結果

問題 No.856 増える演算
ユーザー hitonanodehitonanode
提出日時 2019-07-26 23:23:07
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 488 ms / 3,153 ms
コード長 8,561 bytes
コンパイル時間 2,000 ms
コンパイル使用メモリ 182,648 KB
実行使用メモリ 12,800 KB
最終ジャッジ日時 2024-07-02 09:59:00
合計ジャッジ時間 41,902 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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 438 ms
11,944 KB
testcase_01 AC 438 ms
11,884 KB
testcase_02 AC 433 ms
12,016 KB
testcase_03 AC 431 ms
12,016 KB
testcase_04 AC 434 ms
11,888 KB
testcase_05 AC 440 ms
12,016 KB
testcase_06 AC 438 ms
11,888 KB
testcase_07 AC 434 ms
12,020 KB
testcase_08 AC 433 ms
11,988 KB
testcase_09 AC 435 ms
11,888 KB
testcase_10 AC 436 ms
11,888 KB
testcase_11 AC 433 ms
11,888 KB
testcase_12 AC 432 ms
11,980 KB
testcase_13 AC 435 ms
11,900 KB
testcase_14 AC 436 ms
12,024 KB
testcase_15 AC 435 ms
11,896 KB
testcase_16 AC 435 ms
11,892 KB
testcase_17 AC 436 ms
11,896 KB
testcase_18 AC 438 ms
11,888 KB
testcase_19 AC 437 ms
11,896 KB
testcase_20 AC 438 ms
11,888 KB
testcase_21 AC 438 ms
11,892 KB
testcase_22 AC 436 ms
12,020 KB
testcase_23 AC 433 ms
11,944 KB
testcase_24 AC 437 ms
11,972 KB
testcase_25 AC 437 ms
12,036 KB
testcase_26 AC 436 ms
11,900 KB
testcase_27 AC 435 ms
12,016 KB
testcase_28 AC 436 ms
12,076 KB
testcase_29 AC 440 ms
11,936 KB
testcase_30 AC 438 ms
11,928 KB
testcase_31 AC 435 ms
11,912 KB
testcase_32 AC 433 ms
11,956 KB
testcase_33 AC 441 ms
12,000 KB
testcase_34 AC 439 ms
12,120 KB
testcase_35 AC 436 ms
12,032 KB
testcase_36 AC 442 ms
12,228 KB
testcase_37 AC 436 ms
12,096 KB
testcase_38 AC 448 ms
11,912 KB
testcase_39 AC 451 ms
11,928 KB
testcase_40 AC 436 ms
11,972 KB
testcase_41 AC 436 ms
12,108 KB
testcase_42 AC 440 ms
12,136 KB
testcase_43 AC 439 ms
11,980 KB
testcase_44 AC 432 ms
11,996 KB
testcase_45 AC 433 ms
11,932 KB
testcase_46 AC 433 ms
11,980 KB
testcase_47 AC 440 ms
12,092 KB
testcase_48 AC 443 ms
12,044 KB
testcase_49 AC 439 ms
11,992 KB
testcase_50 AC 438 ms
12,188 KB
testcase_51 AC 442 ms
12,236 KB
testcase_52 AC 441 ms
12,244 KB
testcase_53 AC 462 ms
12,296 KB
testcase_54 AC 455 ms
12,044 KB
testcase_55 AC 470 ms
12,280 KB
testcase_56 AC 454 ms
12,036 KB
testcase_57 AC 466 ms
12,328 KB
testcase_58 AC 464 ms
12,120 KB
testcase_59 AC 477 ms
12,516 KB
testcase_60 AC 461 ms
12,116 KB
testcase_61 AC 477 ms
12,536 KB
testcase_62 AC 474 ms
12,452 KB
testcase_63 AC 441 ms
11,908 KB
testcase_64 AC 468 ms
12,524 KB
testcase_65 AC 452 ms
12,124 KB
testcase_66 AC 458 ms
12,112 KB
testcase_67 AC 467 ms
12,360 KB
testcase_68 AC 472 ms
12,440 KB
testcase_69 AC 467 ms
12,416 KB
testcase_70 AC 484 ms
12,592 KB
testcase_71 AC 476 ms
12,452 KB
testcase_72 AC 475 ms
12,476 KB
testcase_73 AC 482 ms
12,800 KB
testcase_74 AC 482 ms
12,680 KB
testcase_75 AC 482 ms
12,680 KB
testcase_76 AC 487 ms
12,676 KB
testcase_77 AC 488 ms
12,676 KB
testcase_78 AC 485 ms
12,800 KB
testcase_79 AC 485 ms
12,676 KB
testcase_80 AC 488 ms
12,676 KB
testcase_81 AC 487 ms
12,680 KB
testcase_82 AC 466 ms
12,676 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 # 

