#658043 (C++17) No.1510 Simple Integral

提出ソース

結果

問題	No.1510 Simple Integral
ユーザー	haruki_K
提出日時	2021-05-16 16:35:45
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	84 ms / 2,000 ms
コード長	16,929 bytes
コンパイル時間	3,011 ms
コンパイル使用メモリ	224,644 KB
実行使用メモリ	6,824 KB
最終ジャッジ日時	2024-10-04 22:54:25
合計ジャッジ時間	5,115 ms
ジャッジサーバーID （参考情報）	judge2 / 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	2 ms 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,820 KB
testcase_03	AC	2 ms 6,820 KB
testcase_04	AC	2 ms 6,820 KB
testcase_05	AC	1 ms 6,820 KB
testcase_06	AC	48 ms 6,816 KB
testcase_07	AC	48 ms 6,816 KB
testcase_08	AC	48 ms 6,820 KB
testcase_09	AC	49 ms 6,816 KB
testcase_10	AC	48 ms 6,820 KB
testcase_11	AC	48 ms 6,820 KB
testcase_12	AC	48 ms 6,816 KB
testcase_13	AC	77 ms 6,820 KB
testcase_14	AC	82 ms 6,820 KB
testcase_15	AC	61 ms 6,816 KB
testcase_16	AC	59 ms 6,816 KB
testcase_17	AC	75 ms 6,824 KB
testcase_18	AC	84 ms 6,816 KB
testcase_19	AC	75 ms 6,816 KB
testcase_20	AC	73 ms 6,816 KB
testcase_21	AC	62 ms 6,820 KB
testcase_22	AC	78 ms 6,820 KB
testcase_23	AC	9 ms 6,816 KB
testcase_24	AC	9 ms 6,816 KB
testcase_25	AC	8 ms 6,816 KB
testcase_26	AC	8 ms 6,820 KB
testcase_27	AC	9 ms 6,820 KB
testcase_28	AC	8 ms 6,816 KB
testcase_29	AC	8 ms 6,820 KB
testcase_30	AC	8 ms 6,816 KB
testcase_31	AC	8 ms 6,816 KB
testcase_32	AC	9 ms 6,820 KB
testcase_33	AC	49 ms 6,816 KB
testcase_34	AC	51 ms 6,816 KB
testcase_35	AC	48 ms 6,816 KB
testcase_36	AC	46 ms 6,820 KB
testcase_37	AC	55 ms 6,816 KB
testcase_38	AC	50 ms 6,820 KB
testcase_39	AC	45 ms 6,816 KB
testcase_40	AC	45 ms 6,816 KB
testcase_41	AC	46 ms 6,820 KB
testcase_42	AC	48 ms 6,816 KB
testcase_43	AC	2 ms 6,816 KB
testcase_44	AC	1 ms 6,816 KB
testcase_45	AC	15 ms 6,816 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

raw source code

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define rng(x, l, r) begin(x) + (l), begin(x) + (r)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class A, class B> constexpr auto mp(A &&a, B &&b) { return make_pair(forward<A>(a), forward<B>(b)); }
template <class... T> constexpr auto mt(T&&... x) { return make_tuple(forward<T>(x)...); }
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } };
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;
template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) { return os << p.first << " " << p.second; }
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } };
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T, d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T, 0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T, d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; }
template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); }
template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); }
constexpr int64_t mod(int64_t x, int64_t m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr int64_t div_floor(int64_t x, int64_t y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr int64_t div_ceil(int64_t x, int64_t y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
vector<int> &operator--(vector<int> &v) { for (int &x : v) --x; return v; }
vector<int> &operator++(vector<int> &v) { for (int &x : v) ++x; return v; }
// <<<
// >>> modint

