#364618 (C++14) No.856 増える演算

提出ソース

結果

問題	No.856 増える演算
ユーザー	jell
提出日時	2019-08-01 18:06:29
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	102 ms / 3,153 ms
コード長	14,627 bytes
コンパイル時間	1,895 ms
コンパイル使用メモリ	140,944 KB
実行使用メモリ	20,996 KB
最終ジャッジ日時	2024-07-05 07:46:08
合計ジャッジ時間	8,290 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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	41 ms 20,480 KB
testcase_01	AC	40 ms 20,480 KB
testcase_02	AC	39 ms 20,600 KB
testcase_03	AC	39 ms 20,548 KB
testcase_04	AC	38 ms 20,580 KB
testcase_05	AC	37 ms 20,600 KB
testcase_06	AC	38 ms 20,608 KB
testcase_07	AC	37 ms 20,608 KB
testcase_08	AC	38 ms 20,608 KB
testcase_09	AC	38 ms 20,560 KB
testcase_10	AC	39 ms 20,480 KB
testcase_11	AC	36 ms 20,516 KB
testcase_12	AC	39 ms 20,596 KB
testcase_13	AC	38 ms 20,480 KB
testcase_14	AC	37 ms 20,480 KB
testcase_15	AC	37 ms 20,612 KB
testcase_16	AC	36 ms 20,420 KB
testcase_17	AC	38 ms 20,484 KB
testcase_18	AC	38 ms 20,480 KB
testcase_19	AC	39 ms 20,456 KB
testcase_20	AC	39 ms 20,608 KB
testcase_21	AC	39 ms 20,480 KB
testcase_22	AC	35 ms 20,480 KB
testcase_23	AC	38 ms 20,504 KB
testcase_24	AC	39 ms 20,620 KB
testcase_25	AC	38 ms 20,612 KB
testcase_26	AC	38 ms 20,480 KB
testcase_27	AC	39 ms 20,480 KB
testcase_28	AC	39 ms 20,600 KB
testcase_29	AC	40 ms 20,500 KB
testcase_30	AC	39 ms 20,600 KB
testcase_31	AC	39 ms 20,460 KB
testcase_32	AC	39 ms 20,636 KB
testcase_33	AC	42 ms 20,648 KB
testcase_34	AC	47 ms 20,640 KB
testcase_35	AC	43 ms 20,520 KB
testcase_36	AC	47 ms 20,692 KB
testcase_37	AC	47 ms 20,664 KB
testcase_38	AC	38 ms 20,400 KB
testcase_39	AC	38 ms 20,436 KB
testcase_40	AC	36 ms 20,640 KB
testcase_41	AC	39 ms 20,524 KB
testcase_42	AC	46 ms 20,692 KB
testcase_43	AC	39 ms 20,592 KB
testcase_44	AC	36 ms 20,480 KB
testcase_45	AC	37 ms 20,608 KB
testcase_46	AC	41 ms 20,524 KB
testcase_47	AC	39 ms 20,516 KB
testcase_48	AC	44 ms 20,556 KB
testcase_49	AC	40 ms 20,500 KB
testcase_50	AC	45 ms 20,532 KB
testcase_51	AC	47 ms 20,560 KB
testcase_52	AC	46 ms 20,680 KB
testcase_53	AC	78 ms 20,684 KB
testcase_54	AC	61 ms 20,536 KB
testcase_55	AC	78 ms 20,716 KB
testcase_56	AC	59 ms 20,680 KB
testcase_57	AC	77 ms 20,700 KB
testcase_58	AC	69 ms 20,628 KB
testcase_59	AC	90 ms 20,896 KB
testcase_60	AC	62 ms 20,656 KB
testcase_61	AC	93 ms 20,924 KB
testcase_62	AC	88 ms 20,696 KB
testcase_63	AC	41 ms 20,668 KB
testcase_64	AC	85 ms 20,728 KB
testcase_65	AC	57 ms 20,532 KB
testcase_66	AC	64 ms 20,572 KB
testcase_67	AC	70 ms 20,648 KB
testcase_68	AC	87 ms 20,752 KB
testcase_69	AC	86 ms 20,744 KB
testcase_70	AC	96 ms 20,960 KB
testcase_71	AC	87 ms 20,764 KB
testcase_72	AC	87 ms 20,816 KB
testcase_73	AC	102 ms 20,940 KB
testcase_74	AC	102 ms 20,868 KB
testcase_75	AC	101 ms 20,952 KB
testcase_76	AC	99 ms 20,996 KB
testcase_77	AC	99 ms 20,964 KB
testcase_78	AC	101 ms 20,868 KB
testcase_79	AC	100 ms 20,828 KB
testcase_80	AC	99 ms 20,868 KB
testcase_81	AC	99 ms 20,776 KB
testcase_82	AC	80 ms 20,996 KB