#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define POW2(n) (1LL << (n))
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
///// This part below is only for debug, not used /////
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
///// END /////
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
using namespace __gnu_pbds; // find_by_order(), order_of_key()
template<typename TK> using pbds_set = tree<TK, null_type, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename TK, typename TV> using pbds_map = tree<TK, TV, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
*/

vector<lint> A;
long double logval(int i, int j)
{
    return log(A[i] + A[j]) + A[j] * log(A[i]);
}

lint power(lint x, lint n, lint MOD)
{
    lint ans = 1;
    while (n>0)
    {
        if (n & 1) (ans *= x) %= MOD;
        (x *= x) %= MOD;
       n >>= 1;
    }
   return ans;
}
using cmplx = complex<double>;
void fft(int N, vector<cmplx> &a, double dir)
{
    int i = 0;
    FOR(j, 1, N - 1)
    {
        for (int k = N >> 1; k > (i ^= k); k >>= 1);
        if (j < i) swap(a[i], a[j]);
    }

    vector<cmplx> zeta_pow(N);
    REP(i, N)
    {
        double theta = M_PI / N * i * dir;
        zeta_pow[i] = cmplx(cos(theta), sin(theta));
    }

    for (int m = 1; m < N; m *= 2) REP(y, m)
    {
        cmplx fac = zeta_pow[N / m * y];
        for (int x = 0; x < N; x += 2 * m)
        {
            int u = x + y;
            int v = x + y + m;
            cmplx s = a[u] + fac * a[v];
            cmplx t = a[u] - fac * a[v];
            a[u] = s;
            a[v] = t;
        }
    }
}

template<class T>
vector<cmplx> conv_cmplx(const vector<T> &a, const vector<T> &b)
{
    int N = 1;
    while (N < (int)a.size() + (int)b.size()) N *= 2;
    vector<cmplx> a_(N), b_(N);
    REP(i, a.size()) a_[i] = a[i];
    REP(i, b.size()) b_[i] = b[i];
    fft(N, a_, 1);
    fft(N, b_, 1);
    REP(i, N) a_[i] *= b_[i];
    fft(N, a_, -1);
    REP(i, N) a_[i] /= N;
    return a_;
}
vector<lint> conv_lint(const vector<lint> &a, const vector<lint> &b)
{
    vector<cmplx> ans = conv_cmplx(a, b);
    vector<lint> ret(ans.size());
    REP(i, ans.size()) ret[i] = floor(ans[i].real() + 0.5);
    return ret;
}


lint extgcd(lint a, lint b, lint &x, lint &y)
{
    lint d = a;
    if (b != 0) d = extgcd(b, a % b, y, x), y -= (a / b) * x;
    else x = 1, y = 0;
    return d;
}
// Calc a^(-1) (MOD m)
lint mod_inverse(lint a, lint m)
{
    lint x, y;
    extgcd(a, m, x, y);
    return (m + x % m) % m;
}