template <uint32_t md>
class modint {
    static_assert(md < (1u<<31), "");
    using M = modint;
    using i64 = int64_t;
    uint32_t x;
public:
    static constexpr uint32_t mod = md;
    constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { }
    constexpr i64 val() const { return x; }
    constexpr explicit operator i64() const { return x; }
    constexpr bool operator==(M r) const { return x == r.x; }
    constexpr bool operator!=(M r) const { return x != r.x; }
    constexpr M operator+() const { return *this; }
    constexpr M operator-() const { return M()-*this; }
    constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; }
    constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; }
    constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; }
    constexpr M& operator/=(M r) { return *this *= r.inv(); }
    constexpr M operator+(M r) const { return M(*this) += r; }
    constexpr M operator-(M r) const { return M(*this) -= r; }
    constexpr M operator*(M r) const { return M(*this) *= r; }
    constexpr M operator/(M r) const { return M(*this) /= r; }
    friend constexpr M operator+(i64 x, M y) { return M(x)+y; }
    friend constexpr M operator-(i64 x, M y) { return M(x)-y; }
    friend constexpr M operator*(i64 x, M y) { return M(x)*y; }
    friend constexpr M operator/(i64 x, M y) { return M(x)/y; }
    constexpr M inv() const { assert(x > 0); return pow(md-2); }
    constexpr M pow(i64 n) const {
        assert(not (x == 0 and n == 0));
        if (n < 0) return inv().pow(-n);
        M v = *this, r = 1;
        for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
        return r;
    }
#ifdef LOCAL
    friend string to_s(M r) { return to_s(r.val(), mod); }
#endif
    friend ostream& operator<<(ostream& os, M r) { return os << r.val(); }
    friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; }
};

// <<<
constexpr int64_t MOD = 998244353;
//constexpr int64_t MOD = 1e9+7;
using mint = modint<MOD>;
mint sign(int n) { return n & 1 ? -1 : +1; }
// >>> mod table

template <class mint> struct ModTable {
    vector<mint> fact, finv;
    void calc(int n) {
        int old = fact.size();
        if (n < old) return;
        n += 1000;
        fact.resize(n+1);
        finv.resize(n+1);
        if (old == 0) {
            fact[0] = fact[1] = finv[0] = finv[1] = 1;
            old = 2;
        }
        for (auto i = old; i <= n; i++) fact[i] = fact[i-1] * i;
        finv[n] = mint(1) / fact[n];
        for (auto i = n-1; i >= old; i--) finv[i] = finv[i+1] * (i+1);
    }
};
ModTable<mint> mod_tab;

mint fact(int n) {
    assert(0 <= n);
    return mod_tab.calc(n), mod_tab.fact[n];
}
mint finv(int n) {
    assert(0 <= n);
    return mod_tab.calc(n), mod_tab.finv[n];
}
mint comb(int n, int k) {
    if (n < 0 || k < 0 || n < k) return 0;
    mod_tab.calc(n);
    return mod_tab.fact[n] * mod_tab.finv[k] * mod_tab.finv[n-k];
}
mint perm(int n, int k) {
    assert(k >= 0); assert(n >= k);
    mod_tab.calc(n);
    return mod_tab.fact[n] * mod_tab.finv[n-k];
}