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ソースコード

raw source code

#ifndef LOCAL
    #pragma GCC optimize("Ofast")
#endif
#include <cassert>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <functional>
#include <queue>
#include <deque>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <complex>
#include <iomanip>
#include <bitset>
#include <random>

using namespace std;
using i64 = int_fast64_t;
using pii = pair<int, int>;
using pli = pair<int_fast64_t, int>;
using pll = pair<int_fast64_t, int_fast64_t>;
template <class T> using heap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> constexpr T inf = numeric_limits<T>::max() / (T)2 - (T)123456;
constexpr int dx[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
constexpr int dy[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0};
constexpr long double Pi = 3.1415926535897932384626433832;
constexpr long double Golden = 1.61803398874989484820;

#define iostream_untie true
#define stdout_precision 10
#define stderr_precision 10
#define itrep(i,v) for(auto i = begin(v); i != end(v); ++i)
#define ritrep(i,v) for(auto i = rbegin(v); i != rend(v); ++i)
#define rep(i,n) for(int_fast64_t i = 0; i < (int_fast64_t)(n); ++i)
#define rrep(i,n) for(int_fast64_t i = (int_fast64_t)(n) - 1; i >= 0; --i)
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
#define fir first
#define sec second
#define u_map unordered_map
#define u_set unordered_set
#define l_bnd lower_bound
#define u_bnd upper_bound
#define emp emplace
#define emf emplace_front
#define emb emplace_back
#define pof pop_front
#define pob pop_back
#define mkp make_pair
#define mkt make_tuple
#define popcnt __builtin_popcount

namespace setup {
    struct setupper {
        setupper() {
            if(iostream_untie) {
                ios::sync_with_stdio(false);
                std::cin.tie(nullptr);
                std::cout.tie(nullptr);
                std::cerr.tie(nullptr);
            }
            std::cout << std::fixed << std::setprecision(stdout_precision);
            std::cerr << std::fixed << std::setprecision(stderr_precision);
    #ifdef LOCAL
            if(!freopen("stderr.txt","wt",stderr)) {
                freopen("CON","wt",stderr);
                std::cerr << "Failed to open the stderr file\n";
            }
            if(!freopen("stdout.txt","wt",stdout)) {
                freopen("CON","wt",stdout);
                std::cerr << "Failed to open the stdout file\n";
            }
            if(!freopen("stdin.txt","rt",stdin)) {
                freopen("CON","rt",stdin);
                std::cerr << "Failed to open the stdin file.\n";
            }
            // auto print_atexit = []() {
            //     std::cerr << "Exec time : " << clock() / (double)CLOCKS_PER_SEC * 1000.0 << "ms\n";
            //     std::cerr << "------------\n";
            // };
            // atexit((void(*)())print_atexit);
    #endif
        }
    } __setupper;
}

