#859584 (C++23) No.2272 多項式乗算 mod 258280327

提出ソース

結果

問題	No.2272 多項式乗算 mod 258280327
ユーザー	k1suxu
提出日時	2023-04-14 22:50:20
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	WA
実行時間	-
コード長	11,322 bytes
コンパイル時間	5,005 ms
コンパイル使用メモリ	293,684 KB
実行使用メモリ	38,400 KB
最終ジャッジ日時	2024-04-18 20:25:10
合計ジャッジ時間	7,209 ms
ジャッジサーバーID （参考情報）	judge2 / judge5

このコードへのチャレンジ
（要ログイン）

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 5,248 KB
testcase_01	AC	3 ms 5,248 KB
testcase_02	AC	3 ms 5,248 KB
testcase_03	AC	4 ms 5,376 KB
testcase_04	AC	3 ms 5,376 KB
testcase_05	AC	3 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	3 ms 5,376 KB
testcase_08	AC	3 ms 5,376 KB
testcase_09	AC	3 ms 5,376 KB
testcase_10	AC	3 ms 5,376 KB
testcase_11	AC	3 ms 5,376 KB
testcase_12	AC	3 ms 5,376 KB
testcase_13	WA	-
testcase_14	WA	-
testcase_15	AC	3 ms 5,376 KB
testcase_16	AC	3 ms 5,376 KB
testcase_17	AC	3 ms 5,376 KB
testcase_18	AC	3 ms 5,376 KB
testcase_19	AC	3 ms 5,376 KB
testcase_20	AC	4 ms 5,376 KB
testcase_21	AC	3 ms 5,376 KB
testcase_22	AC	3 ms 5,376 KB
testcase_23	AC	3 ms 5,376 KB
testcase_24	AC	6 ms 5,376 KB
testcase_25	AC	14 ms 5,504 KB
testcase_26	AC	14 ms 5,632 KB
testcase_27	AC	29 ms 7,808 KB
testcase_28	AC	27 ms 7,808 KB
testcase_29	WA	-
testcase_30	WA	-
testcase_31	WA	-
testcase_32	WA	-

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

// #pragma GCC target("avx")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>
using namespace std;

#define rep(i,n) for(int i = 0; i < (int)n; i++)
#define FOR(n) for(int i = 0; i < (int)n; i++)
#define repi(i,a,b) for(int i = (int)a; i < (int)b; i++)
#define all(x) x.begin(),x.end()
//#define mp make_pair
#define vi vector<int>
#define vvi vector<vi>
#define vvvi vector<vvi>
#define vvvvi vector<vvvi>
#define pii pair<int,int>
#define vpii vector<pair<int,int>>

template<typename T>
void chmax(T &a, const T &b) {a = (a > b? a : b);}
template<typename T>
void chmin(T &a, const T &b) {a = (a < b? a : b);}

using ll = long long;
using ld = long double;
using ull = unsigned long long;

const ll INF = numeric_limits<long long>::max() / 2;
const ld pi = 3.1415926535897932384626433832795028;
const ll mod = 998244353;
int dx[] = {1, 0, -1, 0, -1, -1, 1, 1};
int dy[] = {0, 1, 0, -1, -1, 1, -1, 1};

#define int long long

template<int MOD>
struct Modular_Int {
    int x;

    Modular_Int() = default;
    Modular_Int(int x_) : x(x_ >= 0? x_%MOD : (MOD-(-x_)%MOD)%MOD) {}

    int val() const {
        return (x%MOD+MOD)%MOD;
    }
    int get_mod() const {
        return MOD;
    }

    Modular_Int<MOD>& operator^=(int d)  {
        Modular_Int<MOD> ret(1);
        int nx = x;
        while(d) {
            if(d&1) ret *= nx;
            (nx *= nx) %= MOD;
            d >>= 1;
        }
        *this = ret;
        return *this;
    }
    Modular_Int<MOD> operator^(int d) const {return Modular_Int<MOD>(*this) ^= d;}
    Modular_Int<MOD> pow(int d) const {return Modular_Int<MOD>(*this) ^= d;}
    
    //use this basically
    Modular_Int<MOD> inv() const {
        return Modular_Int<MOD>(*this) ^ (MOD-2);
    }
    //only if the module number is not prime
    //Don't use. This is broken.
    // Modular_Int<MOD> inv() const {
    //     int a = (x%MOD+MOD)%MOD, b = MOD, u = 1, v = 0;
    //     while(b) {
    //         int t = a/b;
    //         a -= t*b, swap(a, b);
    //         u -= t*v, swap(u, v);
    //     }
    //     return Modular_Int<MOD>(u);
    // }

