結果

問題 No.856 増える演算
ユーザー Sumitacchan
提出日時 2019-08-10 01:22:12
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 223 ms / 3,153 ms
コード長 7,719 bytes
コンパイル時間 1,827 ms
コンパイル使用メモリ 181,640 KB
実行使用メモリ 43,264 KB
最終ジャッジ日時 2024-07-19 16:07:14
合計ジャッジ時間 19,324 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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

#include <bits/stdc++.h>
using namespace std;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << 
    endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << 
    endl; }; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void Ans(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }
using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;
//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};
const int mod = 1000000007;
//const int mod = 998244353;
#define Add(x, y) x = (x + (y)) % mod
#define Mult(x, y) x = (x * (y)) % mod
template<long long MOD>
struct ModInt{
    using ll = long long;
    ll val;
    void setval(ll v) { val = v % MOD; };
    ModInt(): val(0) {}
    ModInt(ll v) { setval(v); };
    ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
    ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
    ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
    ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt operator+=(const ModInt &x) { return *this = *this + x; }
    ModInt operator-=(const ModInt &x) { return *this = *this - x; }
    ModInt operator*=(const ModInt &x) { return *this = *this * x; }
    ModInt operator/=(const ModInt &x) { return *this = *this / x; }
    friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; }
    friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; }
    ModInt pow(ll n) const {
        ModInt a = 1;
        if(n == 0) return a;
        int i0 = 64 - __builtin_clzll(n);
        for(int i = i0 - 1; i >= 0; i--){
            a = a * a;
            if((n >> i) & 1) a *= (*this); 
        }
        return a;
    }
    ModInt inv() const { return this->pow(MOD - 2); }
};
using mint = ModInt<mod>; mint pow(mint x, long long n) { return x.pow(n); }
//using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;
struct Combination{
    vector<mint> fact, invfact;
    Combination(int N){
        fact = vector<mint>({mint(1)});
        invfact = vector<mint>({mint(1)});
        fact_initialize(N);
    }
    void fact_initialize(int N){
        int i0 = fact.size();
        if(i0 >= N + 1) return;
        fact.resize(N + 1);
        invfact.resize(N + 1);
        for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i;
        invfact[N] = (mint)1 / fact[N];
        for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); 
    }
    mint nCr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[r] * invfact[n - r];
    }
    mint nPr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[n - r];
    }
};
//N=2^n
class FFT
{
    using comp = complex<double>;
private:
    vector<comp> f, f_tmp;
    void forward_exec(int l, int r, int t){
        if(t == n) return;
        int sz = (r - l) >> 1;
        REP(i, sz){
            f_tmp[l + i] = f[l + 2 * i];
            f_tmp[l + sz + i] = f[l + 2 * i + 1];
        }
        FOR(i, l, r) f[i] = f_tmp[i];
        forward_exec(l, l + sz, t + 1);
        forward_exec(l + sz, r, t + 1);
        REP(i, sz) f_tmp[l + i] = f[l + i] + f[l + sz + i] * pow_e[i << t];
        REP(i, sz) f_tmp[l + sz + i] = f[l + i] + f[l + sz + i] * pow_e[(sz + i) << t];
        FOR(i, l, r) f[i] = f_tmp[i];
    }
    void inverse_exec(int l, int r, int t){
        if(t == n) return;
        int sz = (r - l) / 2;
        REP(i, sz){
            f_tmp[l + i] = f[l + 2 * i];
            f_tmp[l + sz + i] = f[l + 2 * i + 1];
        }
        FOR(i, l, r) f[i] = f_tmp[i];
        inverse_exec(l, l + sz, t + 1);
        inverse_exec(l + sz, r, t + 1);
        REP(i, sz) f_tmp[l + i] = f[l + i] + f[l + sz + i] * pow_e[N - (i << t)];
        REP(i, sz) f_tmp[l + sz + i] = f[l + i] + f[l + sz + i] * pow_e[N - ((sz + i) << t)];
        FOR(i, l, r) f[i] = f_tmp[i];
    }
public:
    int N, n;
    vector<comp> pow_e;
    FFT(int N): N(N){
        n = 31 - __builtin_clz((signed)N);
        assert(N == (1 << n));
        pow_e.resize(N + 1); 
        pow_e[0] = pow_e[N] = comp(1.0, 0.0);
        double phi = 2.0 * M_PI / N;
        FOR(i, 1, N) pow_e[i] = exp(comp(0, phi * i));
        f.resize(N);
        f_tmp.resize(N);
    }
    void exec(vector<comp> &F, bool inverse = false){
        assert(F.size() == N);
        f.swap(F);
        if(!inverse) forward_exec(0, N, 0);
        else inverse_exec(0, N, 0);
        F.swap(f);
        if(inverse){
            REP(i, N) F[i] /= N;
        }
    }
    vector<comp> convolution(vector<comp> A, vector<comp> B){
        exec(A);
        exec(B);
        vector<comp> C(N);
        REP(i, N) C[i] = A[i] * B[i];
        exec(C, true);
        return C;
    }
    vector<int> int_convolution(vector<int> A, vector<int> B){
        vector<comp> a(N), b(N);
        REP(i, N){
            a[i] = comp(A[i], 0);
            b[i] = comp(B[i], 0);
        }
        vector<comp> c = convolution(a, b);
        vector<int> C(N);
        REP(i, N) C[i] = (int)(c[i].real() + 0.5);
        return C;
    }
};
signed main(){
    int N; cin >> N;
    vec A(N); cin >> A;
    long double vmin = INF;
    int m = A[0];
    mint mmin;
    FOR(i, 1, N){
        long double v = logl((long double)(m + A[i])) + (long double)A[i] * logl((long double)m);
        if(v < vmin){
            vmin = v;
            mmin = (mint)(m + A[i]) * pow((mint)m, A[i]);
        }
        Min(m, A[i]);
    }
    //debug(mmin);
    vec cnt(bit(18), 0);
    FFT fft(bit(18));
    REP(i, N) cnt[A[i]]++;
    cnt = fft.int_convolution(cnt, cnt);
    REP(i, N) cnt[2 * A[i]] -= 1.0;
    mint a1 = 1;
    REP(i, SZ(cnt)){
        a1 *= pow((mint)i, cnt[i] / 2);
    }
    //debug(a1);
    mint a2 = 1;
    int s = 0;
    IREP(i, N){
        a2 *= pow((mint)A[i], s);
        s += A[i];
    }
    mint ans = a1 * a2 / mmin;
    Out(ans);
    return 0;
}
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