namespace std {
    template <class RAitr> void rsort(RAitr __first, RAitr __last) {
        sort(__first, __last, greater<>());
    }
    template <class T> void hash_combine(size_t &seed, T const &key) {
        seed ^= hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
    }
    template <class T, class U> struct hash<pair<T,U>> {
        size_t operator()(pair<T,U> const &pr) const
        {
            size_t seed = 0;
            hash_combine(seed,pr.first);
            hash_combine(seed,pr.second);
            return seed;
        }
    };
    template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1>
    struct hashval_calc {
        static void apply(size_t& seed, tuple_t const& t) {
            hashval_calc<tuple_t, index - 1>::apply(seed, t);
            hash_combine(seed,get<index>(t));
        }
    };
    template <class tuple_t>
    struct hashval_calc<tuple_t, 0> {
        static void apply(size_t& seed, tuple_t const& t) {
            hash_combine(seed,get<0>(t));
        }
    };
    template <class ...T> struct hash<tuple<T...>> {
        size_t operator()(tuple<T...> const& t) const
        {
            size_t seed = 0;
            hashval_calc<tuple<T...>>::apply(seed,t);
            return seed;
        }
    };
}

template <class T, class U> istream &operator>> (istream &s, pair<T,U> &p) { return s >> p.first >> p.second; }
template <class T, class U> ostream &operator<< (ostream &s, const pair<T,U> p) { return s << p.first << " " << p.second; }
template <class T> istream &operator>> (istream &s, vector<T> &v) { for(T &e : v) { s >> e; }   return s; }
template <class T> ostream &operator<< (ostream &s, const vector<T> &v) {
    for(size_t i = 0; i < v.size(); ++i) { s << (i ? " " : "") << v[i]; }   return s;
}
template <class tuple_t, size_t index>
struct tupleos {
    static ostream &apply(ostream &s, const tuple_t &t) {
        tupleos<tuple_t,index - 1>::apply(s,t);
        return s << " " << get<index>(t);
    }
}; 
template <class tuple_t>
struct tupleos<tuple_t, 0> {
    static ostream &apply(ostream &s, const tuple_t &t) {
        return s << get<0>(t);
    }
};
template <class ...T> ostream &operator<< (ostream &s, const tuple<T...> &t) {
    return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(s,t);
}
template <> ostream &operator<< (ostream &s, const tuple<> &t) { return s; }
#define dump(...) cerr << " [ " << __LINE__ << " : " << __FUNCTION__ << " ] " << #__VA_ARGS__ << " : ";\
dump_func(__VA_ARGS__)
template <class T> void dump_func(T x) { cerr << x << '\n'; }
template <class T,class ...Rest> void dump_func(T x, Rest ... rest) { cerr << x << ","; dump_func(rest...); }
template <class T> void write(T x) { cout << x << '\n'; }
template <class T, class ...Rest> void write(T x, Rest ... rest) { cout << x << ' '; write(rest...); }
void writeln() {}
template <class T, class ...Rest> void writeln(T x, Rest ... rest) { cout << x << '\n'; writeln(rest...); }
#define esc(...) writeln(__VA_ARGS__), exit(0)
template <class P> void read(P __first, P __second) {
    for(P i = __first; i != __second; ++i) cin >> *i;
}

namespace updater {
    template <class T> static void add(T &x, const T &y) { x += y; }
    template <class T> static void ext_add(T &x, const T &y, size_t w) { x += y * w; }
    template <class T> static void mul(T &x, const T &y) { x *= y; }
    template <class T> static void ext_mul(T &x, const T &y, size_t w) { x *= (T)pow(y,w); }
    template <class T> static bool chmax(T &x, const T &y) { return x < y ? x = y, true : false; }
    template <class T> static bool chmin(T &x, const T &y) { return x > y ? x = y, true : false; }
};
using updater::add;
using updater::chmax;
using updater::chmin;

