結果

問題 No.2074 Product is Square ?
ユーザー rniyarniya
提出日時 2022-09-16 21:53:21
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 175 ms / 2,000 ms
コード長 10,318 bytes
コンパイル時間 2,894 ms
コンパイル使用メモリ 219,900 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-12-21 19:11:00
合計ジャッジ時間 5,796 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
このコードへのチャレンジ
（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 2 ms
5,248 KB
testcase_01 AC 39 ms
5,248 KB
testcase_02 AC 41 ms
5,248 KB
testcase_03 AC 43 ms
5,248 KB
testcase_04 AC 42 ms
5,248 KB
testcase_05 AC 42 ms
5,248 KB
testcase_06 AC 43 ms
5,248 KB
testcase_07 AC 41 ms
5,248 KB
testcase_08 AC 40 ms
5,248 KB
testcase_09 AC 41 ms
5,248 KB
testcase_10 AC 42 ms
5,248 KB
testcase_11 AC 16 ms
5,248 KB
testcase_12 AC 44 ms
5,248 KB
testcase_13 AC 172 ms
5,248 KB
testcase_14 AC 29 ms
5,248 KB
testcase_15 AC 16 ms
5,248 KB
testcase_16 AC 46 ms
5,248 KB
testcase_17 AC 174 ms
5,248 KB
testcase_18 AC 29 ms
5,248 KB
testcase_19 AC 18 ms
5,248 KB
testcase_20 AC 46 ms
5,248 KB
testcase_21 AC 175 ms
5,248 KB
testcase_22 AC 27 ms
5,248 KB
testcase_23 AC 15 ms
5,248 KB
testcase_24 AC 44 ms
5,248 KB
testcase_25 AC 168 ms
5,248 KB
testcase_26 AC 29 ms
5,248 KB
testcase_27 AC 15 ms
5,248 KB
testcase_28 AC 48 ms
5,248 KB
testcase_29 AC 171 ms
5,248 KB
testcase_30 AC 28 ms
5,248 KB
testcase_31 AC 5 ms
5,248 KB
testcase_32 AC 3 ms
5,248 KB
testcase_33 AC 3 ms
5,248 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 # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}
template <typename T, size_t N> ostream& operator<<(ostream& os, const array<T, N>& v) {
    for (size_t i = 0; i < N; i++) {
        os << v[i] << (i + 1 == N ? "" : " ");
    }
    return os;
}

template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
    if (i) os << ',';
    os << get<i>(t);
    print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
    os << '{';
    print_tuple<0, tuple<Args...>, Args...>(os, t);
    return os << '}';
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) void(0)
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}

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

template <typename T> void mkuni(vector<T>& v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }
#pragma endregion

namespace fast_factorize {
using u64 = uint64_t;

mt19937_64 mt(random_device{}());
u64 rng(u64 n) { return uniform_int_distribution<u64>(0, n - 1)(mt); }

struct montgomery64 {
    using i64 = int64_t;
    using u64 = uint64_t;
    using u128 = __uint128_t;

    static u64 mod, r, n2;

    static u64 get_r() {
        u64 res = mod;
        for (int _ = 0; _ < 5; _++) res *= 2 - mod * res;
        return -res;
    }

    static void set_mod(u64 m) {
        assert(m < (1ULL << 62));
        assert((m & 1) == 1);
        mod = m;
        n2 = -u128(m) % m;
        r = get_r();
        assert(r * mod == -1ULL);
    }
    static u64 get_mod() { return mod; }

    static u64 reduce(const u128& x) noexcept { return (x + u128(u64(x) * r) * mod) >> 64; }

