#798327 (C++17) No.2074 Product is Square ?

• 問題: No.2074 Product is Square ?
• ユーザー: kys
• 提出日時: 2022-09-16 22:53:46
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: TLE
• 実行時間: -
• コード長: 7,667 bytes
• コンパイル時間: 2,390 ms
• コンパイル使用メモリ: 218,824 KB
• 最終ジャッジ日時: 2025-02-07 10:25:16
• ジャッジサーバーID （参考情報）: judge3 / judge1

ファイルパターン	結果
sample	AC * 1
other	AC * 28 TLE * 5

ソースコード

#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#ifdef _MSC_VER
#include <ppl.h>
#else
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
/* const */
constexpr double PI = 3.141592653589793238462643;
/* io */
namespace aux {
    template<typename T, unsigned N, unsigned L> struct tp { static void print(std::ostream& os, const T& v) { os << std::get<N>(v) << ", "; tp<T, N + 1, L>::print(os, v); } };
    template<typename T, unsigned N> struct tp<T, N, N> { static void print(std::ostream& os, const T& v) { os << std::get<N>(v); } };
}
template<typename... Ts> std::ostream& operator<<(std::ostream& os, const std::tuple<Ts...>& t) { os << '['; aux::tp<std::tuple<Ts...>, 0, sizeof...(Ts) - 1>::print(os, t); os << ']'; return os; }
template <class T, class = typename T::iterator, std::enable_if_t<!std::is_same<T, std::string>::value, int> = 0> std::ostream& operator<<(std::ostream& os, T const& a);
template <class T, class S> std::ostream& operator<<(std::ostream& os, std::pair<T, S> const& p) { return os << '[' << p.first << ", " << p.second << ']'; }
template <class T, class S> std::istream& operator>>(std::istream& is, std::pair<T, S>& p) { return is >> p.first >> p.second; }
template <class T, class, std::enable_if_t<!std::is_same<T, std::string>::value, int>>
std::ostream& operator<<(std::ostream& os, T const& a) { bool f = true; os << '['; for (auto const& x : a) { os << (f ? "" : ", ") << x; f = false; } os << ']'; return os; }
template <class T, size_t N, std::enable_if_t<!std::is_same<T, char>::value, int> = 0>
std::ostream& operator<<(std::ostream& os, const T(&a)[N]) { bool f = true; os << '['; for (auto const& x : a) { os << (f ? "" : ", ") << x; f = false; } os << ']'; return os; }
template <class T, class = decltype(std::begin(std::declval<T&>())), class = typename std::enable_if<!std::is_same<T, std::string>::value>::type>
std::istream& operator>>(std::istream& is, T& a) { for (auto& x : a) is >> x; return is; }
struct IOSetup { IOSetup(bool f) { if (f) { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } std::cout << std::fixed << std::setprecision(15); } } iosetup(true);
/* format */
template<typename... Ts> std::string format(const std::string& f, Ts... t) { size_t l = std::snprintf(nullptr, 0, f.c_str(), t...); std::vector<char> b(l + 1); std::snprintf(&b[0], l + 1, f.c_str(), t...); return std::string(&b[0], &b[0] + l); }
/* dump */
#define ENABLE_DUMP
#ifdef ENABLE_DUMP
#define DUMPOUT std::cerr
std::ostringstream DUMPBUF;
#define dump(...) do{DUMPBUF<<"  ";DUMPBUF<<#__VA_ARGS__<<" :[DUMP - "<<__LINE__<<":"<<__FUNCTION__<<"]"<<std::endl;DUMPBUF<<"    ";dump_func(__VA_ARGS__);DUMPOUT<<DUMPBUF.str();DUMPBUF.str("");DUMPBUF.clear();}while(0);
void dump_func() { DUMPBUF << std::endl; }
template <class Head, class... Tail> void dump_func(Head&& head, Tail&&... tail) { DUMPBUF << head; if (sizeof...(Tail) == 0) { DUMPBUF << " "; } else { DUMPBUF << ", "; } dump_func(std::move(tail)...); }
#else
#define dump(...) void(0);
#endif
/* misc */
struct Timer {
    double t = 0, paused = 0, tmp; Timer() { reset(); } static double time() {
#ifdef _MSC_VER
        return __rdtsc() / 3.0e9;
#else
        unsigned long long a, d;
        __asm__ volatile("rdtsc"
            : "=a"(a), "=d"(d));
        return (d << 32 | a) / 3.0e9;
#endif
    } void reset() { t = time(); } void pause() { tmp = time(); } void restart() { paused += time() - tmp; } double elapsedMs() { return (time() - t - paused) * 1000.0; }
} timer;
struct Xorshift {
    uint64_t x = 88172645463325252LL;
    void set_seed(unsigned seed, int rep = 100) { x = (seed + 1) * 10007; for (int i = 0; i < rep; i++) next_int(); }
    unsigned next_int() { x = x ^ (x << 7); return x = x ^ (x >> 9); }
    unsigned next_int(unsigned mod) { x = x ^ (x << 7); x = x ^ (x >> 9); return x % mod; }
    unsigned next_int(unsigned l, unsigned r) { x = x ^ (x << 7); x = x ^ (x >> 9); return x % (r - l + 1) + l; }
    double next_double() { return double(next_int()) / UINT_MAX; }
} rnd;
template<typename T> void shuffle_vector(std::vector<T>& v, Xorshift& rnd) { int n = v.size(); for (int i = n - 1; i >= 1; i--) { int r = rnd.next_int(i); std::swap(v[i], v[r]); } }
std::vector<std::string> split(std::string str, const std::string& delim) { for (char& c : str) if (delim.find(c) != std::string::npos) c = ' '; std::istringstream iss(str); std::vector<std::string> parsed; std::string buf; while (iss >> buf) parsed.push_back(buf); return parsed; }