    Modular_Int<MOD>& operator+=(const Modular_Int<MOD> other) {
        if((x += other.x) >= MOD) x -= MOD;
        return *this;
    }
    Modular_Int<MOD>& operator-=(const Modular_Int<MOD> other) {
        if((x -= other.x) < 0) x += MOD;
        return *this;
    }
    Modular_Int<MOD>& operator*=(const Modular_Int<MOD> other) {
        int z = x;
        z *= other.x;
        z %= MOD;
        x = z;
        if(x < 0) x += MOD;
        return *this;
    }
    Modular_Int<MOD>& operator/=(const Modular_Int<MOD> other) {
        return *this = *this * other.inv();
    }
    Modular_Int<MOD>& operator++() {
        x++;
        if (x == MOD) x = 0;
        return *this;
    }
    Modular_Int<MOD>& operator--() {
        if (x == 0) x = MOD;
        x--;
        return *this;
    }
    
    Modular_Int<MOD> operator+(const Modular_Int<MOD> other) const {return Modular_Int<MOD>(*this) += other;}
    Modular_Int<MOD> operator-(const Modular_Int<MOD> other) const {return Modular_Int<MOD>(*this) -= other;}
    Modular_Int<MOD> operator*(const Modular_Int<MOD> other) const {return Modular_Int<MOD>(*this) *= other;}
    Modular_Int<MOD> operator/(const Modular_Int<MOD> other) const {return Modular_Int<MOD>(*this) /= other;}
    
    Modular_Int<MOD>& operator+=(const int other) {Modular_Int<MOD> other_(other); *this += other_; return *this;}
    Modular_Int<MOD>& operator-=(const int other) {Modular_Int<MOD> other_(other); *this -= other_; return *this;}
    Modular_Int<MOD>& operator*=(const int other) {Modular_Int<MOD> other_(other); *this *= other_; return *this;}
    Modular_Int<MOD>& operator/=(const int other) {Modular_Int<MOD> other_(other); *this /= other_; return *this;}
    Modular_Int<MOD> operator+(const int other) const {return Modular_Int<MOD>(*this) += other;}
    Modular_Int<MOD> operator-(const int other) const {return Modular_Int<MOD>(*this) -= other;}
    Modular_Int<MOD> operator*(const int other) const {return Modular_Int<MOD>(*this) *= other;}
    Modular_Int<MOD> operator/(const int other) const {return Modular_Int<MOD>(*this) /= other;}

    bool operator==(const Modular_Int<MOD> other) const {return (*this).val() == other.val();}
    bool operator!=(const Modular_Int<MOD> other) const {return (*this).val() != other.val();}
    bool operator==(const int other) const {return (*this).val() == other;}
    bool operator!=(const int other) const {return (*this).val() != other;}

    Modular_Int<MOD> operator-() const {return Modular_Int<MOD>(0LL)-Modular_Int<MOD>(*this);}

    //入れ子にしたい
    // friend constexpr istream& operator>>(istream& is, mint& x) noexcept {
    //     int X;
    //     is >> X;
    //     x = X;
    //     return is;
    // }
    // friend constexpr ostream& operator<<(ostream& os, mint& x) {
    //     os << x.val();
    //     return os;
    // }
};

// const int MOD_VAL = 1e9+7;
const int MOD_VAL = 258280327;
using mint = Modular_Int<MOD_VAL>;

istream& operator>>(istream& is, mint& x) {
    int X;
    is >> X;
    x = X;
    return is;
}
ostream& operator<<(ostream& os, mint& x) {
    os << x.val();
    return os;
}

// istream& operator<<(istream& is, mint &a) {
//     int x;
//     is >> x;
//     a = mint(x);
//     return is;
// }
// ostream& operator<<(ostream& os, mint a) {
//     os << a.val();
//     return os;
// }

// vector<mint> f = {1}, rf = {1};
// void init(int n) {
//     f.resize(n, 0);
//     rf.resize(n, 0);
//     f[0] = 1;
//     repi(i, 1, n) f[i] = (f[i - 1] * i);
//     repi(i, 0, n) rf[i] = f[i].inv();
// }
// mint P(int n, int k) {
//     assert(n>=k);
//     while(n > f.size()-1) {
//         f.push_back(f.back() * f.size());
//         rf.push_back(f.back().inv());
//     }
//     return f[n] * f[n-k];
// }
// mint C(int n, int k) {
//     assert(n>=k);
//     while(n > f.size()-1) {
//         f.push_back(f.back() * f.size());
//         rf.push_back(f.back().inv());
//     }
//     return f[n]*rf[n-k]*rf[k];
// }
// mint H(int n, int k) {
//     assert(n>=1);
//     return C(n+k-1, k);
// }
// mint Cat(int n) {
//     return C(2*n, n)-C(2*n, n-1);
// }

namespace FastFourierTransform {
  using real = double;

  struct C {
    real x, y;

