#1020963 (C++23) No.2944 Sigma Partition Problem

• 問題: No.2944 Sigma Partition Problem
• ユーザー: pitP
• 提出日時: 2024-10-18 23:32:01
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: TLE
• 実行時間: -
• コード長: 8,117 bytes
• コンパイル時間: 8,568 ms
• コンパイル使用メモリ: 337,704 KB
• 実行使用メモリ: 13,640 KB
• 最終ジャッジ日時: 2024-10-18 23:36:17
• 合計ジャッジ時間: 49,851 ms
• ジャッジサーバーID （参考情報）: judge6 / judge3

ファイルパターン	結果
sample	AC * 2
other	AC * 21 TLE * 2 -- * 1

ソースコード

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#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); }
istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } 
typedef long long ll;
typedef vector<vector<int>> Graph;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define FOR(i,l,r) for (int i = l;i < (int)(r); i++)
#define rep(i,n) for (int i = 0;i < (int)(n); i++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define my_sort(x) sort(x.begin(), x.end())
#define my_max(x) *max_element(all(x))
#define my_min(x) *min_element(all(x))
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const int INF = (1<<30) - 1;
const ll LINF = (1LL<<62) - 1;
const int MOD = 998244353;
const int MOD2 = 1e9+7;
const double PI = acos(-1);
vector<int> di = {1,0,-1,0};
vector<int> dj = {0,1,0,-1};
#ifdef LOCAL
#  include <debug_print.hpp>
#  define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define debug(...) (static_cast<void>(0))
#endif
//形式的冪級数
//https://qiita.com/gg_hatano/items/3591ddf267092c235a23
#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
template<class T>
struct FormalPowerSeries : vector<T> {
    using vector<T>::vector;
    using vector<T>::operator=;
    using F = FormalPowerSeries;
 
    F operator-() const {
        F res(*this);
        for (auto &e : res) e = -e;
        return res;
    }
    F &operator*=(const T &g) {
        for (auto &e : *this) e *= g;
        return *this;
    }
    F &operator/=(const T &g) {
        assert(g != T(0));
        *this *= g.inv();
        return *this;
    }
    F &operator+=(const F &g) {
        int n = (*this).size(), m = g.size();
        rep(i, min(n, m)) (*this)[i] += g[i];
        return *this;
    }
    F &operator-=(const F &g) {
        int n = (*this).size(), m = g.size();
        rep(i, min(n, m)) (*this)[i] -= g[i];
        return *this;
    }
    F &operator<<=(const int d) {
        int n = (*this).size();
        (*this).insert((*this).begin(), d, 0);
        (*this).resize(n);
        return *this;
    }
    F &operator>>=(const int d) {
        int n = (*this).size();
        (*this).erase((*this).begin(), (*this).begin() + min(n, d));
        (*this).resize(n);
        return *this;
    }
    F inv(int d = -1) const {
        int n = (*this).size();
        assert(n != 0 && (*this)[0] != 0);
        if (d == -1) d = n;
        assert(d > 0);
        F res{(*this)[0].inv()};
        while (res.size() < d) {
            int m = size(res);
            F f(begin(*this), begin(*this) + min(n, 2*m));
            F r(res);
            f.resize(2*m), internal::butterfly(f);
            r.resize(2*m), internal::butterfly(r);
            rep(i, 2*m) f[i] *= r[i];
            internal::butterfly_inv(f);
            f.erase(f.begin(), f.begin() + m);
            f.resize(2*m), internal::butterfly(f);
            rep(i, 2*m) f[i] *= r[i];
            internal::butterfly_inv(f);
            T iz = T(2*m).inv(); iz *= -iz;
            rep(i, m) f[i] *= iz;
            res.insert(res.end(), f.begin(), f.begin() + m);
        }
        return {res.begin(), res.begin() + d};
    }
 
    // fast: FMT-friendly modulus only
    F &operator*=(const F &g) {
        int n = (*this).size();
        *this = convolution(*this, g);
        (*this).resize(n);
        return *this;
    }
    F &operator/=(const F &g) {
        int n = (*this).size();
        *this = convolution(*this, g.inv(n));
        (*this).resize(n);
        return *this;
    }
 
