.NET 10.0.101) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 17,349 bytes |
| 記録 | |
| コンパイル時間 | 11,119 ms |
| コンパイル使用メモリ | 171,172 KB |
| 実行使用メモリ | 84,736 KB |
| 最終ジャッジ日時 | 2024-12-22 01:02:48 |
| 合計ジャッジ時間 | 106,087 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 2 TLE * 31 |
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 (96 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;
if (n <= 1) return false;
long d = n - 1;
while ((d & 1) == 0) d >>= 1;
var aarr = new long[] { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 };
var mont = new Montgomery(n);
foreach (var a in aarr)
{
if (n <= a) break;
long t = d, x = a, y = 1;
while (t > 0)
{
if ((t & 1) == 1) y = mont.Mul(x, y);
x = mont.Mul(x, x);
t >>= 1;
}
t = d;
while (t != n - 1 && y != 1 && y != n - 1)
{
y = mont.Mul(y, y);
t <<= 1;
}
if (y != n - 1 && (t & 1) == 0) return false;
}
return true;
}
long FindFactorRho(long n)
{
var mont = new Montgomery(n);
long m = 1;
while (m * m * m * m * m * m * m * m < n) m++;
for (int c = 1; c < 10000; c++)
{
long x = 1, y = c, ys = 0, q = 1;
long g = 1;
for (int r = 1; g == 1; r <<= 1)
{
x = y;
for (int i = 0; i < r; ++i) y = mont.Conv(mont.Mul(y, y) + c);
for (long k = 0; g == 1 && k < r; k += m)
{
ys = y;
for (int i = 0; i < m && i < r - k; ++i)
{
y = mont.Conv(mont.Mul(y, y) + c);
q = mont.Mul(q, Math.Abs(x - y));
}
g = Math.Abs(Gcd(q, n));
}
}
if (g == n)
{
do
{
ys = mont.Conv(mont.Mul(ys, ys) + c);
g = Gcd(Math.Abs(x - ys), n);
}
while (g == 1);
}
if (g != n) return g;
}
return n;
}
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;
}
class Montgomery
{
long n, nr, mask;
UInt128 r2;
int nb;
public Montgomery(long _n)
{
n = _n;
nb = 0;
while (n >= (1L << nb)) nb++;
r2 = ((UInt128)1 << (nb * 2)) % n;
mask = (1L << nb) - 1;
nr = 0;
long t = 0, vi = 1;
for (int i = 0; i < nb; i++)
{
if ((t & 1) == 0)
{
t += n;
nr += vi;
}
t >>= 1;
vi <<= 1;
}
}
public long Reduction(UInt128 t)
{
UInt128 c = t * nr;
c &= mask;
c *= n;
c += t;
c >>= nb;
if (c >= n) c -= n;
return c;
}
public long Conv(UInt128 a) => Reduction(Reduction(a) * r2);
public long Mul(UInt128 a, UInt128 b) => Reduction(Reduction(a * b) * r2);
public long Pow(UInt128 a, long b)
{
long p = Reduction(a * r2);
long x = Reduction(r2);
long y = b;
while (y > 0)
{
if ((y & 1) == 1) x = Reduction(x * p);
p = Reduction(p * p);
y >>= 1;
}
return Reduction(x);
}
}
struct UInt128
{
private const int l = 64;
private const ulong MaxValue = ulong.MaxValue;
public ulong t, b;
public UInt128(long n) : this(0, (ulong)n) { }
public UInt128(ulong n) : this(0, n) { }
public UInt128(long _t, long _b) : this((ulong)_t, (ulong)_b) { }
public UInt128(ulong _t, ulong _b)
{
t = _t;
b = _b;
}
public static implicit operator UInt128(int n) => new UInt128(n);
public static implicit operator UInt128(long n) => new UInt128(n);
public static implicit operator UInt128(ulong n) => new UInt128(n);
public static implicit operator ulong(UInt128 n) => n.b;
public static implicit operator long(UInt128 n) => (long)n.b;
public override bool Equals(object obj)
{
if (obj == null || GetType() != obj.GetType()) return false;
var x = (UInt128)obj;
return x.t == t && x.b == b;
}
public override int GetHashCode() => t.GetHashCode() ^ b.GetHashCode();
public override string ToString() => $"UInt128({t},{b})";
public static bool operator ==(UInt128 x, UInt128 y) => Equals(x, y);
public static bool operator !=(UInt128 x, UInt128 y) => !Equals(x, y);
public static bool operator <(UInt128 x, UInt128 y) => x.t != y.t ? x.t < y.t : x.b < y.b;
public static bool operator >(UInt128 x, UInt128 y) => x.t != y.t ? x.t > y.t : x.b > y.b;
public static bool operator <=(UInt128 x, UInt128 y) => x.t != y.t ? x.t < y.t : x.b <= y.b;
