#859439 (C++17) 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	siganai
提出日時	2023-04-14 22:21:17
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	WA
実行時間	-
コード長	17,021 bytes
コンパイル時間	3,389 ms
コンパイル使用メモリ	235,444 KB
実行使用メモリ	16,160 KB
最終ジャッジ日時	2024-10-10 13:14:02
合計ジャッジ時間	6,548 ms
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
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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 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	2 ms 5,248 KB
testcase_05	AC	2 ms 5,248 KB
testcase_06	AC	2 ms 5,248 KB
testcase_07	AC	2 ms 5,248 KB
testcase_08	AC	2 ms 5,248 KB
testcase_09	AC	2 ms 5,248 KB
testcase_10	AC	2 ms 5,248 KB
testcase_11	AC	2 ms 5,248 KB
testcase_12	AC	2 ms 5,248 KB
testcase_13	WA	-
testcase_14	WA	-
testcase_15	AC	2 ms 5,248 KB
testcase_16	AC	2 ms 5,248 KB
testcase_17	AC	2 ms 5,248 KB
testcase_18	AC	2 ms 5,248 KB
testcase_19	AC	2 ms 5,248 KB
testcase_20	AC	2 ms 5,248 KB
testcase_21	AC	2 ms 5,248 KB
testcase_22	AC	2 ms 5,248 KB
testcase_23	AC	2 ms 5,248 KB
testcase_24	AC	4 ms 5,248 KB
testcase_25	AC	13 ms 5,248 KB
testcase_26	AC	12 ms 5,248 KB
testcase_27	AC	25 ms 5,248 KB
testcase_28	AC	26 ms 5,248 KB
testcase_29	AC	116 ms 9,600 KB
testcase_30	AC	238 ms 16,032 KB
testcase_31	AC	232 ms 16,160 KB
testcase_32	AC	236 ms 16,084 KB
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ソースコード

raw source code
#line 1 "main.cpp"
//#pragma GCC target("avx")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>

#ifdef LOCAL
#include <debug.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif
using namespace std;
using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
using pii = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vs = vector<string>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(a,b,c,name,...) name
#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)
#define rep2(i, n) for (ll i = 0; i < (n); ++i)
#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)
#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define all1(i) begin(i) , end(i)
#define all2(i,a) begin(i) , begin(i) + a
#define all3(i,a,b) begin(i) + a , begin(i) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }
template<class T> auto min(const T& a){ return *min_element(all(a)); }
template<class T> auto max(const T& a){ return *max_element(all(a)); }
template<class... Ts> void in(Ts&... t);
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) vector<type> name(size); in(name)
#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)
ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}
ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;if(a < 0) a += p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
ll GCD(ll a,ll b) { if(a == 0 || b == 0) return 0; if(a % b == 0) return b; else return GCD(b,a%b);}
ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;}
namespace IO{
#define VOID(a) decltype(void(a))
struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(30);}} setting;
template<int I> struct P : P<I-1>{};
template<> struct P<0>{};
template<class T> void i(T& t){ i(t, P<3>{}); }
void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }
template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }
template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }
template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){
    in(get<idx>(t)...);}
template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){
    ituple(t, make_index_sequence<tuple_size<T>::value>{});}
#undef VOID
}
#define unpack(a) (void)initializer_list<int>{(a, 0)...}
template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }
#undef unpack
static const double PI = 3.1415926535897932;
template <class F> struct REC {
    F f;
    REC(F &&f_) : f(forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};
//constexpr int mod = 1000000007;
constexpr int mod = 998244353;

#line 2 "library/modint/LazyMontgomeryModint.hpp"
template <uint32_t mod>
struct LazyMontgomeryModInt {
    using mint = LazyMontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;
    static constexpr u32 get_r() {
        u32 ret = mod;
        for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
        return ret;
    }
    static constexpr u32 r = get_r();
    static constexpr u32 n2 = -u64(mod) % mod;
    static_assert(r * mod == 1);
    static_assert(mod < (1 << 30));
    static_assert((mod & 1) == 1);
    u32 a;
    constexpr LazyMontgomeryModInt() : a(0) {}
    constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