template<typename T, typename ...Args> auto make_vector(T x, int arg, Args ...args) { if constexpr (sizeof...(args) == 0)return std::vector<T>(arg, x); else return std::vector(arg, make_vector<T>(x, args...)); }
template<typename T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; }
template<typename T> bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;
using pdd = std::pair<double, double>;

using namespace std;
// Miller-Rabin 素数判定法
template<class T> T pow_mod(T A, T N, T M) {
    T res = 1 % M;
    A %= M;
    while (N) {
        if (N & 1) res = (res * A) % M;
        A = (A * A) % M;
        N >>= 1;
    }
    return res;
}

bool is_prime(long long N) {
    if (N <= 1) return false;
    if (N == 2 || N == 3) return true;
    if (N % 2 == 0) return false;
    vector<long long> A = {2, 325, 9375, 28178, 450775,
                           9780504, 1795265022};
    long long s = 0, d = N - 1;
    while (d % 2 == 0) {
        ++s;
        d >>= 1;
    }
    for (auto a : A) {
        if (a % N == 0) return true;
        long long t, x = pow_mod<__int128_t>(a, d, N);
        if (x != 1) {
            for (t = 0; t < s; ++t) {
                if (x == N - 1) break;
                x = __int128_t(x) * x % N;
            }
            if (t == s) return false;
        }
    }
    return true;
}

// Pollard のロー法
long long gcd(long long A, long long B) {
    A = abs(A), B = abs(B);
    if (B == 0) return A;
    else return gcd(B, A % B);
}
    
long long pollard(long long N) {
    if (N % 2 == 0) return 2;
    if (is_prime(N)) return N;

    auto f = [&](long long x) -> long long {
        return (__int128_t(x) * x + 1) % N;
    };
    long long step = 0;
    while (true) {
        ++step;
        long long x = step, y = f(x);
        while (true) {
            long long p = gcd(y - x + N, N);
            if (p == 0 || p == N) break;
            if (p != 1) return p;
            x = f(x);
            y = f(f(y));
        }
    }
}

vector<long long> prime_factorize(long long N) {
    if (N == 1) return {};
    long long p = pollard(N);
    if (p == N) return {p};
    vector<long long> left = prime_factorize(p);
    vector<long long> right = prime_factorize(N / p);
    left.insert(left.end(), right.begin(), right.end());
    sort(left.begin(), left.end());
    return left;
}

int main() {
    int T;
    cin >> T;
    for (int t = 0; t < T; t++) {
        int N;
        cin >> N;
        vector<long long> A(N);
        cin >> A;
        set<int> res;
        for (auto a: A) {
            auto x = prime_factorize(a);
            for (auto y: x) {
                if (res.find(y) == res.end()) {
                    res.insert(y);
                } else {
                    res.erase(y);
                }
            }
            // dump(x);
        }
        // dump(res);
        if (res.empty()) {
            cout << "Yes" << endl;
        } else {
            cout << "No" << endl;
        }
    }
}