結果

問題 No.856 増える演算
ユーザー square1001
提出日時 2019-07-26 21:42:33
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 197 ms / 3,153 ms
コード長 6,299 bytes
コンパイル時間 1,074 ms
コンパイル使用メモリ 91,460 KB
実行使用メモリ 24,960 KB
最終ジャッジ日時 2024-07-02 06:51:14
合計ジャッジ時間 8,042 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 80
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 #
プレゼンテーションモードにする

#ifndef CLASS_POLYNOMIAL
#define CLASS_POLYNOMIAL
#include <vector>
#include <complex>
#include <cstdint>
#include <algorithm>
class polynomial {
private:
    using type = long double;
    const type epsilon = 1.0e-9;
    std::size_t sz;
    std::vector<type> a;
    inline bool equivalent(type ra, type rb) const {
        return (epsilon <= ra - rb && ra - rb <= epsilon);
    }
    void discrete_fourier_transform(std::vector<std::complex<type> >& v, bool rev) {
        std::size_t n = v.size();
        const type pi = acos(type(-1));
        for (std::size_t i = 0, j = 1; j < n - 1; ++j) {
            for (std::size_t k = n >> 1; k > (i ^= k); k >>= 1);
            if (i > j) std::swap(v[i], v[j]);
        }
        for (std::size_t b = 1; b < n; b <<= 1) {
            std::complex<type> wr = std::polar(type(1), (rev ? type(-1) : type(1)) * pi / b);
            for (std::size_t i = 0; i < n; i += 2 * b) {
                std::complex<type> w = type(1);
                for (std::size_t j = 0; j < b; ++j) {
                    std::complex<type> v0 = v[i + j];
                    std::complex<type> v1 = w * v[i + j + b];
                    v[i + j] = v0 + v1;
                    v[i + j + b] = v0 - v1;
                    w *= wr;
                }
            }
        }
        if (!rev) return;
        for (std::size_t i = 0; i < n; i++) v[i] /= n;
    }
public:
    explicit polynomial() : sz(1), a(std::vector<type>({ type() })) {};
    explicit polynomial(std::size_t sz_) : sz(sz_), a(std::vector<type>(sz_, type())) {};
    explicit polynomial(std::vector<type> a_) : sz(a_.size()), a(a_) {};
    polynomial& operator=(const polynomial& p) {
        sz = p.sz;
        a = p.a;
        return (*this);
    }
    std::size_t size() const { return sz; }
    std::size_t degree() const { return sz - 1; }
    type operator[](std::size_t idx) const {
        return a[idx];
    }
    type& operator[](std::size_t idx) {
        return a[idx];
    }
    bool operator==(const polynomial& p) const {
        for (std::size_t i = 0; i < sz || i < p.sz; ++i) {
            if (!equivalent(i < sz ? a[i] : type(0), i < p.sz ? p.a[i] : type(0))) {
                return false;
            }
        }
        return true;
    }
    bool operator!=(const polynomial& p) const {
        return !(operator==(p));
    }
    polynomial resize_transform(std::size_t d) const {
        // Resize polynomial to d: in other words, f(x) := f(x) mod x^d
        polynomial ans(*this);
        ans.sz = d;
        ans.a.resize(d, type(0));
        return ans;
    }
    polynomial star_transform() const {
        // f*(x) = x^degree * f(1/x)
        polynomial ans(*this);
        reverse(ans.a.begin(), ans.a.end());
        return ans;
    }
    polynomial inverse(std::size_t d) const {
        // Find g(x) where g(x) * f(x) = 1 (mod x^d)
        polynomial ans(std::vector<type>({ type(1) / a[0] }));
        while (ans.size() < d) {
            polynomial nxt;
            nxt = -ans * resize_transform(ans.size() * 2);
            nxt.a[0] += type(2);
            nxt *= ans;
            ans = nxt.resize_transform(ans.size() * 2);
        }
        ans = ans.resize_transform(d);
        return ans;
    }
    polynomial& operator+=(const polynomial& p) {
        sz = std::max(sz, p.sz);
        a.resize(sz);
        for (std::size_t i = 0; i < sz; ++i) a[i] += p.a[i];
        return (*this);
    }
