結果

問題 No.856 増える演算
ユーザー kimiyukikimiyuki
提出日時 2020-08-11 19:48:41
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 8,418 bytes
コンパイル時間 2,481 ms
コンパイル使用メモリ 213,088 KB
実行使用メモリ 11,552 KB
最終ジャッジ日時 2024-10-09 11:38:33
合計ジャッジ時間 25,201 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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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
9,984 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 WA -
testcase_04 WA -
testcase_05 WA -
testcase_06 AC 1 ms
5,248 KB
testcase_07 WA -
testcase_08 WA -
testcase_09 AC 2 ms
5,248 KB
testcase_10 WA -
testcase_11 WA -
testcase_12 AC 2 ms
5,248 KB
testcase_13 WA -
testcase_14 WA -
testcase_15 WA -
testcase_16 WA -
testcase_17 WA -
testcase_18 WA -
testcase_19 WA -
testcase_20 WA -
testcase_21 WA -
testcase_22 WA -
testcase_23 WA -
testcase_24 RE -
testcase_25 WA -
testcase_26 WA -
testcase_27 WA -
testcase_28 WA -
testcase_29 WA -
testcase_30 RE -
testcase_31 WA -
testcase_32 WA -
testcase_33 WA -
testcase_34 RE -
testcase_35 WA -
testcase_36 TLE -
testcase_37 TLE -
testcase_38 WA -
testcase_39 WA -
testcase_40 WA -
testcase_41 WA -
testcase_42 TLE -
testcase_43 -- -
testcase_44 -- -
testcase_45 -- -
testcase_46 -- -
testcase_47 -- -
testcase_48 -- -
testcase_49 -- -
testcase_50 -- -
testcase_51 -- -
testcase_52 -- -
testcase_53 -- -
testcase_54 -- -
testcase_55 -- -
testcase_56 -- -
testcase_57 -- -
testcase_58 -- -
testcase_59 -- -
testcase_60 -- -
testcase_61 -- -
testcase_62 -- -
testcase_63 -- -
testcase_64 -- -
testcase_65 -- -
testcase_66 -- -
testcase_67 -- -
testcase_68 -- -
testcase_69 -- -
testcase_70 -- -
testcase_71 -- -
testcase_72 -- -
testcase_73 -- -
testcase_74 -- -
testcase_75 -- -
testcase_76 -- -
testcase_77 -- -
testcase_78 -- -
testcase_79 -- -
testcase_80 -- -
testcase_81 -- -
testcase_82 -- -
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 # 

#line 1 "main.cpp"
#include <bits/stdc++.h>
#line 2 "/home/user/Library/utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 4 "/home/user/Library/modulus/modpow.hpp"

inline int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) {
    assert (/* 0 <= x and */ x < (uint_fast64_t)MOD);
    uint_fast64_t y = 1;
    for (; k; k >>= 1) {
        if (k & 1) (y *= x) %= MOD;
        (x *= x) %= MOD;
    }
    assert (/* 0 <= y and */ y < (uint_fast64_t)MOD);
    return y;
}
#line 5 "/home/user/Library/modulus/modinv.hpp"

inline int32_t modinv_nocheck(int32_t value, int32_t MOD) {
    assert (0 <= value and value < MOD);
    if (value == 0) return -1;
    int64_t a = value, b = MOD;
    int64_t x = 0, y = 1;
    for (int64_t u = 1, v = 0; a; ) {
        int64_t q = b / a;
        x -= q * u; std::swap(x, u);
        y -= q * v; std::swap(y, v);
        b -= q * a; std::swap(b, a);
    }
    if (not (value * x + MOD * y == b and b == 1)) return -1;
    if (x < 0) x += MOD;
    assert (0 <= x and x < MOD);
    return x;
}

inline int32_t modinv(int32_t x, int32_t MOD) {
    int32_t y = modinv_nocheck(x, MOD);
    assert (y != -1);
    return y;
}
#line 6 "/home/user/Library/modulus/mint.hpp"

/**
 * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
 */
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
    inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
    inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator + (int64_t value, mint<MOD> n) { return mint<MOD>(value) + n; }
template <int32_t MOD> mint<MOD> operator - (int64_t value, mint<MOD> n) { return mint<MOD>(value) - n; }
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }
#line 5 "/home/user/Library/number/karatsuba.hpp"

