結果

問題 No.1510 Simple Integral
ユーザー rniyarniya
提出日時 2021-05-16 14:29:16
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 262 ms / 2,000 ms
コード長 11,643 bytes
コンパイル時間 3,095 ms
コンパイル使用メモリ 222,476 KB
実行使用メモリ 8,188 KB
最終ジャッジ日時 2024-10-04 19:15:10
合計ジャッジ時間 9,728 ms
ジャッジサーバーID
（参考情報） 		judge2 / 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 12 ms
8,004 KB
testcase_01 AC 12 ms
8,004 KB
testcase_02 AC 12 ms
8,132 KB
testcase_03 AC 13 ms
7,944 KB
testcase_04 AC 12 ms
8,128 KB
testcase_05 AC 12 ms
8,144 KB
testcase_06 AC 14 ms
8,128 KB
testcase_07 AC 14 ms
8,136 KB
testcase_08 AC 13 ms
8,188 KB
testcase_09 AC 13 ms
8,096 KB
testcase_10 AC 13 ms
8,016 KB
testcase_11 AC 13 ms
8,120 KB
testcase_12 AC 13 ms
8,124 KB
testcase_13 AC 119 ms
8,120 KB
testcase_14 AC 110 ms
7,996 KB
testcase_15 AC 151 ms
8,072 KB
testcase_16 AC 157 ms
8,096 KB
testcase_17 AC 123 ms
8,008 KB
testcase_18 AC 106 ms
8,144 KB
testcase_19 AC 124 ms
8,012 KB
testcase_20 AC 126 ms
8,092 KB
testcase_21 AC 145 ms
8,080 KB
testcase_22 AC 117 ms
8,124 KB
testcase_23 AC 261 ms
8,096 KB
testcase_24 AC 262 ms
8,128 KB
testcase_25 AC 259 ms
8,176 KB
testcase_26 AC 260 ms
8,116 KB
testcase_27 AC 262 ms
8,116 KB
testcase_28 AC 259 ms
8,084 KB
testcase_29 AC 259 ms
8,132 KB
testcase_30 AC 260 ms
8,152 KB
testcase_31 AC 260 ms
8,124 KB
testcase_32 AC 260 ms
8,012 KB
testcase_33 AC 176 ms
8,180 KB
testcase_34 AC 169 ms
8,148 KB
testcase_35 AC 175 ms
8,088 KB
testcase_36 AC 181 ms
8,100 KB
testcase_37 AC 162 ms
8,132 KB
testcase_38 AC 173 ms
8,112 KB
testcase_39 AC 180 ms
8,072 KB
testcase_40 AC 183 ms
8,072 KB
testcase_41 AC 181 ms
8,040 KB
testcase_42 AC 175 ms
8,040 KB
testcase_43 AC 12 ms
7,940 KB
testcase_44 AC 12 ms
8,012 KB
testcase_45 AC 17 ms
8,108 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 # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U, typename V> ostream& operator<<(ostream& os, const tuple<T, U, V>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')';
    return os;
}
template <typename T, typename U, typename V, typename W> ostream& operator<<(ostream& os, const tuple<T, U, V, W>& t) {
    os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
#pragma endregion

/**
 * @brief modint
 * @docs docs/modulo/modint.md
 */
template <uint32_t mod> class modint {
    using i64 = int64_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

public:
    u32 v;
    constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}
    constexpr u32& value() noexcept { return v; }
    constexpr const u32& value() const noexcept { return v; }
    constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
    constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
    constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
    constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
    constexpr modint& operator+=(const modint& rhs) noexcept {
        v += rhs.v;
        if (v >= mod) v -= mod;
        return *this;
    }
    constexpr modint& operator-=(const modint& rhs) noexcept {
        if (v < rhs.v) v += mod;
        v -= rhs.v;
        return *this;
    }
    constexpr modint& operator*=(const modint& rhs) noexcept {
        v = (u64)v * rhs.v % mod;
        return *this;
    }
    constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.pow(mod - 2); }
    constexpr modint pow(u64 exp) const noexcept {
        modint self(*this), res(1);
        while (exp > 0) {
            if (exp & 1) res *= self;
            self *= self;
            exp >>= 1;
        }
        return res;
    }
    constexpr modint& operator++() noexcept {
        if (++v == mod) v = 0;
        return *this;
    }
    constexpr modint& operator--() noexcept {
        if (v == 0) v = mod;
        return --v, *this;
    }
    constexpr modint operator++(int) noexcept {
        modint t = *this;
        return ++*this, t;
    }
    constexpr modint operator--(int) noexcept {
        modint t = *this;
        return --*this, t;
    }
    constexpr modint operator-() const noexcept { return modint(mod - v); }
    template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }
    template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }
    template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }
    template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }
    constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }
    constexpr bool operator!() const noexcept { return !v; }
    friend istream& operator>>(istream& s, modint& rhs) noexcept {
        i64 v;
        rhs = modint{(s >> v, v)};
        return s;
    }
    friend ostream& operator<<(ostream& s, const modint& rhs) noexcept { return s << rhs.v; }
};