    static constexpr u32 reduce(const u64 &b) {
        return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
    }
    constexpr mint &operator+=(const mint &b) {
        if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }
    constexpr mint &operator-=(const mint &b) {
        if (i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }
    constexpr mint &operator*=(const mint &b) {
        a = reduce(u64(a) * b.a);
        return *this;
    }
    constexpr mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }
    constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
    constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
    constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
    constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
    constexpr bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr mint operator-() const { return mint() - mint(*this); }
    constexpr mint pow(u64 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
        if (n & 1) ret *= mul;
        mul *= mul;
        n >>= 1;
        }
        return ret;
    }
    constexpr mint inverse() const { return pow(mod - 2); }
    friend ostream &operator<<(ostream &os, const mint &b) {
        return os << b.get();
    }
    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = LazyMontgomeryModInt<mod>(t);
        return (is);
    }
    constexpr u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }
    static constexpr u32 get_mod() { return mod; }
};
#line 2 "library/ntt/ntt.hpp"
template<typename mint>
struct NTT{
    static constexpr uint32_t get_pr() {
        uint32_t _mod = mint::get_mod();
        using u64 = uint64_t;
        u64 ds[32] = {};
        int idx = 0;
        u64 m = _mod - 1;
        for(u64 i = 2;i * i <= m; ++i) {
            if(m % i == 0) {
                ds[idx++] = i;
                while(m % i == 0) m /= i;
            }
        }
        if (m != 1) ds[idx++] = m;
        uint32_t _pr = 2;
        while(1) {
            int flg = 1;
            for(int i = 0;i < idx; ++i) {
                u64 a = _pr, b = (_mod - 1) / ds[i],r = 1;
                while(b) {
                    if(b & 1) r = r * a % _mod;
                    a = a * a % _mod;
                    b >>= 1;
                }
                if(r == 1) {
                    flg = 0;
                    break;
                }
            }
            if (flg == 1) break;
            ++_pr;
        }
        return _pr;
    };
    static constexpr uint32_t mod = mint::get_mod();
    static constexpr uint32_t pr = get_pr();
    static constexpr int level = __builtin_ctzll(mod - 1);
    mint dw[level], dy[level];
    void setwy(int k) {
        mint w[level],y[level];
        w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
        y[k - 1] = w[k - 1].inverse();
        for(int i = k - 2;i > 0; --i) w[i] = w[i+1] * w[i+1],y[i] = y[i+1] * y[i+1];
        dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
        for(int i = 3;i < k;++i) {
            dw[i] = dw[i-1] * y[i-2] * w[i];
            dy[i] = dy[i-1] * w[i-2] * y[i];
        }
    }
    NTT() {setwy(level);}
    void fft4(vector<mint> &a,int k) {
        if((int)a.size() <= 1) return;
        if(k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        if (k & 1) {
            int v = 1 << (k - 1);
            for(int j = 0;j < v; ++j) {
                mint ajv = a[j + v];
                a[j + v] = a[j] - ajv;
                a[j] += ajv;
            }
        }
        int u = 1 << (2 + (k & 1));
        int v = 1 << (k - 2 - (k & 1));
        mint one = mint(1);
        mint imag = dw[1];
        while(v) {
            {
                int j0 = 0,j1 = v;
                int j2 = j1 + v;
                int j3 = j2 + v;
                for(;j0 < v; ++j0,++j1,++j2,++j3) {
                    mint t0 = a[j0], t1 = a[j1],t2 = a[j2],t3 = a[j3];
                    mint t0p2 = t0 + t2,t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2,t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
                }
            }
            mint ww = one,xx = one * dw[2],wx = one;
            for(int jh = 4;jh < u;) {
                ww = xx * xx,wx = ww * xx;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for(;j0 < je;++j0,++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx;
                    mint t0p2 = t0 + t2,t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2,t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
                }
                xx *= dw[__builtin_ctzll((jh += 4))];
            }
            u <<= 2;
            v >>= 2;
        }
    }
    void ifft4(vector<mint> &a,int k) {
        if((int)a.size() <= 1) return;
        if(k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        int u = 1 << (k - 2);
        int v = 1;
        mint one = mint(1);
        mint imag = dy[1];
        while(u) {
            {
                int j0 = 0,j1 = v;
                int j2 = j1 + v;
                int j3 = j2 + v;
                for(;j0 < v;++j0,++j1,++j2,++j3) {
                    mint t0 = a[j0],t1 = a[j1],t2 = a[j2],t3 = a[j3];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
                    a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
                    a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
                }
            }
            mint ww = one,xx = one * dy[2],yy = one;
            u <<= 2;
            for(int jh = 4;jh < u;) {
                ww = xx * xx,yy = xx * imag;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for(;j0 < je;++j0,++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
                    a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
                    a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;       
                }
                xx *= dy[__builtin_ctzll(jh += 4)];
            }
            u >>= 4;
            v <<= 2;
        }
        if(k & 1) {
            u = 1 << (k - 1);
            for(int j = 0;j < u;++j) {
                mint ajv = a[j] - a[j+u];
                a[j] += a[j+u];
                a[j+u] = ajv;
            }
        }
    }
    void ntt(vector<mint> &a) {
        if((int)a.size() <= 1) return;
        fft4(a,__builtin_ctz(a.size()));
    }
    void intt(vector<mint> &a) {
        if((int)a.size() <= 1) return;
        ifft4(a,__builtin_ctz(a.size()));
        mint iv = mint(a.size()).inverse();
        for(auto &x:a) x *= iv;
    }
    vector<mint> multiply(const vector<mint> &a,const vector<mint> &b) {
        int l = a.size() + b.size() - 1;
        if(min<int>(a.size(),b.size()) <= 40) {
            vector<mint> s(l);
            for(int i = 0;i < (int)a.size();++i) for(int j = 0;j < (int)b.size();++j) s[i+j] += a[i] * b[j];
            return s;
        }
        int k = 2, M = 4;
        while(M < l) M <<= 1, ++k;
        //setwy(k);
        vector<mint> s(M), t(M);
        for(int i = 0;i < (int)a.size();++i) s[i] = a[i];
        for(int i = 0;i < (int)b.size();++i) t[i] = b[i];
        fft4(s,k);
        fft4(t,k);
        for(int i = 0;i < M;++i) s[i] *= t[i];
        ifft4(s,k);
        s.resize(l);
        mint invm = mint(M).inverse();
        for(int i = 0;i < l;++i) s[i] *= invm;
        return s;
    }
    void ntt_doubling(vector<mint> &a) {
        int M = (int)a.size();
        auto b = a;
        intt(b);
        mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
        for(int i = 0;i < M;++i) b[i] *= r,r *= zeta;
        ntt(b);
        copy(begin(b),end(b),back_inserter(a));
    }
};
#line 4 "library/ntt/ArbitraryNTT.hpp"
namespace ArbitraryNTT {
using i64 = int64_t;
using u128 = __uint128_t;
constexpr int32_t m0 = 167772161;
constexpr int32_t m1 = 469762049;
constexpr int32_t m2 = 754974721;
using mint0 = LazyMontgomeryModInt<m0>;
using mint1 = LazyMontgomeryModInt<m1>;
using mint2 = LazyMontgomeryModInt<m2>;
constexpr int r01 = mint1(m0).inverse().get();
constexpr int r02 = mint2(m0).inverse().get();
constexpr int r12 = mint2(m1).inverse().get();
constexpr int r02r12 = i64(r02) * r12 % m2;
constexpr i64 w1 = m0;
constexpr i64 w2 = i64(m0) * m1;

