結果

問題 No.2074 Product is Square ?
ユーザー ei1333333ei1333333
提出日時 2022-09-16 22:09:33
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 40 ms / 2,000 ms
コード長 11,613 bytes
コンパイル時間 2,579 ms
コンパイル使用メモリ 222,864 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-08-23 15:44:36
合計ジャッジ時間 4,482 ms
ジャッジサーバーID
(参考情報)
judge15 / judge12
このコードへのチャレンジ(β)

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 2 ms
4,376 KB
testcase_01 AC 15 ms
4,380 KB
testcase_02 AC 15 ms
4,376 KB
testcase_03 AC 16 ms
4,380 KB
testcase_04 AC 15 ms
4,376 KB
testcase_05 AC 15 ms
4,376 KB
testcase_06 AC 17 ms
4,380 KB
testcase_07 AC 17 ms
4,380 KB
testcase_08 AC 16 ms
4,376 KB
testcase_09 AC 16 ms
4,380 KB
testcase_10 AC 16 ms
4,376 KB
testcase_11 AC 11 ms
4,380 KB
testcase_12 AC 35 ms
4,380 KB
testcase_13 AC 7 ms
4,380 KB
testcase_14 AC 20 ms
4,376 KB
testcase_15 AC 11 ms
4,376 KB
testcase_16 AC 36 ms
4,376 KB
testcase_17 AC 6 ms
4,380 KB
testcase_18 AC 22 ms
4,376 KB
testcase_19 AC 11 ms
4,376 KB
testcase_20 AC 36 ms
4,376 KB
testcase_21 AC 6 ms
4,376 KB
testcase_22 AC 19 ms
4,376 KB
testcase_23 AC 11 ms
4,376 KB
testcase_24 AC 37 ms
4,380 KB
testcase_25 AC 6 ms
4,380 KB
testcase_26 AC 22 ms
4,376 KB
testcase_27 AC 10 ms
4,376 KB
testcase_28 AC 40 ms
4,380 KB
testcase_29 AC 6 ms
4,380 KB
testcase_30 AC 20 ms
4,376 KB
testcase_31 AC 2 ms
4,380 KB
testcase_32 AC 2 ms
4,380 KB
testcase_33 AC 3 ms
4,376 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

#include<bits/stdc++.h>
using namespace std;

using int64 = long long;

const int mod = 998244353;

const int64 infll = (1LL << 62) - 1;

const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for (int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for (T &in: v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for (auto &e: t) fill_v(e, v);
}

template< typename F >
struct FixPoint: F {
  explicit FixPoint(F &&f): F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

// submitting https://judge.yosupo.jp/submission/85445 with pragmas

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")


/*vvvvvvvvvvvvvvvvvvv LIBRARIES, TYPE DEFINITIONS, MACROS vvvvvvvvvvvvvvvvvvv*/
#include <algorithm>
#include <array>
#include <cassert>
#include <cctype>
#include <chrono>
#include <cstdint>
#include <cstdio>
#include <functional>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <string>
#include <type_traits>

using namespace std;

using namespace chrono;


// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
// template<class k_t, class m_t>
// using ordered_map = tree<k_t, m_t, less<T>, rb_tree_tag,
//	tree_order_statistics_node_update>;
// template<class T>
// using ordered_set = ordered_map<T, null_type>;

using i8 = int8_t;
using u8 = uint8_t;
using i16 = int16_t;
using u16 = uint16_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using f32 = float;
using f64 = double;
using fe = long double;
using i128 = __int128_t;
using u128 = __uint128_t;
template<class T>
using eueuq_ytiroirp = priority_queue<T, vector<T>, greater<T>>;

#define bend(a) (a).begin(), (a).end()
#define rbend(a) (a).rbegin(), (a).rend()
#define binlow(a, v) (lower_bound(bend(a), v) - (a).begin())
#define binup(a, v) (upper_bound(bend(a), v) - (a).begin())
/*^^^^^^^^^^^^^^^^^^^ LIBRARIES, TYPE DEFINITIONS, MACROS ^^^^^^^^^^^^^^^^^^^*/

/*vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv FAST IO vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv*/
template<class T>
void readu(T& a) {
  char c; do c = getchar(); while (!isdigit(c)); a = c & 15;
  for (;;) {c = getchar(); if (!isdigit(c)) break; a = a * 10 + (c & 15);}
}
template<class T>
void readi(T& a) {
  char c; bool n = false; do c = getchar(); while (!isdigit(c) && c != '-');
  if (c == '-') n = true, c = getchar(); a = c & 15;
  for (;;) {c = getchar(); if (!isdigit(c)) break; a = a * 10 + (c & 15);}
  if (n) a = -a;
}
/*^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ FAST IO ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*/