/**
 * @brief Karatsuba method ($O(n^{\log_2 3})$)
 */
template <class CommutativeRing>
std::vector<CommutativeRing> karatsuba_convolution(const std::vector<CommutativeRing> & x, const std::vector<CommutativeRing> & y) {
    int n = x.size();
    int m = y.size();
    if ((int64_t)n * m <= 100) {
        std::vector<CommutativeRing> z(n + m - 1);
        REP (i, n) REP (j, m) {
            z[i + j] += x[i] * y[j];
        }
        return z;
    }
    int half = (std::max(n, m) + 1) / 2;

    std::vector<CommutativeRing> x0(x.begin(), x.begin() + std::min(n, half));
    std::vector<CommutativeRing> y0(y.begin(), y.begin() + std::min(m, half));
    std::vector<CommutativeRing> z0 = karatsuba_convolution(x0, y0);

    std::vector<CommutativeRing> x1(x.begin() + std::min(n, half), x.end());
    std::vector<CommutativeRing> y1(y.begin() + std::min(m, half), y.end());
    std::vector<CommutativeRing> z2 = karatsuba_convolution(x1, y1);

    assert (x1.size() <= x0.size());
    std::vector<CommutativeRing> dx = x0;
    REP (i, x1.size()) dx[i] -= x1[i];
    assert (y1.size() <= y0.size());
    std::vector<CommutativeRing> dy = y0;
    REP (i, y1.size()) dy[i] -= y1[i];
    std::vector<CommutativeRing> dz = karatsuba_convolution(dx, dy);

    std::vector<CommutativeRing> z(n + m - 1);
    REP (i, z0.size()) {
        z[i] += z0[i];
        if (half + i < (int)z.size()) z[half + i] += z0[i];
    }
    REP (i, dz.size()) {
        if (half + i < (int)z.size()) z[half + i] -= dz[i];
    }
    REP (i, z2.size()) {
        z[half + i] += z2[i];
        if (2 * half + i < (int)z.size()) z[2 * half + i] += z2[i];
    }
    return z;
}
#line 5 "main.cpp"
using namespace std;

template <class CommutativeRing>
std::vector<CommutativeRing> karatsuba_special_convolution(const std::vector<CommutativeRing> & x) {
    int n = x.size();
    if ((int64_t)n * n <= 100) {
        std::vector<CommutativeRing> z(2 * n - 1);
        REP (i, n) REP3 (j, i + 1, n) {
            z[i + j] += x[i] * x[j];
        }
        return z;
    }
    int half = (n + 1) / 2;

    std::vector<CommutativeRing> x0(x.begin(), x.begin() + std::min(n, half));
    std::vector<CommutativeRing> x1(x.begin() + std::min(n, half), x.end());
    std::vector<CommutativeRing> z0 = karatsuba_special_convolution(x0);
    std::vector<CommutativeRing> z1 = karatsuba_convolution(x0, x1);
    std::vector<CommutativeRing> z2 = karatsuba_special_convolution(x1);

    std::vector<CommutativeRing> z(2 * n - 1);
    REP (i, z0.size()) {
        z[i] += z0[i];
        if (half + i < (int)z.size()) z[half + i] += z0[i];
    }
    REP (i, z1.size()) {
        if (half + i < (int)z.size()) z[half + i] += z1[i];
    }
    REP (i, z2.size()) {
        if (2 * half + i < (int)z.size()) z[2 * half + i] += z2[i];
    }
    return z;
}

constexpr int64_t MOD = 1000000007;

// the commutative ring (F, *, +) for the finite field (F, +, *)
struct cring_t {
    mint<MOD> value;
    cring_t() : value(1) {}
};
cring_t & operator += (cring_t & a, cring_t b) {
    a.value *= b.value; return a;
}
cring_t & operator -= (cring_t & a, cring_t b) {
    a.value /= b.value; return a;
}
cring_t & operator *= (cring_t & a, cring_t b) {
    a.value += b.value; return a;
}
cring_t operator + (cring_t a, cring_t b) {
    return a += b;
}
cring_t operator - (cring_t a, cring_t b) {
    return a -= b;
}
cring_t operator * (cring_t a, cring_t b) {
    return a *= b;
}

mint<MOD> solve(int n, const vector<int64_t> &a) {
    mint<MOD> x = 1;
    {
        vector<cring_t> b(n);
        REP (i, n) {
            b[i].value = a[i];
        }
        auto c = karatsuba_special_convolution<cring_t>(b);
        for (auto c_i : c) {
            x *= c_i.value;
        }
    }

    mint<MOD> y = 1;
    {
        int64_t sum_a_j = 0;
        REP_R (i, n) {
            y *= mint<MOD>(a[i]).pow(sum_a_j);
            sum_a_j += a[i];
        }
    }

    mint<MOD> z = 0;
    {
        double log_z = INFINITY;
        int64_t a_j = a[n - 1];
        REP_R (i, n - 1) {
            double log_a_i_a_j = log(a[i] + a_j) + a_j * log(a[i]);
            if (log_a_i_a_j < log_z) {
                log_z = log_a_i_a_j;
                z = mint<MOD>(a[i] + a_j) * mint<MOD>(a[i]).pow(a_j);
            }
            a_j = min(a[i], a_j);
        }
    }
    return x * y / z;
}

int main() {
    int n; cin >> n;
    vector<int64_t> a(n);
    REP (i, n) {
        cin >> a[i];
    }
    auto ans = solve(n, a);
    cout << ans << endl;
    return 0;
}
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