// <<<
// >>> FPS
template <class NTT>
struct FormalPowerSeries : NTT, vector<typename NTT::modint> {
    using mint = typename NTT::modint;
    using NTT::conv;
    using vector<mint>::vector; // inherit constructors
    using FPS = FormalPowerSeries;
    FormalPowerSeries() : vector<mint>() {}
    FormalPowerSeries(vector<mint> const& v) : vector<mint>(v) {}
    FormalPowerSeries(mint const& x) : vector<mint>({x}) {}
    void shrink() { while (this->size() and this->back() == 0) this->pop_back(); }
    mint get(int i) const {
        assert(i >= 0);
        if (i < (int)this->size()) return (*this)[i];
        else return 0;
    }
    mint &set(int i, mint x) {
        assert(i >= 0);
        if (i >= (int)this->size()) this->resize(i+1);
        return (*this)[i] = x;
    }
    bool operator==(FPS const& r) const {
        const int n = min(this->size(), r.size());
        rep (i, n) {
            if ((*this)[i] != r[i]) return false;
        }
        for (int i = n; i < (int)this->size(); ++i) {
            if ((*this)[i] != mint(0)) return false;
        }
        for (int i = n; i < (int)r.size(); ++i) {
            if (r[i] != mint(0)) return false;
        }
        return true;
    }
    bool operator!=(FPS const& r) const { return !((*this) == r); }
    FPS operator+(FPS const& r) const { return FPS(*this) += r; }
    FPS operator-(FPS const& r) const { return FPS(*this) -= r; }
    FPS& operator+=(FPS const& r) {
        if (r.size() > this->size()) this->resize(r.size());
        rep (i, r.size()) (*this)[i] += r[i];
        return *this;
    }
    FPS& operator-=(FPS const& r) {
        if (r.size() > this->size()) this->resize(r.size());
        rep (i, r.size()) (*this)[i] -= r[i];
        return *this;
    }
    FPS operator*(FPS const& r) const {
        if (this->empty() || r.empty()) return {};
        return conv(*this, r);
    }
    FPS& operator*=(FPS const& r) { return *this = *this * r; }
    friend FPS operator+(mint const& x, FPS const& f) { return FPS{x}+f; }
    friend FPS operator-(mint const& x, FPS const& f) { return FPS{x}-f; }
    friend FPS operator*(mint const& x, FPS const& f) { return FPS{x}*f; }
    friend FPS operator+(FPS const& f, mint const& x) { return f+FPS{x}; }
    friend FPS operator-(FPS const& f, mint const& x) { return f-FPS{x}; }
    friend FPS operator*(FPS const& f, mint const& x) { return f*FPS{x}; }
    FPS take(int sz) const {
        FPS ret(this->begin(), this->begin() + min<int>(this->size(), sz));
        ret.resize(sz);
        return ret;
    }
    FPS inv(int sz = -1) const {
        assert(this->size()); assert((*this)[0] != mint(0));
        if (sz < 0) sz = this->size();
        FPS ret = { mint(1)/(*this)[0] };
        for (int i = 1; i < sz; i <<= 1) {
            ret = ret + ret - ret*ret*take(i<<1);
            ret.resize(i<<1);
        }
        ret.resize(sz);
        return ret;
    }
    FPS diff() const {
        FPS ret(max<int>(0, this->size()-1));
        rep (i, ret.size()) ret[i] = (*this)[i+1]*mint(i+1);
        return ret;
    }
    FPS integral() const {
        FPS ret(this->size()+1);
        ret[0] = 0;
        rep (i, this->size()) ret[i+1] = (*this)[i]/mint(i+1);
        return ret;
    }
    FPS log(int sz = -1) const {
        assert(this->size()); assert((*this)[0] == mint(1));
        if (sz < 0) sz = this->size();
        return (diff()*inv(sz)).take(sz-1).integral();
    }
    // FPS log(int sz = -1) const {
    //     assert(this->size()); assert((*this)[0] == mint(1));
    //     if (sz < 0) sz = this->size();
    //     auto ret = diff()*inv(sz);
    //     ret.resize(sz);
    //     for (int i = sz-1; i > 0; --i) ret[i] = ret[i-1]/mint(i);
    //     ret[0] = 0;
    //     return ret;
    // }
    FPS exp(int sz = -1) const {
        FPS ret = {mint(1)};
        if (this->empty()) return ret;
        assert((*this)[0] == mint(0));
        if (sz < 0) sz = this->size();
        for (int i = 1; i < sz; i <<= 1) {
            ret *= take(i<<1) + mint(1) - ret.log(i<<1);
            ret.resize(i<<1);
        }
        ret.resize(sz);
        return ret;
    }
    FPS pow(int64_t k, int sz = -1) const {
        if (sz < 0) sz = this->size();
        int deg = 0;
        while (deg < sz && (*this).get(deg) == mint(0)) ++deg;
        assert(k >= 0 || deg == 0);

        auto c = mint(1)/(*this).get(deg);
        FPS ret(sz-deg);
        rep (i, sz-deg) ret[i] = (*this).get(deg+i)*c;
        ret = (ret.log()*k).exp() * (*this).get(deg).pow(k);

        ret.resize(sz);
        for (int i = sz-1; i >= 0; --i) {
            int j = i-deg*k;
            ret[i] = (j >= 0 ? ret[j] : mint(0));
        }
        return ret;
    }
    mint eval(mint x) const {
        mint p = 1, ret = 0;
        rep (i, this->size()) {
            ret += (*this)[i] * p;
            p *= x;
        }
        return ret;
    }
};
// <<<
// >>> NTT
template <class ModInt, int64_t g>
struct NTT {
    using modint = ModInt;
    static constexpr int64_t mod = ModInt::mod, gen = g, max_lg = __builtin_ctzll(mod-1);
    // mod:prime, g:primitive root
    static_assert(mod > 0 && g > 0 && max_lg > 0, "");