/*vvvvvvvvvvvvvvvvvvvvvvvvvvvv COMMON FUNCTIONS vvvvvvvvvvvvvvvvvvvvvvvvvvvv*/
template<class T1, class T2>
T1& cmin(T1& a, const T2& b) {return a < b ? a : a = b;}
template<class T1, class T2>
T1& cmax(T1& a, const T2& b) {return a < b ? a = b : a;}
u64 gt() {return steady_clock::now().time_since_epoch().count();};
const f64 gtp = (f64) steady_clock::period::num / steady_clock::period::den;
void sleep(long double t) {t = t / gtp + gt(); while (gt() < t);}
/*^^^^^^^^^^^^^^^^^^^^^^^^^^^^ COMMON FUNCTIONS ^^^^^^^^^^^^^^^^^^^^^^^^^^^^*/

/*vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv LIBRARY vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv*/
template<i32 m>
class mint {
  using t = mint;
  static_assert(m < 1 << 30);
  static constexpr i32 inv(i32 x) { i32 b = 1, a = m, c = 0, d;
    while (x) d = a / x; a -= d * x; c -= d * b; swap(a, x); swap(b, c);
    return c;
  }
public:
  i32 v; mint(i32 v = 0) : v(v) {if ((v %= m) < 0) v += m;}
  t& operator+=(const t& r) {if ((v += r.v) >= m) v -= m; return *this;}
  t& operator-=(const t& r) {if ((v -= r.v) < 0) v += m; return *this;}
  t& operator*=(const t& r) {v = (u64) v * r.v % m; return *this;}
  t& operator/=(const t& r) {return *this *= inv(r.v);}
  t& operator++() {if (++v == m) v = 0; return *this;}
  t& operator--() {if (--v == -1) v = m - 1; return *this;}
  t operator+(const t& r) const {return t(*this) += r;}
  t operator-(const t& r) const {return t(*this) -= r;}
  t operator*(const t& r) const {return t(*this) *= r;}
  t operator/(const t& r) const {return t(*this) /= r;}
  t operator++(int) {t u = v; operator++(); return u;}
  t operator--(int) {t u = v; operator--(); return u;}
  bool operator==(const t& r) const {return v == r.v;}
  bool operator!=(const t& r) const {return v != r.v;}
  bool operator<(const t& r) const {return v < r.v;}
  bool operator>(const t& r) const {return v > r.v;}
  bool operator<=(const t& r) const {return v <= r.v;}
  bool operator>=(const t& r) const {return v >= r.v;}
};
template<class T>
constexpr T inv(T x, T y) {
  T Y = y, a = 1, b = 0, d = 0;
  while (x) d = y / x, y -= d * x, b -= d * a, swap(x, y), swap(a, b);
  assert(y == 1); return b + Y;
}
template<class T, class T2>
struct lazy_mont {
  const T n, n2, ni, r2, r3;
  constexpr T redc(T2 x) const {
    return T(x) * ni * T2(n) + x >> 8 * sizeof(T);
  }
  constexpr lazy_mont(T n) : n(n), n2(n * 2), r2(T2(-1) % n + 1), ni([n]() {
    T r = -n; while (n * r + 1) r *= 2 + n * r; return r;}()),
                             r3(mul(r2, r2)) {assert(n & 1 && n <= numeric_limits<T>::max() / 4);}
  T mul(const T &x, const T &y) const {return redc(T2(x) * y);}
  T operator()(const T &x) const {return mul(x, r2);}
  T get(T x) const {x = redc(x); return x - n * (x >= n);}
  T add(const T &x, T y) const {y = x + y; return y < x ? y - n2 : y;}
  T neg(const T &x) const {return n2 - x;}
  T sub(const T &x, T y) const {y = x - y; return y < x ? y : y + n2;}
  T inv(const T &x) const {return mul(inv(x), r3);}
  bool neq(const T &x, const T &y) const {
    return x - y && x + n - y && y + n - x;
  }
  bool eq(const T &x, const T &y) const {return !neq(x, y);}
};
using lm32 = lazy_mont<u32, u64>;
using lm64 = lazy_mont<u64, u128>;
bool mr32(const lm32 &lm, u32 a) {
  if (!(a %= lm.n)) return 1;
  a = lm(a); u8 r = __builtin_ctz(lm.n - 1); u32 d = lm.n >> r, p = lm(1);
  for (; d; d >>= 1, a = lm.mul(a, a)) if (d & 1) p = lm.mul(p, a);
  if (lm.eq(p, lm(1))) return 1;
  while (lm.neq(p, lm(lm.n - 1)) && --r) p = lm.mul(p, p);
  return lm.eq(p, lm(lm.n - 1));
}
bool mr64(const lm64 &lm, u64 a) {
  if (!(a %= lm.n)) return 1;
  a = lm(a); u8 r = __builtin_ctzll(lm.n - 1); u64 d = lm.n >> r, p = lm(1);
  for (; d; d >>= 1, a = lm.mul(a, a)) if (d & 1) p = lm.mul(p, a);
  if (lm.eq(p, lm(1))) return 1;
