#798030 (C++17) No.2074 Product is Square ?

提出ソース

結果

問題	No.2074 Product is Square ?
ユーザー	tokusakurai
提出日時	2022-09-16 22:04:03
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	156 ms / 2,000 ms
コード長	9,574 bytes
コンパイル時間	3,467 ms
コンパイル使用メモリ	220,808 KB
実行使用メモリ	4,380 KB
最終ジャッジ日時	2023-08-23 15:37:02
合計ジャッジ時間	5,506 ms
ジャッジサーバーID （参考情報）	judge12 / judge11

このコードへのチャレンジ
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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 4,380 KB
testcase_01	AC	34 ms 4,380 KB
testcase_02	AC	35 ms 4,380 KB
testcase_03	AC	34 ms 4,380 KB
testcase_04	AC	37 ms 4,380 KB
testcase_05	AC	36 ms 4,380 KB
testcase_06	AC	36 ms 4,380 KB
testcase_07	AC	37 ms 4,380 KB
testcase_08	AC	35 ms 4,376 KB
testcase_09	AC	36 ms 4,376 KB
testcase_10	AC	34 ms 4,376 KB
testcase_11	AC	12 ms 4,376 KB
testcase_12	AC	35 ms 4,376 KB
testcase_13	AC	153 ms 4,376 KB
testcase_14	AC	23 ms 4,376 KB
testcase_15	AC	12 ms 4,376 KB
testcase_16	AC	38 ms 4,376 KB
testcase_17	AC	156 ms 4,380 KB
testcase_18	AC	26 ms 4,380 KB
testcase_19	AC	12 ms 4,376 KB
testcase_20	AC	37 ms 4,376 KB
testcase_21	AC	148 ms 4,376 KB
testcase_22	AC	24 ms 4,380 KB
testcase_23	AC	12 ms 4,376 KB
testcase_24	AC	38 ms 4,380 KB
testcase_25	AC	149 ms 4,380 KB
testcase_26	AC	25 ms 4,376 KB
testcase_27	AC	12 ms 4,376 KB
testcase_28	AC	41 ms 4,380 KB
testcase_29	AC	150 ms 4,376 KB
testcase_30	AC	23 ms 4,380 KB
testcase_31	AC	5 ms 4,380 KB
testcase_32	AC	1 ms 4,380 KB
testcase_33	AC	2 ms 4,376 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;

struct Random_Number_Generator {
    mt19937_64 mt;

    Random_Number_Generator() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}

    int64_t operator()(int64_t l, int64_t r) {
        uniform_int_distribution<int64_t> dist(l, r - 1);
        return dist(mt);
    }

    int64_t operator()(int64_t r) { return (*this)(0, r); }
} rng;

struct Montgomery_Mod_Int_64 {
    using u64 = uint64_t;
    using u128 = __uint128_t;

    static u64 mod;
    static u64 r;  // m*r ≡ 1 (mod 2^64)
    static u64 n2; // 2^128 (mod mod)

    u64 x;

    Montgomery_Mod_Int_64() : x(0) {}

    Montgomery_Mod_Int_64(long long b) : x(reduce((u128(b) + mod) * n2)) {}

    static u64 get_r() { // mod 2^64 での逆元
        u64 ret = mod;
        for (int i = 0; i < 5; i++) ret *= 2 - mod * ret;
        return ret;
    }

    static u64 get_mod() { return mod; }

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

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

    Montgomery_Mod_Int_64 &operator+=(const Montgomery_Mod_Int_64 &p) {
        if ((x += p.x) >= 2 * mod) x -= 2 * mod;
        return *this;
    }

    Montgomery_Mod_Int_64 &operator-=(const Montgomery_Mod_Int_64 &p) {
        if ((x += 2 * mod - p.x) >= 2 * mod) x -= 2 * mod;
        return *this;
    }

    Montgomery_Mod_Int_64 &operator*=(const Montgomery_Mod_Int_64 &p) {
        x = reduce(u128(x) * p.x);
        return *this;
    }

    Montgomery_Mod_Int_64 &operator/=(const Montgomery_Mod_Int_64 &p) {
        *this *= p.inverse();
        return *this;
    }

    Montgomery_Mod_Int_64 &operator++() { return *this += Montgomery_Mod_Int_64(1); }

    Montgomery_Mod_Int_64 operator++(int) {
        Montgomery_Mod_Int_64 tmp = *this;
        ++*this;
        return tmp;
    }

    Montgomery_Mod_Int_64 &operator--() { return *this -= Montgomery_Mod_Int_64(1); }

    Montgomery_Mod_Int_64 operator--(int) {
        Montgomery_Mod_Int_64 tmp = *this;
        --*this;
        return tmp;
    }

    Montgomery_Mod_Int_64 operator+(const Montgomery_Mod_Int_64 &p) const { return Montgomery_Mod_Int_64(*this) += p; };

