結果

問題 No.856 増える演算
コンテスト
ユーザー hitonanode
提出日時 2019-07-26 23:03:08
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 6,123 bytes
コンパイル時間 1,754 ms
コンパイル使用メモリ 177,336 KB
実行使用メモリ 17,404 KB
最終ジャッジ日時 2024-07-02 09:02:07
合計ジャッジ時間 12,719 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 64 WA * 16
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[i] * log(A[j]);
}

constexpr lint MOD = 1000000007;
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;
}


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 = conv_lint(cou, cou);

    lint den = (A[m1] + A[m2]) % MOD * power(A[m1], A[m2], MOD) % MOD;
    // dbg(den);
    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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