template <class T> constexpr T minf(const T &x, const T &y) { return min(x,y); }
template <class T> constexpr T maxf(const T &x, const T &y) { return max(x,y); }
constexpr bool bit(i64 n, int e) { return (n >> e) & 1; }
constexpr int_fast64_t mask(int_fast64_t n, int e) { return n & ((1 << e) - 1); }
constexpr int ilog(int_fast64_t x, int_fast64_t b = 2) { return x ? 1 + ilog(x / b, b) : -1; }
int_fast64_t binry(int_fast64_t ok, int_fast64_t ng, const function<bool(int_fast64_t)> &fn) {
    while (abs(ok - ng) > 1) {
        int_fast64_t mid = (ok + ng) / 2;
        (fn(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <class A, size_t N, class T> void init(A (&array)[N], const T &val) { fill((T*)array,(T*)(array + N),val); }
template <class T> vector<int> cmprs(const vector<T> &v) {
    vector<T> tmp = v; vector<int> ret;
    sort(begin(tmp),end(tmp));
    tmp.erase(unique(begin(tmp),end(tmp)), end(tmp));
    for(T i : v) ret.emplace_back(lower_bound(begin(tmp),end(tmp),i) - begin(tmp));
    return ret;
}
template <class T> vector<int> cmprs(const T *__first, const T *__last) {
    return cmprs(vector<T>(__first, __last));
}
void for_subset(int_fast64_t s, const function<void(int_fast64_t)> &fn) {
    int_fast64_t tmp = s;
    do { fn(tmp); } while((--tmp &= s) != s);
}



/* The main code follows. */

template <int32_t mod>
struct modint {
    int x;
    constexpr modint() : x(0) {}
    constexpr modint(int_fast64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    constexpr modint &operator+=(const modint &p) {
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }

    constexpr modint &operator++() { return ++x,*this; }

    constexpr modint operator++(int) {
        modint t = *this;
        return ++x,t;
    }

    constexpr modint &operator-=(const modint &p) {
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    constexpr modint &operator--() { return --x, *this; }

    constexpr modint operator--(int) {
        modint t = *this;
        return --x,t;
    }

    constexpr modint &operator*=(const modint &p) {
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }

    constexpr modint &operator/=(const modint &p) {
        *this *= inverse(p);
        return *this;
    }

    constexpr modint operator-() const { return modint(-x); }

    constexpr modint operator+(const modint &p) const { return modint(*this) += p; }

    constexpr modint operator-(const modint &p) const { return modint(*this) -= p; }

    constexpr modint operator*(const modint &p) const { return modint(*this) *= p; }

    constexpr modint operator/(const modint &p) const { return modint(*this) /= p; }

    constexpr bool operator==(const modint &p) const { return x == p.x; }

    constexpr bool operator!=(const modint &p) const { return x != p.x; }

    constexpr bool operator!() const { return !x; }

    // constexpr bool operator>(const modint &p) const { return x > p.x; }

    // constexpr bool operator<(const modint &p) const { return x <  p.x; }

    // constexpr bool operator>=(const modint &p) const { return x >= p.x; }

    // constexpr bool operator<=(const modint &p) const { return x <= p.x; }

    constexpr static modint inverse(const modint &p) {
        int a = p.x, b = mod, u = 1, v = 0;
        while(b > 0) {
            int t = a / b;
            a -= t * b;
            a ^= b ^= a ^= b;
            u -= t * v;
            u ^= v ^= u ^= v;
        }
        return modint(u);
    }

    constexpr static modint pow(modint p, int_fast64_t e) {
        if(!e) return 1;
        if(e < 0) e = (e % (mod - 1) + mod - 1) % (mod - 1);
        return pow(p * p, e >> 1) * (e & 1 ? p : 1);
    }

    friend ostream &operator<<(ostream &s, const modint &p) { return s << p.x; }

    friend istream &operator>>(istream &s, modint &p) {
        uint_fast64_t x;
        p = modint((s >> x,x));
        return s;
    }
};

namespace FFT {
    template <class Real>
    vector<complex<Real>> fft(vector<complex<Real>> x, bool inverse = false) {
        size_t n = x.size(),mask = n - 1;   //"n" must be a power of two.
        static vector<complex<Real>> tmp;
        tmp.resize(n);
        for(size_t i = n >> 1; i; i >>= 1) {
            Real theta = Pi * 2 * i * (inverse ? -1 : 1) / n;
            complex<Real> zeta(cos(theta),sin(theta));
            complex<Real> powzeta = 1;
            for(size_t j = 0; j < n; j += i) {
                for(size_t k = 0; k < i; ++k) {
                    tmp[j + k] = x[k + (mask & j << 1)] + powzeta * x[k + (mask & i + (j << 1))];
                }
                powzeta *= zeta;
            }
            swap(x,tmp);
        }
        if(inverse) for(size_t i = 0; i < n; ++i) x[i] /= n;
        return x;
    }