    Montgomery_Mod_Int_64 operator-(const Montgomery_Mod_Int_64 &p) const { return Montgomery_Mod_Int_64(*this) -= p; };

    Montgomery_Mod_Int_64 operator*(const Montgomery_Mod_Int_64 &p) const { return Montgomery_Mod_Int_64(*this) *= p; };

    Montgomery_Mod_Int_64 operator/(const Montgomery_Mod_Int_64 &p) const { return Montgomery_Mod_Int_64(*this) /= p; };

    bool operator==(const Montgomery_Mod_Int_64 &p) const { return (x >= mod ? x - mod : x) == (p.x >= mod ? p.x - mod : p.x); };

    bool operator!=(const Montgomery_Mod_Int_64 &p) const { return (x >= mod ? x - mod : x) != (p.x >= mod ? p.x - mod : p.x); };

    Montgomery_Mod_Int_64 inverse() const {
        assert(*this != Montgomery_Mod_Int_64(0));
        return pow(mod - 2);
    }

    Montgomery_Mod_Int_64 pow(long long k) const {
        Montgomery_Mod_Int_64 now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    u64 get() const {
        u64 ret = reduce(x);
        return ret >= mod ? ret - mod : ret;
    }

    friend ostream &operator<<(ostream &os, const Montgomery_Mod_Int_64 &p) { return os << p.get(); }

    friend istream &operator>>(istream &is, Montgomery_Mod_Int_64 &p) {
        long long a;
        is >> a;
        p = Montgomery_Mod_Int_64(a);
        return is;
    }
};

typename Montgomery_Mod_Int_64::u64 Montgomery_Mod_Int_64::mod, Montgomery_Mod_Int_64::r, Montgomery_Mod_Int_64::n2;

bool Miller_Rabin(unsigned long long n, vector<unsigned long long> as) {
    using Mint = Montgomery_Mod_Int_64;
    if (Mint::get_mod() != n) Mint::set_mod(n);
    unsigned long long d = n - 1;
    while (!(d & 1)) d >>= 1;
    Mint e = 1, rev = n - 1;
    for (unsigned long long a : as) {
        if (n <= a) break;
        unsigned long long t = d;
        Mint y = Mint(a).pow(t);
        while (t != n - 1 && y != e && y != rev) {
            y *= y;
            t <<= 1;
        }
        if (y != rev && (!(t & 1))) return false;
    }
    return true;
}

bool is_prime(unsigned long long n) {
    if (!(n & 1)) return n == 2;
    if (n <= 1) return false;
    if (n < (1LL << 30)) return Miller_Rabin(n, {2, 7, 61});
    return Miller_Rabin(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

unsigned long long Pollard_rho(unsigned long long n) {
    using Mint = Montgomery_Mod_Int_64;
    if (!(n & 1)) return 2;
    if (is_prime(n)) return n;
    if (Mint::get_mod() != n) Mint::set_mod(n);
    Mint R, one = 1;
    auto f = [&](Mint x) { return x * x + R; };
    auto rnd = [&]() { return rng(n - 2) + 2; };
    while (true) {
        Mint x, y, ys, q = one;
        R = rnd(), y = rnd();
        unsigned long long g = 1;
        int m = 128;
        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 < m && i < r - k; i++) q *= x - (y = f(y));
                g = gcd(q.get(), n);
            }
        }
        if (g == n) {
            do { g = gcd((x - (ys = f(ys))).get(), n); } while (g == 1);
        }
        if (g != n) return g;
    }
    return 0;
}

vector<unsigned long long> factorize(unsigned long long n) {
    if (n <= 1) return {};
    unsigned long long p = Pollard_rho(n);
    if (p == n) return {n};
    auto l = factorize(p);
    auto r = factorize(n / p);
    copy(begin(r), end(r), back_inserter(l));
    return l;
}

vector<pair<unsigned long long, int>> prime_factor(unsigned long long n) {
    auto ps = factorize(n);
    sort(begin(ps), end(ps));
    vector<pair<unsigned long long, int>> ret;
    for (auto &e : ps) {
        if (!ret.empty() && ret.back().first == e) {
            ret.back().second++;
        } else {
            ret.emplace_back(e, 1);
        }
    }
    return ret;
}

using ull = unsigned long long;

int main() {
    int T;
    cin >> T;

    while (T--) {
        int N;
        cin >> N;

        vector<ull> a(N);
        rep(i, N) cin >> a[i];

        map<ull, int> mp;

        rep(i, N) {
            auto ps = prime_factor(a[i]);
            each(e, ps) mp[e.first] += e.second;
        }

        bool flag = true;
        each(e, mp) {
            if (e.second & 1) flag = false;
        }
        cout << (flag ? "Yes\n" : "No\n");
    }
}

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結果

テストケース

ソースコード