    polynomial& operator-=(const polynomial& p) {
        sz = std::max(sz, p.sz);
        a.resize(sz);
        for (std::size_t i = 0; i < sz; ++i) a[i] -= p.a[i];
        return (*this);
    }
    polynomial& operator*=(const polynomial& p) {
        std::size_t n = 2;
        while (n < sz * 2 || n < p.sz * 2) n <<= 1;
        std::vector<std::complex<type> > v(n), pv(n);
        for (std::size_t i = 0; i < sz; ++i) v[i] = a[i];
        for (std::size_t i = 0; i < p.sz; ++i) pv[i] = p.a[i];
        discrete_fourier_transform(v, false);
        discrete_fourier_transform(pv, false);
        for (std::size_t i = 0; i < n; ++i) v[i] *= pv[i];
        discrete_fourier_transform(v, true);
        sz += p.sz - 1;
        a.resize(sz, type(0));
        for (std::size_t i = 0; i < sz; ++i) a[i] = v[i].real();
        return (*this);
    }
    polynomial operator+() const {
        return polynomial(*this);
    }
    polynomial operator-() const {
        return polynomial() - polynomial(*this);
    }
    polynomial operator+(const polynomial& p) const {
        return polynomial(*this) += p;
    }
    polynomial operator-(const polynomial& p) const {
        return polynomial(*this) -= p;
    }
    polynomial operator*(const polynomial& p) const {
        return polynomial(*this) *= p;
    }
};
#endif
#ifndef CLASS_MODINT
#define CLASS_MODINT
#include <cstdint>
template <std::uint32_t mod>
class modint {
private:
    std::uint32_t n;
public:
    modint() : n(0) {};
    modint(std::int64_t n_) : n((n_ >= 0 ? n_ : mod - (-n_) % mod) % mod) {};
    static constexpr std::uint32_t get_mod() { return mod; }
    std::uint32_t get() const { return n; }
    bool operator==(const modint& m) const { return n == m.n; }
    bool operator!=(const modint& m) const { return n != m.n; }
    modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; }
    modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; }
    modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; }
    modint operator+(const modint& m) const { return modint(*this) += m; }
    modint operator-(const modint& m) const { return modint(*this) -= m; }
    modint operator*(const modint& m) const { return modint(*this) *= m; }
    modint inv() const { return (*this).pow(mod - 2); }
    modint pow(std::uint64_t b) const {
        modint ans = 1, m = modint(*this);
        while (b) {
            if (b & 1) ans *= m;
            m *= m;
            b >>= 1;
        }
        return ans;
    }
};
#endif // CLASS_MODINT
#include <vector>
#include <iostream>
using namespace std;
using modulo = modint<1000000007>;
int main() {
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    int N;
    cin >> N;
    vector<int> A(N);
    for (int i = 0; i < N; ++i) cin >> A[i];
    int mx = *max_element(A.begin(), A.end());
    polynomial hist(mx + 1);
    for (int i = 0; i < N; ++i) hist[A[i]] += 1.0;
    hist *= hist;
    for (int i = 0; i < N; ++i) hist[A[i] * 2] -= 1.0;
    for (int i = 0; i <= 2 * mx; ++i) hist[i] *= 0.5;
    modulo ans = 1;
    for (int i = 0; i <= 2 * mx; ++i) {
        if (hist[i] > 0) {
            ans *= modulo(i).pow((long long)(hist[i] + 0.5));
        }
    }
    long long sum = 0;
    for (int i = N - 1; i >= 0; --i) {
        ans *= modulo(A[i]).pow(sum);
        sum += A[i];
    }
    int curmin = 1 << 30, p1 = -1, p2 = -1; double curlog = 1.0e+99;
    for (int i = N - 1; i >= 0; --i) {
        double newlog = log(A[i]) * curmin + log(A[i] + curmin);
        if (curlog > newlog) {
            curlog = newlog;
            p1 = A[i];
            p2 = curmin;
        }
        curmin = min(curmin, A[i]);
    }
    ans *= modulo(p1 + p2).inv() * modulo(p1).pow(p2).inv();
    cout << ans.get() << endl;
    return 0;
}
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