// mod: 素数, primitive_root: modの原始根 is_inverse: trueならば逆変換
void fft_mod(vector<lint> &a, lint mod, lint primitive_root, bool is_inverse=false)
{
    int n = a.size();
    lint h = power(primitive_root, (mod - 1) / n, mod);
    if (is_inverse) h = mod_inverse(h, mod);

    int i = 0;
    FOR(j, 1, n - 1) {
        for (int k = n >> 1; k > (i ^= k); k >>= 1);
        if (j < i) swap(a[i], a[j]);
    }
    for (int m = 1; m < n; m *= 2) {
        int m2 = 2 * m;
        lint base = power(h, n / m2, mod);
        lint w = 1;
        REP(x, m) {
            for (int s = x; s < n; s += m2) {
                lint u = a[s], d = a[s + m] * w % mod;
                a[s] = u + d - (u + d >= mod ? mod : 0), a[s + m] = u - d + (u - d < 0 ? mod : 0);
            }
            w = w * base % mod;
        }
    }
    for (auto &v : a) v = (v < 0 ? v + mod : v);
    if (is_inverse)
    {
        lint n_inv = mod_inverse(n, mod);
        for (auto &v : a) v = v * n_inv % mod;
    }
}
// MOD modにおける畳み込み演算 retval[i] = \sum_j a[j] b[i - j]
vector<lint> convolution_mod(vector<lint> a, vector<lint> b, lint mod, lint primitive_root)
{
    int sz = 1;
    while (sz < a.size() + b.size()) sz <<= 1;
    a.resize(sz), b.resize(sz);
    fft_mod(a, mod, primitive_root, false), fft_mod(b, mod, primitive_root, false);
    REP(i, sz) a[i] = a[i] * b[i] % mod;
    fft_mod(a, mod, primitive_root, true);
    return a;
}

plint linear_congruence(const vector<lint> &A, const vector<lint> &B, const vector<lint> &M)
{
    lint x = 0, m = 1;
    REP(i, A.size())
    {
        lint a = A[i] * m, b = B[i] - A[i] * x, d = __gcd(M[i], a);
        if (b % d != 0) return plint(0, -1); // 解なし
        lint t = b / d * mod_inverse(a / d, M[i] / d) % (M[i] / d);
        x += m * t;
        m *= M[i] / d;
    }
    return plint((x < 0 ? x + m : x), m);
}

constexpr lint MOD = 1000000007;
int main()
{
    int N;
    cin >> N;
    A.resize(N);
    cin >> A;
    int m1 = 0, m2 = 1, mini = 0;
    vector<lint> cou(100001);
    for (auto v : A) cou[v]++;
    FOR(i, 1, N)
    {
        if (logval(mini, i) < logval(m1, m2)) m1 = mini, m2 = i;
        if (A[i] < A[mini]) mini = i;
    }

    auto vconv = convolution_mod(cou, cou, 1224736769, 3);
    auto vconv2 = convolution_mod(cou, cou, 469762049, 3);
    FOR(d, 1, vconv.size())
    {
        auto p = linear_congruence(vector<lint>{1, 1}, vector<lint>{vconv[d], vconv2[d]}, vector<lint>{1224736769, 469762049});
        vconv[d] = p.first;
    }

    lint den = (A[m1] + A[m2]) % MOD * power(A[m1], A[m2], MOD) % MOD;
    lint num = 1;
    vector<lint> AA(N + 1);
    REP(i, N) AA[i + 1] = A[i] + AA[i];
    REP(i, N) num = num * power(A[i], AA[N] - AA[i + 1], MOD) % MOD;

    FOR(d, 1, vconv.size()) if (vconv[d])
    {
        if (d % 2)
        {
            num = num * power(d, vconv[d] / 2, MOD) % MOD;
        } 
        else
        {
            lint n = (vconv[d] - cou[d / 2] * cou[d / 2]) / 2 + cou[d / 2] * (cou[d / 2] - 1) / 2;
            num = num * power(d, n, MOD) % MOD;
        }
    }


    cout << num * power(den, MOD - 2, MOD) % MOD << endl;
}
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