結果
| 問題 | No.577 Prime Powerful Numbers |
| ユーザー |
 りあん
|
| 提出日時 | 2017-10-13 23:33:26 |
| 言語 | C#(csc) (csc 3.9.0) |
| 結果 |
AC
|
| 実行時間 | 1,941 ms / 2,000 ms |
| コード長 | 14,599 bytes |
| コンパイル時間 | 1,314 ms |
| コンパイル使用メモリ | 116,096 KB |
| 実行使用メモリ | 22,528 KB |
| 最終ジャッジ日時 | 2024-11-17 18:14:23 |
| 合計ジャッジ時間 | 7,232 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
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 | 50 ms
21,472 KB |
| testcase_01 | AC | 176 ms
22,136 KB |
| testcase_02 | AC | 29 ms
18,304 KB |
| testcase_03 | AC | 422 ms
22,132 KB |
| testcase_04 | AC | 70 ms
22,400 KB |
| testcase_05 | AC | 1,768 ms
22,136 KB |
| testcase_06 | AC | 323 ms
22,396 KB |
| testcase_07 | AC | 1,941 ms
22,528 KB |
| testcase_08 | AC | 437 ms
22,260 KB |
| testcase_09 | AC | 342 ms
22,136 KB |
| testcase_10 | AC | 27 ms
18,012 KB |
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.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;
using System.Numerics;
using static util;
using P = pair<int, int>;
using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;
class Program
{
static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
static Scan sc = new Scan();
const int M = 1000000007;
const double eps = 1e-11;
static readonly int[] dd = { 0, 1, 0, -1, 0 };
static void Main()
{
int q = sc.Int;
var prs = mymath.getprimes(40000);
for (int i = 0; i < q; i++)
{
var n = sc.Long;
if (n < 4) {
Prt("No");
continue;
}
if (n % 2 == 0) {
Prt("Yes");
continue;
}
long p2 = 1;
while (p2 * 2 < n) {
p2 *= 2;
long m = n - p2;
if (m <= 1) break;
if (isprime(m)) {
goto A;
}
long d = Math.Max((long)Math.Pow(m, 1.0 / 2) - 3, 3);
for (long j = d; j * j <= m; j++)
{
if (isprime(j) && j * j == m) {
goto A;
}
}
d = Math.Max((long)Math.Pow(m, 1.0 / 3) - 3, 3);
for (long j = d; (double)j * j * j - 1 <= m; j++)
{
if (isprime(j) && j * j * j == m) {
goto A;
}
}
foreach (var item in prs)
{
if ((double)item * item * item * item - 1 > m) break;
long t = m;
while (t % item == 0)
{
t /= item;
}
if (t == 1) {
goto A;
}
}
}
Prt("No");
continue;
A:
Prt("Yes");
}
sw.Flush();
}
static BigInteger powmod(BigInteger a, BigInteger b, BigInteger M)
{
if (b == 0) return 1;
if (b == 1) return a % M;
var t = powmod(a, b / 2, M);
if ((b & 1) == 0) return t * t % M;
else return t * t * a % M;
}
static bool suspect(BigInteger a, int s, BigInteger d, BigInteger n)
{
BigInteger x = powmod(a, d, n);
if (x == 1) return true;
for (int r = 0; r < s; ++r)
{
if (x == n - 1) return true;
x = x * x % n;
}
return false;
}
// {2,7,61,-1} is for n < 4759123141 (= 2^32)
// {2,3,5,7,11,13,17,19,23,-1} is for n < 10^16 (at least)
static bool isprime(long n)
{
if (n <= 1 || (n > 2 && n % 2 == 0)) return false;
var test = new int[] { 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,-1 };
long d = n - 1;
int s = 0;
while (d % 2 == 0)
{
++s;
d /= 2;
}
for (int i = 0; test[i] < n && test[i] != -1; ++i)
if (!suspect(test[i], s, d, n))
return false;
return true;
}
static void DBG(string a) { Console.WriteLine(a); }
static void DBG<T>(IEnumerable<T> a) { DBG(string.Join(" ", a)); }
static void DBG(params object[] a) { DBG(string.Join(" ", a)); }
static void Prt(string a) { sw.WriteLine(a); }
static void Prt<T>(IEnumerable<T> a) { Prt(string.Join(" ", a)); }
static void Prt(params object[] a) { Prt(string.Join(" ", a)); }
// for AOJ
// static string Join<T>(string sep, IEnumerable<T> a) { return string.Join(sep, a.Select(x => x.ToString()).ToArray()); }
// static void DBG<T>(IEnumerable<T> a) { DBG(Join(" ", a)); }
// static void DBG(params object[] a) { DBG(Join(" ", a)); }
// static void Prt<T>(IEnumerable<T> a) { Prt(Join(" ", a)); }
// static void Prt(params object[] a) { Prt(Join(" ", a)); }
}