/**
 * @brief Number Theoretic Transform
 * @docs docs/convolution/NumberTheoreticTransform.md
 */
template <int mod> struct NumberTheoreticTransform {
    using Mint = modint<mod>;
    vector<Mint> roots;
    vector<int> rev;
    int base, max_base;
    Mint root;
    NumberTheoreticTransform() : base(1), rev{0, 1}, roots{Mint(0), Mint(1)} {
        int tmp = mod - 1;
        for (max_base = 0; tmp % 2 == 0; max_base++) tmp >>= 1;
        root = 2;
        while (root.pow((mod - 1) >> 1) == 1) root++;
        root = root.pow((mod - 1) >> max_base);
    }
    void ensure_base(int nbase) {
        if (nbase <= base) return;
        rev.resize(1 << nbase);
        for (int i = 0; i < (1 << nbase); i++) {
            rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (nbase - 1));
        }
        roots.resize(1 << nbase);
        for (; base < nbase; base++) {
            Mint z = root.pow(1 << (max_base - 1 - base));
            for (int i = 1 << (base - 1); i < (1 << base); i++) {
                roots[i << 1] = roots[i];
                roots[i << 1 | 1] = roots[i] * z;
            }
        }
    }
    void ntt(vector<Mint>& a) {
        const int n = a.size();
        int zeros = __builtin_ctz(n);
        ensure_base(zeros);
        int shift = base - zeros;
        for (int i = 0; i < n; i++) {
            if (i < (rev[i] >> shift)) {
                swap(a[i], a[rev[i] >> shift]);
            }
        }
        for (int k = 1; k < n; k <<= 1) {
            for (int i = 0; i < n; i += (k << 1)) {
                for (int j = 0; j < k; j++) {
                    Mint z = a[i + j + k] * roots[j + k];
                    a[i + j + k] = a[i + j] - z;
                    a[i + j] = a[i + j] + z;
                }
            }
        }
    }
    vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
        int need = a.size() + b.size() - 1;
        int nbase = 1;
        while ((1 << nbase) < need) nbase++;
        ensure_base(nbase);
        int sz = 1 << nbase;
        a.resize(sz, Mint(0));
        b.resize(sz, Mint(0));
        ntt(a);
        ntt(b);
        Mint inv_sz = 1 / Mint(sz);
        for (int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
        reverse(a.begin() + 1, a.end());
        ntt(a);
        a.resize(need);
        return a;
    }
    vector<int> multiply(vector<int> a, vector<int> b) {
        vector<Mint> A(a.size()), B(b.size());
        for (int i = 0; i < a.size(); i++) A[i] = Mint(a[i]);
        for (int i = 0; i < b.size(); i++) B[i] = Mint(b[i]);
        vector<Mint> C = multiply(A, B);
        vector<int> res(C.size());
        for (int i = 0; i < C.size(); i++) res[i] = C[i].v;
        return res;
    }
};

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
// const long long MOD = 1000000007;
const long long MOD = 998244353;

// https://ei1333.github.io/luzhiled/snippets/math/mod-log.html
int64_t mod_log(int64_t a, int64_t b, int64_t p) {
    int64_t g = 1;

    for (int64_t i = p; i; i /= 2) (g *= a) %= p;
    g = __gcd(g, p);

    int64_t t = 1, c = 0;
    for (; t % g; c++) {
        if (t == b) return c;
        (t *= a) %= p;
    }
    if (b % g) return -1;

    t /= g;
    b /= g;

    int64_t n = p / g, h = 0, gs = 1;

    for (; h * h < n; h++) (gs *= a) %= n;

    unordered_map<int64_t, int64_t> bs;
    for (int64_t s = 0, e = b; s < h; bs[e] = ++s) {
        (e *= a) %= n;
    }

    for (int64_t s = 0, e = t; s < n;) {
        (e *= gs) %= n;
        s += h;
        if (bs.count(e)) return c + s - bs[e];
    }
    return -1;
}

/**
 * @brief 繰り返し2乗法
 */
long long modpow(long long x, long long n, long long mod) {
    long long res = 1;
    while (n > 0) {
        if (n & 1LL) res = res * x % mod;
        x = x * x % mod;
        n >>= 1LL;
    }
    return res;
}
long long modinv(long long x, long long p) { return modpow(x, p - 2, p); }

using mint = modint<MOD>;
const int root = 3, MAX_A = 1000010;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    mint iroot = modpow(root, mod_log(root, MOD - 1, MOD) / 2, MOD);

    int N;
    cin >> N;
    vector<int> A(N), cnt(MAX_A, 0);
    for (int& x : A) {
        cin >> x;
        cnt[x]++;
    }
    for (int i = 0; i < N; i++) A.emplace_back(-A[i]);
    NumberTheoreticTransform<MOD> NTT;
    mint ans = 0;

    for (int i = 0; i < MAX_A; i++) {
        if (!cnt[i]) continue;
        vector<mint> f(N + 1, 0);
        f[0] = 1;

        for (int& z : A) {
            if (z == i) continue;
            mint inv = mint(1) / (iroot * (z - i));
            vector<mint> g(N + 1);
            g[0] = -inv;
            for (int i = 1; i <= N; i++) g[i] = g[i - 1] * inv;

            f = NTT.multiply(f, g);
            while (f.size() > N + 1) f.pop_back();
        }

        ans += f[cnt[i] - 1] * 2 * iroot;
    }

    cout << ans << '\n';
    return 0;
}
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