結果

問題 No.2635 MST on Line++ 2
コンテスト
ユーザー Forested
提出日時 2024-02-16 22:53:22
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 118 ms / 2,000 ms
コード長 6,581 bytes
コンパイル時間 4,020 ms
コンパイル使用メモリ 239,448 KB
最終ジャッジ日時 2025-02-19 14:36:22
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
（要ログイン）
ファイルパターン 結果
sample AC * 4
other AC * 41
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 # 

#ifndef LOCAL
#define FAST_IO
#endif

// ============
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
    return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
    return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
    V<i32> ret(arr.size());
    iota(ALL(ret), 0);
    sort(ALL(ret), [&](i32 i, i32 j) -> bool {
        if (arr[i] == arr[j]) {
            return i < j;
        } else {
            return arr[i] < arr[j];
        }
    });
    return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
    for (T &ele : x) {
        scan(ele);
    }
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
    scan(head);
    read(tail...);
}
#define CHAR(...)     \
    char __VA_ARGS__; \
    read(__VA_ARGS__);
#define U32(...)     \
    u32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define U64(...)     \
    u64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I32(...)     \
    i32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I64(...)     \
    i64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define STR(...)        \
    string __VA_ARGS__; \
    read(__VA_ARGS__);
#define VEC(type, name, size) \
    V<type> name(size);       \
    read(name);
#define VVEC(type, name, size1, size2)    \
    VV<type> name(size1, V<type>(size2)); \
    read(name);
// ============

#ifdef DEBUGF
#else
#define DBG(...) (void)0
#endif

// ============

// ============

// ============

#include <algorithm>
#include <iostream>
#include <atcoder/convolution>

namespace poly {

using Mint = atcoder::modint998244353;
using Poly = std::vector<Mint>;

Poly add(Poly f, Poly g) {
    if (f.size() < g.size()) {
        std::swap(f, g);
    }
    for (int i = 0; i < (int)g.size(); ++i) {
        f[i] += g[i];
    }
    return f;
}

Poly sub(Poly f, Poly g) {
    if (f.size() < g.size()) {
        std::swap(f, g);
    }
    for (int i = 0; i < (int)g.size(); ++i) {
        f[i] -= g[i];
    }
    return f;
}

Poly mul(const Poly &f, const Poly &g) {
    return atcoder::convolution(f, g);
}

void dft(Poly &f) {
    atcoder::internal::butterfly(f);
}

void idft(Poly &f) {
    atcoder::internal::butterfly_inv(f);
    int ctz = __builtin_ctz((int)f.size());
    Mint inv = Mint::raw(Mint::mod() - (Mint::mod() >> ctz));
    for (Mint &cf : f) {
        cf *= inv;
    }
}

} // namespace poly
// ============

namespace poly {

class Factorial {
    std::vector<Mint> fac;
    std::vector<Mint> ifac;
    
public:
    Factorial() : fac(1, Mint::raw(1)), ifac(1, Mint::raw(1)) {}
    
    void reserve(int n) {
        int m = (int)fac.size() - 1;
        if (n <= m) {
            return;
        }
        fac.resize(n + 1);
        for (int i = m + 1; i <= n; ++i) {
            fac[i] = fac[i - 1] * Mint::raw(i);
        }
        ifac.resize(n + 1);
        ifac[n] = fac[n].inv();
        for (int i = n - 1; i >= m; --i) {
            ifac[i] = ifac[i + 1] * Mint::raw(i + 1);
        }
    }
    
    Mint fact(int n) const {
        assert(n < (int)fac.size());
        return fac[n];
    }
    
    Mint inv_fact(int n) const {
        assert(n < (int)fac.size());
        return ifac[n];
    }
    
    Mint inv_n(int n) const {
        assert(n < (int)fac.size());
        return ifac[n] * fac[n - 1];
    }
    
    Mint binom(int n, int r) const {
        assert(n < (int)fac.size());
        return fac[n] * ifac[r] * ifac[n - r];
    }
} factorial;

} // namespace poly
// ============

namespace poly {

Poly taylor_shift(Poly f, Mint c) {
    int n = (int)f.size();
    factorial.reserve(n);
    for (int i = 0; i < n; ++i) {
        f[i] *= factorial.fact(i);
    }
    std::reverse(f.begin(), f.end());
    Mint pw(1);
    Poly g(n);
    for (int i = 0; i < n; ++i) {
        g[i] = pw * factorial.inv_fact(i);
        pw *= c;
    }
    Poly h = mul(f, g);
    h.resize(n);
    std::reverse(h.begin(), h.end());
    for (int i = 0; i < n; ++i) {
        h[i] *= factorial.inv_fact(i);
    }
    return h;
}

} // namespace poly
// ============

void solve() {
    using M = poly::Mint;
    I32(n, k);
    VEC(i32, a, n);
    poly::factorial.reserve(n);
    sort(ALL(a));
    reverse(ALL(a));
    poly::Poly f(n);
    REP(i, n) {
        f[i] = M::raw(a[i]);
    }
    poly::Poly g = poly::taylor_shift(f, M(1));
    g.insert(g.begin(), M());
    DBG(g);
    REP(i, n + 1) {
        g[i] /= poly::factorial.binom(n, i);
    }
    M exp;
    REP(i, n - 1) {
        i32 len = min(i + 1, k) + min(n - 1 - i, k);
        exp += g[len];
    }
    exp *= poly::factorial.fact(n);
    cout << exp.val() << '\n';
}

int main() {
    i32 t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }
}
0