class pair<T, U> : IComparable<pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
public T v1;
public U v2;
public pair(T v1, U v2) {
this.v1 = v1;
this.v2 = v2;
}
public int CompareTo(pair<T, U> a) {
return v1.CompareTo(a.v1) != 0 ? v1.CompareTo(a.v1) : v2.CompareTo(a.v2);
}
public override string ToString() {
return v1 + " " + v2;
}
}
static class util
{
public static pair<T, U> make_pair<T, U>(T v1, U v2) where T : IComparable<T> where U : IComparable<U> {
return new pair<T, U>(v1, v2);
}
public static T Max<T>(params T[] a) { return a.Max(); }
public static T Min<T>(params T[] a) { return a.Min(); }
public static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
public static void swap<T>(this IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
public static T[] copy<T>(this IList<T> a) {
var ret = new T[a.Count];
for (int i = 0; i < a.Count; i++) ret[i] = a[i];
return ret;
}
}
static class Operator<T>
{
static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
public static Func<T, T, T> Lambda(Binary op) { return Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile(); }
public static Func<T, T> Lambda(Unary op) { return Expression.Lambda<Func<T, T>>(op(x), x).Compile(); }
}
class Scan
{
public int Int { get { return int.Parse(Str); } }
public long Long { get { return long.Parse(Str); } }
public double Double { get { return double.Parse(Str); } }
public string Str { get { return Console.ReadLine().Trim(); } }
public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } }
public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } }
public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } }
public string[] StrArr { get { return Str.Split(); } }
bool eq<T, U>() { return typeof(T).Equals(typeof(U)); }
T ct<T, U>(U a) { return (T)Convert.ChangeType(a, typeof(T)); }
T cv<T>(string s) { return eq<T, int>() ? ct<T, int>(int.Parse(s))
: eq<T, long>() ? ct<T, long>(long.Parse(s))
: eq<T, double>() ? ct<T, double>(double.Parse(s))
: eq<T, char>() ? ct<T, char>(s[0])
: ct<T, string>(s); }
public void Multi<T>(out T a) { a = cv<T>(Str); }
public void Multi<T, U>(out T a, out U b)
{ var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
public void Multi<T, U, V>(out T a, out U b, out V c)
{ var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
{ var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
{ var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
{ var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); }
public void Multi<T, U, V, W, X, Y, Z>(out T a, out U b, out V c, out W d, out X e, out Y f, out Z g)
{ var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); g = cv<Z>(ar[6]);}
}
static class mymath
{
public static long Mod = 1000000007;
public static bool isprime(long a) {
if (a < 2) return false;
for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
return true;
}
public static bool[] sieve(int n) {
var p = new bool[n + 1];
for (int i = 2; i <= n; i++) p[i] = true;
for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false;
return p;
}
public static List<int> getprimes(int n) {
var prs = new List<int>();
var p = sieve(n);
for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i);
return prs;
}
public static long[][] E(int n) {
var ret = new long[n][];
for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; }
return ret;
}
public static double[][] dE(int n) {
var ret = new double[n][];
for (int i = 0; i < n; i++) { ret[i] = new double[n]; ret[i][i] = 1; }
return ret;
}
public static long[][] pow(long[][] A, long n) {
if (n == 0) return E(A.Length);
var t = pow(A, n / 2);
if ((n & 1) == 0) return mul(t, t);
return mul(mul(t, t), A);
}
public static double[][] pow(double[][] A, long n) {
if (n == 0) return dE(A.Length);