    C() : x(0), y(0) {}

    C(real x, real y) : x(x), y(y) {}

    inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

    inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

    inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }

    inline C conj() const { return C(x, -y); }
  };

  const real PI = acosl(-1);
  int base = 1;
  vector< C > rts = { {0, 0},
                     {1, 0} };
  vector< int > rev = {0, 1};


  void ensure_base(int nbase) {
    if(nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for(int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    while(base < nbase) {
      real angle = PI * 2.0 / (1 << (base + 1));
      for(int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        real angle_i = angle * (2 * i + 1 - (1 << base));
        rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
      }
      ++base;
    }
  }

  void fft(vector< C > &a, int n) {
    assert((n & (n - 1)) == 0);
    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 += 2 * k) {
        for(int j = 0; j < k; j++) {
          C z = a[i + j + k] * rts[j + k];
          a[i + j + k] = a[i + j] - z;
          a[i + j] = a[i + j] + z;
        }
      }
    }
  }

  vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
    int need = (int) a.size() + (int) b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < sz; i++) {
      int x = (i < (int) a.size() ? a[i] : 0);
      int y = (i < (int) b.size() ? b[i] : 0);
      fa[i] = C(x, y);
    }
    fft(fa, sz);
    C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
      fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
      fa[i] = z;
    }
    for(int i = 0; i < (sz >> 1); i++) {
      C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
      C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
      fa[i] = A0 + A1 * s;
    }
    fft(fa, sz >> 1);
    vector< int64_t > ret(need);
    for(int i = 0; i < need; i++) {
      ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
    }
    return ret;
  }
};

template< typename T >
struct ArbitraryModConvolutionLong {
  using real = FastFourierTransform::real;
  using C = FastFourierTransform::C;
 
  ArbitraryModConvolutionLong() = default;
 
  vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
    if(need == -1) need = a.size() + b.size() - 1;
    int nbase = 0;
    while((1 << nbase) < need) nbase++;
    FastFourierTransform::ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < a.size(); i++) {
      fa[i] = C(a[i].x & ((1 << 19) - 1), a[i].x >> 19);
    }
    fft(fa, sz);
    vector< C > fb(sz);
    if(a == b) {
      fb = fa;
    } else {
      for(int i = 0; i < b.size(); i++) {
        fb[i] = C(b[i].x & ((1 << 19) - 1), b[i].x >> 19);
      }
      fft(fb, sz);
    }
    real ratio = 0.25 / sz;
    C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C a1 = (fa[i] + fa[j].conj());
      C a2 = (fa[i] - fa[j].conj()) * r2;
      C b1 = (fb[i] + fb[j].conj()) * r3;
      C b2 = (fb[i] - fb[j].conj()) * r4;
      if(i != j) {
        C c1 = (fa[j] + fa[i].conj());
        C c2 = (fa[j] - fa[i].conj()) * r2;
        C d1 = (fb[j] + fb[i].conj()) * r3;
        C d2 = (fb[j] - fb[i].conj()) * r4;
        fa[i] = c1 * d1 + c2 * d2 * r5;
        fb[i] = c1 * d2 + c2 * d1;
      }
      fa[j] = a1 * b1 + a2 * b2 * r5;
      fb[j] = a1 * b2 + a2 * b1;
    }
    fft(fa, sz);
    fft(fb, sz);
    vector< T > ret(need);
    auto mul1 = T(2).pow(19);
    auto mul2 = T(2).pow(38);
    for(int i = 0; i < need; i++) {
      int64_t aa = llround(fa[i].x);
      int64_t bb = llround(fb[i].x);
      int64_t cc = llround(fa[i].y);
      aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
      ret[i] = (mul1 * bb) + (mul2 * cc) + aa;
    }
    return ret;
  }
};

void solve() {
    int n;
    cin >> n;
    ArbitraryModConvolutionLong<mint> convolution;
    vector<mint> f(n+1);
    FOR(n+1) cin >> f[i];
    int m;
    cin >> m;
    vector<mint> g(m+1);
    FOR(m+1) cin >> g[i];

    vector<mint> ans = convolution.multiply(f, g);

    cout << ans.size() - 1 << endl;
    for(auto e : ans) cout << e << " "; cout << "\n";
}

signed main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    solve();
    return 0;
}

yukicoder

結果

テストケース

ソースコード