    template <class T>
    vector<T> conv(const vector<T> &a, const vector<T> &b) {
        size_t n = 1;
        while(n + 1 < a.size() + b.size()) n <<= 1;
        vector<complex<double>> x(n),y(n);
        for(size_t i = 0; i != a.size(); ++i) x[i].real(a[i]);
        for(size_t i = 0; i != b.size(); ++i) x[i].imag(b[i]);
        x = fft(x,false);
        for(int i = 0; i < n; ++i) {
            int j = i ? n - i : 0;
            y[i] = (x[i] + conj(x[j])) * (x[i] - conj(x[j])) * complex<double>(0,-.25);
        }
        y = fft(y,true);
        vector<T> c(n);
        for(size_t i = 0; i < n; ++i) c[i] = y[i].real();
        return c;
    }

    template <>
    vector<int_fast64_t> conv(const vector<int_fast64_t> &a, const vector<int_fast64_t> &b) {
        size_t n = 1;
        while(n + 1 < a.size() + b.size()) n <<= 1;
        vector<complex<double>> x(n),y(n);
        for(size_t i = 0; i != a.size(); ++i) x[i].real(a[i]);
        for(size_t i = 0; i != b.size(); ++i) x[i].imag(b[i]);
        x = fft(x,false);
        for(int i = 0; i < n; ++i) {
            int j = i ? n - i : 0;
            y[i] = (x[i] + conj(x[j])) * (x[i] - conj(x[j])) * complex<double>(0,-.25);
        }
        y = fft(y,true);
        vector<int_fast64_t> c(n);
        for(size_t i = 0; i < n; ++i) c[i] = round(y[i].real());
        return c;
    }

    template <>
    vector<int> conv(const vector<int> &a, const vector<int> &b) {
        size_t n = 1;
        while(n + 1 < a.size() + b.size()) n <<= 1;
        vector<complex<double>> x(n), y(n);
        for(size_t i = 0; i != a.size(); ++i) x[i].real(a[i]);
        for(size_t i = 0; i != b.size(); ++i) x[i].imag(b[i]);
        x = fft(x,false);
        for(int i = 0; i < n; ++i) {
            int j = i ? n - i : 0;
            y[i] = (x[i] + conj(x[j])) * (x[i] - conj(x[j])) * complex<double>(0,-.25);
        }
        y = fft(y,true);
        vector<int> c(n);
        for(size_t i = 0; i < n; ++i) c[i] = round(y[i].real());
        return c;
    }
}


using mint=modint<1000000007>;
int n;
int a[1<<17];


void solve() {
    mint ans=1;
    for(i64 i=n-1,r=0; i>=0; r+=a[i--]) {
        ans*=mint::pow(a[i],r);
    }
    vector<i64> cnt(100001);
    for(int i=0; i<n; ++i) {
        cnt[a[i]]++;
    }
    auto ccv=FFT::conv(cnt,cnt);
    for(int i=0; i<n; ++i) {
        ccv[a[i]*2]--;
    }
    for(int i=0; i<=200000; ++i) {
        ccv[i]/=2;
    }
    for(int i=2; i<=200000; ++i) {
        ans*=mint::pow(i,ccv[i]);
    }
    int *p=min_element(a,a+n);
    int *l=min_element(a,p);
    int *r=min_element(p+1,a+n);
    if(p==l) {
        ans/=*r+*p;
        ans/=mint::pow(*p,*r);
    } else if(p==a+n-1) {
        ans/=*l+*p;
        ans/=mint::pow(*l,*p);
    } else {
        auto f=[&](double x, double y) -> double {
            return y*log(x)+log(x+y);
        };
        if(f(*l,*p)>f(*p,*r)) {
            ans/=*r+*p;
            ans/=mint::pow(*p,*r);
        } else {
            ans/=*l+*p;
            ans/=mint::pow(*l,*p);
        }
    }
    cout<<ans<<endl;
}

signed main() {
    cin>>n;
    rep(i,n) cin>>a[i];
    solve();
}

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結果

テストケース

ソースコード