結果

問題 No.856 増える演算
ユーザー SumitacchanSumitacchan
提出日時 2019-08-10 01:24:30
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,037 ms / 3,153 ms
コード長 7,719 bytes
コンパイル時間 2,050 ms
コンパイル使用メモリ 182,852 KB
実行使用メモリ 159,952 KB
最終ジャッジ日時 2024-07-19 16:09:52
合計ジャッジ時間 80,270 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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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 878 ms
158,992 KB
testcase_01 AC 857 ms
159,172 KB
testcase_02 AC 844 ms
159,148 KB
testcase_03 AC 854 ms
158,992 KB
testcase_04 AC 856 ms
158,968 KB
testcase_05 AC 838 ms
159,000 KB
testcase_06 AC 860 ms
158,992 KB
testcase_07 AC 868 ms
159,072 KB
testcase_08 AC 832 ms
159,088 KB
testcase_09 AC 831 ms
159,004 KB
testcase_10 AC 872 ms
159,104 KB
testcase_11 AC 880 ms
158,968 KB
testcase_12 AC 847 ms
159,032 KB
testcase_13 AC 855 ms
159,004 KB
testcase_14 AC 843 ms
159,000 KB
testcase_15 AC 843 ms
159,024 KB
testcase_16 AC 886 ms
159,140 KB
testcase_17 AC 869 ms
158,996 KB
testcase_18 AC 853 ms
159,036 KB
testcase_19 AC 864 ms
158,996 KB
testcase_20 AC 845 ms
159,212 KB
testcase_21 AC 854 ms
159,100 KB
testcase_22 AC 875 ms
159,124 KB
testcase_23 AC 844 ms
159,160 KB
testcase_24 AC 844 ms
159,220 KB
testcase_25 AC 853 ms
159,124 KB
testcase_26 AC 847 ms
158,908 KB
testcase_27 AC 858 ms
159,000 KB
testcase_28 AC 896 ms
158,996 KB
testcase_29 AC 887 ms
159,180 KB
testcase_30 AC 889 ms
159,080 KB
testcase_31 AC 909 ms
158,928 KB
testcase_32 AC 889 ms
159,116 KB
testcase_33 AC 896 ms
159,172 KB
testcase_34 AC 895 ms
159,328 KB
testcase_35 AC 888 ms
159,220 KB
testcase_36 AC 914 ms
159,204 KB
testcase_37 AC 882 ms
159,240 KB
testcase_38 AC 864 ms
158,928 KB
testcase_39 AC 868 ms
159,104 KB
testcase_40 AC 877 ms
159,276 KB
testcase_41 AC 888 ms
159,064 KB
testcase_42 AC 893 ms
159,284 KB
testcase_43 AC 889 ms
159,096 KB
testcase_44 AC 873 ms
158,976 KB
testcase_45 AC 869 ms
159,012 KB
testcase_46 AC 877 ms
159,160 KB
testcase_47 AC 867 ms
159,248 KB
testcase_48 AC 871 ms
159,220 KB
testcase_49 AC 889 ms
159,164 KB
testcase_50 AC 896 ms
159,204 KB
testcase_51 AC 895 ms
159,224 KB
testcase_52 AC 869 ms
159,336 KB
testcase_53 AC 912 ms
159,456 KB
testcase_54 AC 902 ms
159,196 KB
testcase_55 AC 926 ms
159,436 KB
testcase_56 AC 912 ms
159,256 KB
testcase_57 AC 914 ms
159,440 KB
testcase_58 AC 914 ms
159,332 KB
testcase_59 AC 948 ms
159,744 KB
testcase_60 AC 900 ms
159,168 KB
testcase_61 AC 901 ms
159,680 KB
testcase_62 AC 950 ms
159,660 KB
testcase_63 AC 883 ms
159,076 KB
testcase_64 AC 931 ms
159,504 KB
testcase_65 AC 1,037 ms
159,104 KB
testcase_66 AC 890 ms
159,436 KB
testcase_67 AC 900 ms
159,404 KB
testcase_68 AC 933 ms
159,580 KB
testcase_69 AC 924 ms
159,552 KB
testcase_70 AC 937 ms
159,768 KB
testcase_71 AC 962 ms
159,592 KB
testcase_72 AC 909 ms
159,576 KB
testcase_73 AC 922 ms
159,944 KB
testcase_74 AC 936 ms
159,944 KB
testcase_75 AC 933 ms
159,800 KB
testcase_76 AC 918 ms
159,876 KB
testcase_77 AC 962 ms
159,800 KB
testcase_78 AC 945 ms
159,952 KB
testcase_79 AC 951 ms
159,908 KB
testcase_80 AC 942 ms
159,908 KB
testcase_81 AC 925 ms
159,896 KB
testcase_82 AC 920 ms
159,804 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;
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(20), 0);
    FFT fft(bit(20));
    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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