    using arr_t = array<ModInt, max_lg+1>;
    static arr_t ws, iws;
    static void init() {
        static bool built = false;
        if (built) return;
        for (int i = 0; i <= max_lg; i++) {
            ws[i] = -ModInt(g).pow((mod-1)>>(i+2));
            iws[i] = ModInt(1)/ws[i];
        }
        built = true;
    }
    static void ntt(ModInt a[], int lg) {
        for (int b = lg-1; b >= 0; b--) {
            ModInt w = 1;
            for (int i = 0, k = 0; i < (1<<lg); i += 1<<(b+1)) {
                for (int j = i; j < (i|(1<<b)); j++) {
                    const int k = j|(1<<b);
                    const auto x = a[j], y = a[k];
                    a[j] = x + y*w;
                    a[k] = x - y*w;
                }
                w *= ws[__builtin_ctz(++k)];
            }
        }
//        bit_reverse(a, 1<<lg);
    }
    static void intt(ModInt a[], int lg) {
//        bit_reverse(a, 1<<lg);
        for (int b = 0; b < lg; b++) {
            ModInt w = 1;
            for (int i = 0, k = 0; i < (1<<lg); i += 1<<(b+1)) {
                for (int j = i; j < (i|(1<<b)); j++) {
                    const int k = j|(1<<b);
                    const auto x = a[j], y = a[k];
                    a[j] = x + y;
                    a[k] = w*(x - y);
                }
                w *= iws[__builtin_ctz(++k)];
            }
        }
    }
    template <class T>
    static vector<ModInt> conv(vector<T> const& a, vector<T> const& b) {
        if (a.empty() || b.empty()) return {};
        init();
        const int s = a.size() + b.size() - 1, lg = __lg(2*s-1);
        assert(lg <= max_lg);

        vector<ModInt> aa(1<<lg);
        rep (i, a.size()) aa[i] = (int64_t)a[i];
        ntt(aa.data(), lg);

        vector<ModInt> bb(1<<lg);
        rep (i, b.size()) bb[i] = (int64_t)b[i];
        ntt(bb.data(), lg);

        const auto x = ModInt(1)/ModInt(1<<lg);
        rep (i, 1<<lg) aa[i] *= bb[i]*x;
        intt(aa.data(), lg); aa.resize(s);
        return aa;
    }
    template <class T>
    static vector<ModInt> conv(vector<T> const& a) {
        if (a.empty()) return {};
        init();
        const int s = a.size()*2 - 1, lg = __lg(2*s-1);
        assert(lg <= max_lg);

        vector<ModInt> aa(1<<lg);
        rep (i, a.size()) aa[i] = (int64_t)a[i];
        ntt(aa.data(), lg);

        const auto x = ModInt(1)/ModInt(1<<lg);
        rep (i, 1<<lg) aa[i] *= aa[i]*x;
        intt(aa.data(), lg); aa.resize(s);
        return aa;
    }
};
template <class ModInt, int64_t g>
typename NTT<ModInt, g>::arr_t NTT<ModInt, g>::ws;
template <class ModInt, int64_t g>
typename NTT<ModInt, g>::arr_t NTT<ModInt, g>::iws;
// <<<
using ntt = NTT<mint, 3>;
using FPS = FormalPowerSeries<ntt>;

const mint I = mint(3).pow((MOD-1)/4);

int32_t main() {
    int n; cin >> n;
    vector<int> a(n); cin >> a;

    map<int, int> cnt;
    for (int x : a) cnt[x]++;

    mint ans = 0;
    for (auto [x, num] : cnt) {
        FPS f = { 1 };
        rep (i, n) {
            if (a[i] != x) {
                mint k = mint(-x*I+a[i]*I).inv();
                FPS g(num);
                rep (j, num) g[j] = -k.pow(j+1);
                f *= g;
            }
            mint k = mint(-x*I-a[i]*I).inv();
            FPS g(num);
            rep (j, num) g[j] = -k.pow(j+1);
            f *= g;
        }
        dump(f, x, num);
        ans += f.get(num-1);
    }
    ans *= 2*I;
    cout << ans << '\n';

}

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結果

テストケース

ソースコード