var t = pow(A, n / 2);
if ((n & 1) == 0) return mul(t, t);
return mul(mul(t, t), A);
}
public static double dot(double[] x, double[] y) {
int n = x.Length;
double ret = 0;
for (int i = 0; i < n; i++) ret += x[i] * y[i];
return ret;
}
public static double _dot(double[] x, double[] y) {
int n = x.Length;
double ret = 0, r = 0;
for (int i = 0; i < n; i++) {
double s = ret + (x[i] * y[i] + r);
r = (x[i] * y[i] + r) - (s - ret);
ret = s;
}
return ret;
}
public static long dot(long[] x, long[] y) {
int n = x.Length;
long ret = 0;
for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
return ret;
}
public static T[][] trans<T>(T[][] A) {
int n = A[0].Length, m = A.Length;
var ret = new T[n][];
for (int i = 0; i < n; i++) { ret[i] = new T[m]; for (int j = 0; j < m; j++) ret[i][j] = A[j][i]; }
return ret;
}
public static double[] mul(double[][] A, double[] x) {
int n = A.Length;
var ret = new double[n];
for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
return ret;
}
public static long[] mul(long[][] A, long[] x) {
int n = A.Length;
var ret = new long[n];
for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
return ret;
}
public static long[][] mul(long[][] A, long[][] B) {
int n = A.Length;
var Bt = trans(B);
var ret = new long[n][];
for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
return ret;
}
public static double[][] mul(double[][] A, double[][] B) {
int n = A.Length;
var Bt = trans(B);
var ret = new double[n][];
for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
return ret;
}
public static long[] add(long[] x, long[] y) {
int n = x.Length;
var ret = new long[n];
for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
return ret;
}
public static long[][] add(long[][] A, long[][] B) {
int n = A.Length;
var ret = new long[n][];
for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
return ret;
}
public static long pow(long a, long b) {
if (a >= Mod) return pow(a % Mod, b);
if (a == 0) return 0;
if (b == 0) return 1;
var t = pow(a, b / 2);
if ((b & 1) == 0) return t * t % Mod;
return t * t % Mod * a % Mod;
}
public static long inv(long a) { return pow(a, Mod - 2); }
public static long gcd(long a, long b) {
while (b > 0) { var t = a % b; a = b; b = t; } return a;
}
// a x + b y = gcd(a, b)
public static long extgcd(long a, long b, out long x, out long y) {
long g = a; x = 1; y = 0;
if (b > 0) { g = extgcd(b, a % b, out y, out x); y -= a / b * x; }
return g;
}
public static long lcm(long a, long b) { return a / gcd(a, b) * b; }
static long[] facts;
public static long[] setfacts(int n) {
facts = new long[n + 1];
facts[0] = 1;
for (int i = 0; i < n; i++) facts[i + 1] = facts[i] * (i + 1) % Mod;
return facts;
}
public static long comb(int n, int r) {
if (n < 0 || r < 0 || r > n) return 0;
if (n - r < r) r = n - r;
if (r == 0) return 1;
if (r == 1) return n;
if (facts != null && facts.Length > n) return facts[n] * inv(facts[r]) % Mod * inv(facts[n - r]) % Mod;
int[] numer = new int[r], denom = new int[r];
for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; }
for (int p = 2; p <= r; p++) {
int piv = denom[p - 1];
if (piv > 1) {
int ofst = (n - r) % p;
for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; }
}
}
long ret = 1;
for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod;
return ret;
}
public static long[][] getcombs(int n) {
var ret = new long[n + 1][];
for (int i = 0; i <= n; i++) {
ret[i] = new long[i + 1];
ret[i][0] = ret[i][i] = 1;
for (int j = 1; j < i; j++) ret[i][j] = (ret[i - 1][j - 1] + ret[i - 1][j]) % Mod;
}
return ret;
}
// nC0, nC2, ..., nCn
public static long[] getcomb(int n) {
var ret = new long[n + 1];
ret[0] = 1;
for (int i = 0; i < n; i++) ret[i + 1] = ret[i] * (n - i) % Mod * inv(i + 1) % Mod;
return ret;
}
}