    // // naive
    // F &operator*=(const F &g) {
    //   int n = (*this).size(), m = g.size();
    //   drep(i, n) {
    //     (*this)[i] *= g[0];
    //     rep2(j, 1, min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j];
    //   }
    //   return *this;
    // }
    // F &operator/=(const F &g) {
    //   assert(g[0] != T(0));
    //   T ig0 = g[0].inv();
    //   int n = (*this).size(), m = g.size();
    //   rep(i, n) {
    //     rep2(j, 1, min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j];
    //     (*this)[i] *= ig0;
    //   }
    //   return *this;
    // }
 
    // sparse
    F &operator*=(vector<pair<int, T>> g) {
        int n = (*this).size();
        auto [d, c] = g.front();
        if (d == 0) g.erase(g.begin());
        else c = 0;
        drep(i, n) {
            (*this)[i] *= c;
            for (auto &[j, b] : g) {
                if (j > i) break;
                (*this)[i] += (*this)[i-j] * b;
            }
        }
        return *this;
    }
    F &operator/=(vector<pair<int, T>> g) {
        int n = (*this).size();
        auto [d, c] = g.front();
        assert(d == 0 && c != T(0));
        T ic = c.inv();
        g.erase(g.begin());
        rep(i, n) {
            for (auto &[j, b] : g) {
            if (j > i) break;
              (*this)[i] -= (*this)[i-j] * b;
            }
            (*this)[i] *= ic;
        }
        return *this;
    }
 
    // multiply and divide (1 + cz^d)
    void multiply(const int d, const T c) { 
        int n = (*this).size();
        if (c == T(1)) drep(i, n-d) (*this)[i+d] += (*this)[i];
        else if (c == T(-1)) drep(i, n-d) (*this)[i+d] -= (*this)[i];
        else drep(i, n-d) (*this)[i+d] += (*this)[i] * c;
    }
    void divide(const int d, const T c) {
        int n = (*this).size();
        if (c == T(1)) rep(i, n-d) (*this)[i+d] -= (*this)[i];
        else if (c == T(-1)) rep(i, n-d) (*this)[i+d] += (*this)[i];
        else rep(i, n-d) (*this)[i+d] -= (*this)[i] * c;
    }
 
    T eval(const T &a) const {
        T x(1), res(0);
        for (auto e : *this) res += e * x, x *= a;
        return res;
    }
 
    F operator*(const T &g) const { return F(*this) *= g; }
    F operator/(const T &g) const { return F(*this) /= g; }
    F operator+(const F &g) const { return F(*this) += g; }
    F operator-(const F &g) const { return F(*this) -= g; }
    F operator<<(const int d) const { return F(*this) <<= d; }
    F operator>>(const int d) const { return F(*this) >>= d; }
    F operator*(const F &g) const { return F(*this) *= g; }
    F operator/(const F &g) const { return F(*this) /= g; }
    F operator*(vector<pair<int, T>> g) const { return F(*this) *= g; }
    F operator/(vector<pair<int, T>> g) const { return F(*this) /= g; }
};
using mint = modint998244353;
using fps = FormalPowerSeries<mint>;
using sfps = vector<pair<int, mint>>; // (次数，係数)
int main(){
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    int Q; cin >> Q;
    while(Q--){
        int flg, N, K; cin >> flg >> N >> K;
        if(flg == 1 || flg == 2){
            mint ans = 0;
            fps f(N + 1);
            f[0] = 1;
            FOR(j, 1, K + 1){
                int m = N / j;
                sfps g10 = {{j, 1}, {(m + 1) * j, -1}};
                sfps g11 = {{0, 1}, {j, -1}};
                fps h = f;
                h *= g10;
                h /= g11;
                ans += h[N];
                sfps g00 = {{0, 1}, {(m + 1) * j, -1}};
                sfps g01 = {{0, 1}, {j, -1}};
                f *= g00;
                f /= g01;
            }
            cout << ans << endl;
        }
        else{
            mint ans = 0;
            fps f(N + 1);
            FOR(i, 1, N + 1) f[i] = 1;
            sfps g = {{0, 1}, {1, -1}};
            rep(i, K - 1){
                ans += f[N];
                f /= g;
            }
            cout << -1 << endl;
        }
    }
}
 
 
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