public static bool operator >=(UInt128 x, UInt128 y) => x.t != y.t ? x.t > y.t : x.b >= y.b;
public static UInt128 operator +(UInt128 x, UInt128 y) => x.b <= MaxValue - y.b ? new UInt128(x.t + y.t, x.b + y.b) : new UInt128(x.t + y.t + 1, x.b + y.b);
public static UInt128 operator -(UInt128 x, UInt128 y) => x.b >= y.b ? new UInt128(x.t - y.t, x.b - y.b) : new UInt128(x.t - y.t - 1, x.b + (MaxValue - y.b) + 1);
public static UInt128 operator *(UInt128 x, UInt128 y)
{
const ulong mask = (1UL << (l / 4)) - 1;
var p = new ulong[8];
var q = new ulong[8];
for (int i = 0; i < 4; i++)
{
p[i] = (x.b >> (l / 4 * i)) & mask;
p[i + 4] = (x.t >> (l / 4 * i)) & mask;
q[i] = (y.b >> (l / 4 * i)) & mask;
q[i + 4] = (y.t >> (l / 4 * i)) & mask;
}
var r = new ulong[8];
for (int i = 0; i < 8; i++)
for (int j = 0; i + j < 8; j++)
r[i + j] += p[i] * q[j];
for (int i = 0; i < 7; i++) r[i + 1] += r[i] >> (l / 4);
for (int i = 0; i < 8; i++) r[i] &= mask;
ulong t = 0, b = 0;
for (int i = 0; i < 4; i++)
{
b |= r[i] << (l / 4 * i);
t |= r[i + 4] << (l / 4 * i);
}
return new UInt128(t, b);
}
public static UInt128 operator /(UInt128 x, UInt128 y)
{
ulong a = (ulong)1 << (l - 1), b = 0;
var t = y >> 1;
while (t > 0)
{
if (a == 1)
{
a = 0;
b = (ulong)1 << (l - 1);
}
else if (a > 0) a >>= 1;
else b >>= 1;
t >>= 1;
}
const ulong mask = (1UL << (l / 4)) - 1;
ulong[] p, q, r;
ulong aprv = a, bprv = b;
while (true)
{
p = new ulong[16]; q = new ulong[16];
for (int i = 0; i < 4; i++)
{
p[i] = (y.b >> (l / 4 * i)) & mask;
p[i + 4] = (y.t >> (l / 4 * i)) & mask;
q[i] = (b >> (l / 4 * i)) & mask;
q[i + 4] = (a >> (l / 4 * i)) & mask;
}
r = new ulong[16];
for (int i = 0; i < 16; i++)
for (int j = 0; i + j < 16; j++)
r[i + j] += p[i] * q[j];
for (int j = 0; j < 15; j++)
{
r[j + 1] += r[j] >> (l / 4);
r[j] &= mask;
}
for (int i = 0; i < 8; i++) p[i] = mask - r[i];
for (int i = 0; i < 8; i++)
{
if (p[i] != mask)
{
p[i]++;
break;
}
else p[i] = 0;
}
p[8]++;
r = new ulong[16];
for (int i = 0; i < 16; i++)
for (int j = 0; i + j < 16; j++)
r[i + j] += p[i] * q[j];
for (int i = 0; i < 15; i++)
{
r[i + 1] += r[i] >> (l / 4);
r[i] &= mask;
}
a = 0; b = 0;
for (int i = 0; i < 4; i++)
{
a |= r[i + 12] << (l / 4 * i);
b |= r[i + 8] << (l / 4 * i);
}
if (a == aprv && b == bprv) break;
aprv = a; bprv = b;
}
p = new ulong[16]; q = new ulong[16];
for (int j = 0; j < 4; j++)
{
p[j] = (x.b >> (l / 4 * j)) & mask;
p[j + 4] = (x.t >> (l / 4 * j)) & mask;
q[j] = (b >> (l / 4 * j)) & mask;
q[j + 4] = (a >> (l / 4 * j)) & mask;
}
r = new ulong[16];
for (int j = 0; j < 8; j++)
for (int k = 0; k < 8; k++)
r[j + k] += q[j] * p[k];
for (int j = 0; j < 15; j++)
{
r[j + 1] += r[j] >> (l / 4);
r[j] &= mask;
}
a = 0; b = 0;
for (int j = 0; j < 4; j++)
{
a |= r[j + 12] << (l / 4 * j);
b |= r[j + 8] << (l / 4 * j);
}
var n = new UInt128(a, b);
return x >= y * (n + 1) ? n + 1 : n;
}
public static UInt128 operator %(UInt128 x, UInt128 y) => x - (x / y) * y;
public static UInt128 operator >>(UInt128 x, int d)
{
if (d >= 2 * l) return new UInt128(0);
if (d >= l) return new UInt128(0, x.t >> (d - l));
return new UInt128(x.t >> d, ((x.t ^ ((x.t >> d) << d)) << (l - d)) | (x.b >> d));
}
public static UInt128 operator <<(UInt128 x, int d)
{
if (d >= 2 * l) return new UInt128(0);
if (d >= l) return new UInt128(x.b << (d - l), 0);
return new UInt128((x.t << d) | ((x.b ^ ((x.b << d) >> d)) >> (l - d)), x.b << d);
}
public static UInt128 operator &(UInt128 x, UInt128 y) => new UInt128(x.t & y.t, x.b & y.b);
public static UInt128 operator |(UInt128 x, UInt128 y) => new UInt128(x.t | y.t, x.b | y.b);
}
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()); }
}