template <typename T, typename submint>
vector<submint> mul(const vector<T> &a, const vector<T> &b) {
    static NTT<submint> ntt;
    vector<submint> s(a.size()), t(b.size());
    for (int i = 0; i < (int)a.size(); ++i) s[i] = i64(a[i] % submint::get_mod());
    for (int i = 0; i < (int)b.size(); ++i) t[i] = i64(b[i] % submint::get_mod());
    return ntt.multiply(s, t);
}

template <typename T>
vector<int> multiply(const vector<T> &s, const vector<T> &t, int mod) {
    auto d0 = mul<T, mint0>(s, t);
    auto d1 = mul<T, mint1>(s, t);
    auto d2 = mul<T, mint2>(s, t);
    int n = d0.size();
    vector<int> ret(n);
    const int W1 = w1 % mod;
    const int W2 = w2 % mod;
    for (int i = 0; i < n; i++) {
        int n1 = d1[i].get(), n2 = d2[i].get(), a = d0[i].get();
        int b = i64(n1 + m1 - a) * r01 % m1;
        int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2;
        ret[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod;
    }
    return ret;
}

template <typename mint>
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
    if (a.size() == 0 && b.size() == 0) return {};
    if (min<int>(a.size(), b.size()) < 128) {
        vector<mint> ret(a.size() + b.size() - 1);
        for (int i = 0; i < (int)a.size(); ++i)
        for (int j = 0; j < (int)b.size(); ++j) ret[i + j] += a[i] * b[j];
        return ret;
    }
    vector<int> s(a.size()), t(b.size());
    for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i].get();
    for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i].get();
    vector<int> u = multiply<int>(s, t, mint::get_mod());
    vector<mint> ret(u.size());
    for (int i = 0; i < (int)u.size(); ++i) ret[i] = mint(u[i]);
    return ret;
}

template <typename T>
vector<u128> multiply_u128(const vector<T> &s, const vector<T> &t) {
    if (s.size() == 0 && t.size() == 0) return {};
    if (min<int>(s.size(), t.size()) < 128) {
        vector<u128> ret(s.size() + t.size() - 1);
        for (int i = 0; i < (int)s.size(); ++i)
        for (int j = 0; j < (int)t.size(); ++j) ret[i + j] += i64(s[i]) * t[j];
        return ret;
    }
    auto d0 = mul<T, mint0>(s, t);
    auto d1 = mul<T, mint1>(s, t);
    auto d2 = mul<T, mint2>(s, t);
    int n = d0.size();
    vector<u128> ret(n);
    for (int i = 0; i < n; i++) {
        i64 n1 = d1[i].get(), n2 = d2[i].get();
        i64 a = d0[i].get();
        i64 b = (n1 + m1 - a) * r01 % m1;
        i64 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2;
        ret[i] = a + b * w1 + u128(c) * w2;
    }
    return ret;
}
}  // namespace ArbitraryNTT
#line 88 "main.cpp"
using mint = LazyMontgomeryModInt<258280327>;
int main() {
    INT(n);
    VEC(mint,a,n+1);
    INT(m);
    VEC(mint,b,m+1);
    auto c = ArbitraryNTT::multiply(a,b);
    cout << (int)c.size() - 1 << '\n';
    rep(i,c.size()) {
        if(i > 0) cout << " ";
        cout << c[i];
    }
    cout << '\n';
}
yukicoder

結果

テストケース

ソースコード