    u64 v;
    montgomery64() : v(0) {}
    montgomery64(const i64& v) : v(reduce((u128(v) + mod) * n2)) {}
    u64 value() const {
        u64 res = reduce(v);
        return res >= mod ? res - mod : res;
    }
    montgomery64& operator+=(const montgomery64& rhs) {
        if (i64(v += rhs.v - (mod << 1)) < 0) v += mod << 1;
        return *this;
    }
    montgomery64& operator-=(const montgomery64& rhs) {
        if (i64(v -= rhs.v) < 0) v += mod << 1;
        return *this;
    }
    montgomery64& operator*=(const montgomery64& rhs) {
        v = reduce(u128(v) * rhs.v);
        return *this;
    }
    montgomery64 operator+(const montgomery64& rhs) const { return montgomery64(*this) += rhs; }
    montgomery64 operator-(const montgomery64& rhs) const { return montgomery64(*this) -= rhs; }
    montgomery64 operator*(const montgomery64& rhs) const { return montgomery64(*this) *= rhs; }
    bool operator==(const montgomery64& rhs) const {
        return (v >= mod ? v - mod : v) == (rhs.v >= mod ? rhs.v - mod : rhs.v);
    }
    bool operator!=(const montgomery64& rhs) const {
        return (v >= mod ? v - mod : v) != (rhs.v >= mod ? rhs.v - mod : rhs.v);
    }
    montgomery64 pow(u64 n) const {
        montgomery64 self(*this), res(1);
        while (n > 0) {
            if (n & 1) res *= self;
            self *= self;
            n >>= 1;
        }
        return res;
    }
    friend istream& operator>>(istream& s, montgomery64& rhs) {
        i64 v;
        rhs = montgomery64{(s >> v, v)};
        return s;
    }
    friend ostream& operator<<(ostream& s, const montgomery64& rhs) { return s << rhs.v; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;

bool miller_rabin(const u64& n, const vector<u64>& as) {
    if (montgomery64::get_mod() != n) montgomery64::set_mod(n);
    const u64 d = (n - 1) >> __builtin_ctzll(n - 1);
    const montgomery64 one(1), minus_one(n - 1);
    for (u64 a : as) {
        if (n <= a) break;
        u64 t = d;
        montgomery64 y = montgomery64(a).pow(t);
        while (t != n - 1 && y != one && y != minus_one) {
            y *= y;
            t <<= 1;
        }
        if (y != minus_one && t % 2 == 0) return false;
    }
    return true;
}
bool is_prime(const u64& n) {
    if (n == 2 || n == 3 || n == 5 || n == 7) return true;
    if (n % 2 == 0 || n % 3 == 0 || n % 5 == 0 || n % 7 == 0) return false;
    if (n < 121) return n > 1;
    if (n < (1ULL << 32)) return miller_rabin(n, {2, 7, 61});
    return miller_rabin(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

u64 pollard_rho(const u64& n) {
    if (~n & 1) return 2;
    if (is_prime(n)) return n;
    if (montgomery64::get_mod() != n) montgomery64::set_mod(n);
    montgomery64 R, one(1);
    auto f = [&](const montgomery64& x) { return x * x + R; };
    constexpr int m = 128;
    while (1) {
        montgomery64 x, y, ys, q = one;
        R = rng(n - 2) + 2, y = rng(n - 2) + 2;
        u64 g = 1;
        for (int r = 1; g == 1; r <<= 1) {
            x = y;
            for (int i = 0; i < r; i++) y = f(y);
            for (int k = 0; g == 1 && k < r; k += m) {
                ys = y;
                for (int i = 0; i < min(m, r - k); i++) q *= x - (y = f(y));
                g = gcd(q.value(), n);
            }
        }
        if (g == n) {
            do g = gcd((x - (ys = f(ys))).value(), n);
            while (g == 1);
        }
        if (g != n) return g;
    }
    cerr << "failed" << '\n';
    assert(false);
    return -1;
}

vector<u64> inner_factorize(u64 n) {
    if (n <= 1) return {};
    u64 p = pollard_rho(n);
    if (p == n) return {p};
    auto l = inner_factorize(p);
    auto r = inner_factorize(n / p);
    copy(r.begin(), r.end(), back_inserter(l));
    return l;
}
vector<u64> factorize(u64 n) {
    auto res = inner_factorize(n);
    sort(res.begin(), res.end());
    return res;
}
}  // namespace fast_factorize

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;

void solve() {
    int N;
    cin >> N;

    map<ll, int> mp;
    for (; N--;) {
        ll A;
        cin >> A;
        auto res = fast_factorize::factorize(A);
        for (auto& x : res) mp[x]++;
    }

    for (auto p : mp) {
        if (p.second & 1) {
            cout << "No" << '\n';
            return;
        }
    }

    cout << "Yes" << '\n';
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int T;
    cin >> T;
    for (; T--;) solve();
    return 0;
}
0