  while (lm.neq(p, lm(lm.n - 1)) && --r) p = lm.mul(p, p);
  return lm.eq(p, lm(lm.n - 1));
}
// deterministic miller rabin
// bases obtained from
// https://miller-rabin.appspot.com/
bool dmr32(const lm32 &lm) {
  if (lm.n > 316349280) return mr32(lm, 2) && mr32(lm, 7) && mr32(lm, 61);
  if (lm.n > 49140) return mr32(lm, 11000544) && mr32(lm, 31481107);
  return mr32(lm, 921211727);
}
bool dmr64(const lm64 &lm) {
  if (lm.n > 585226005592931976) return mr64(lm, 2) && mr64(lm, 325) &&
                                        mr64(lm, 9375) && mr64(lm, 28178) && mr64(lm, 450775) &&
                                        mr64(lm, 9780504) && mr64(lm, 1795265022);
  if (lm.n > 7999252175582850) return mr64(lm, 2) &&
                                      mr64(lm, 123635709730000) && mr64(lm, 9233062284813009) &&
                                      mr64(lm, 43835965440333360) && mr64(lm, 761179012939631437) &&
                                      mr64(lm, 1263739024124850375);
  if (lm.n > 55245642489450) return mr64(lm, 2) && mr64(lm, 4130806001517) &&
                                    mr64(lm, 149795463772692060) && mr64(lm, 186635894390467037) &&
                                    mr64(lm, 3967304179347715805);
  if (lm.n > 350269456336) return mr64(lm, 2) && mr64(lm, 141889084524735) &&
                                  mr64(lm, 1199124725622454117) && mr64(lm, 11096072698276303650u);
  if (lm.n > 0x3FFFFFFF) return mr64(lm, 4230279247111683200) &&
                                mr64(lm, 14694767155120705706u) && mr64(lm, 16641139526367750375u);
  return dmr32(lm.n);
}
bool is_prime(u64 n) {
  for (u8 i : {2, 3, 5, 7}) {if (n % i == 0) return n == i;}
  return n < 121 ? n > 2 : dmr64(n);
}
vector<u64> factorise(u64 n) {
  /*
    factorises integers 1 <= n <= 2^62
    bad cases: all prime factors are large
    very bad cases:
      1e18: 999995891929828291, 3 times worse than other bad cases
      2^62: 4611653436861561323, 7 times worse than other bad cases
          = 0x3fffe25e0357b9eb
  */
  vector<u64> pf;
  for (u8 i : {2, 3, 5}) while (!(n % i)) pf.push_back(i), n /= i;
  for (u16 i = 7; i * i <= n && i <= 211; i += 6) for (u16 j : {0, 4})
      while (n % (i + j) == 0) pf.push_back(i + j), n /= i + j;
  if (n == 1) return pf;
  vector<u64> q{n};
  while (!q.empty()) {
    n = q.back(); q.pop_back();
    if (n < 49729) {pf.push_back(n); continue;}
    u64 r = sqrt(n) + 0.5;
    if (r * r == n) {q.resize(q.size() + 2, r); continue;}
    lm64 lm(n);
    if (dmr64(lm)) {pf.push_back(n); continue;}
    u64 g = n, ni = lm.ni;
    auto f = [lm](u64 x) {return lm.redc(u128(x) * x + 1);};
    const u64 m = 1 << (51 - __builtin_clzll(n) >> 2);
    for (u64 x0 = 0; g == n; ++x0) {
      u64 x, y = x0, q = g = 1, ys;
      for (u64 r = 1; g == 1; r <<= 1) {
        x = y;
        for (u64 _ = r; _--;) y = f(y);
        for (u64 k = 0; k < r && g == 1; k += m) {
          ys = y;
          for (u64 _ = min(m, r - k); _--;)
            y = f(y), q = lm.mul(max(x, y) - min(x, y), q);
          g = gcd(q, n);
        }
      }
      if (g == n) for (g = 1; g == 1;)
          ys = f(ys), g = gcd(max(x, ys) - min(x, ys), n);
    }
    q.push_back(g); q.push_back(n / g);
  }
  sort(bend(pf));
  return pf;
}
/*^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ LIBRARY ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*/

int main() {
  int T;
  cin >> T;
  while(T--) {
    int N;
    cin >> N;
    vector< int64 > A(N);
    cin >> A;
    map< uint64_t, int > mp;
    for(auto& a : A) {
      for(auto& f : factorise(a)) {
        mp[f] ^= 1;
      }
    }
    bool ok = true;
    for(auto& p : mp) ok &= not p.second;
    if(ok) cout << "Yes" << endl;
    else cout << "No" << endl;
  }
}
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