結果
問題 | No.931 Multiplicative Convolution |
ユーザー | jell |
提出日時 | 2020-07-08 01:40:26 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 138 ms / 2,000 ms |
コード長 | 6,775 bytes |
コンパイル時間 | 2,368 ms |
コンパイル使用メモリ | 211,416 KB |
実行使用メモリ | 9,320 KB |
最終ジャッジ日時 | 2024-10-02 00:04:02 |
合計ジャッジ時間 | 5,414 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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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
6,816 KB |
testcase_01 | AC | 2 ms
6,820 KB |
testcase_02 | AC | 2 ms
6,820 KB |
testcase_03 | AC | 2 ms
6,820 KB |
testcase_04 | AC | 2 ms
6,820 KB |
testcase_05 | AC | 2 ms
6,816 KB |
testcase_06 | AC | 3 ms
6,816 KB |
testcase_07 | AC | 16 ms
6,816 KB |
testcase_08 | AC | 134 ms
9,320 KB |
testcase_09 | AC | 85 ms
9,144 KB |
testcase_10 | AC | 138 ms
8,992 KB |
testcase_11 | AC | 87 ms
9,088 KB |
testcase_12 | AC | 85 ms
6,820 KB |
testcase_13 | AC | 132 ms
9,140 KB |
testcase_14 | AC | 135 ms
9,316 KB |
testcase_15 | AC | 133 ms
9,320 KB |
testcase_16 | AC | 133 ms
9,148 KB |
コンパイルメッセージ
main.cpp:141:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type] 141 | main() | ^~~~
ソースコード
#ifndef number_theoretic_transform_hpp #define number_theoretic_transform_hpp #include <algorithm> #include <cassert> #include <iostream> #include <vector> namespace number_theoretic_transform { constexpr int mod = 998244353; constexpr int primitive = 3; class modint { int val; public: constexpr modint() noexcept : val{0} {} constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {} constexpr long long value() const noexcept { return val; } constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; } constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; } constexpr modint &operator++() noexcept { return ++val, *this; } constexpr modint &operator--() noexcept { return --val, *this; } constexpr modint operator-() const noexcept { return modint(-val); } constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; } constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); } constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; } constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; } constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; } constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; } constexpr bool operator==(const modint &other) const noexcept { return val == other.val; } constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; } constexpr bool operator!() const noexcept { return !val; } friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; } friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; } friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; } friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; } static constexpr modint inverse(const modint &other) noexcept { assert(other != 0); int a{mod}, b{other.val}, u{}, v{1}, t{}; while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v; return {u}; } static constexpr modint pow(modint other, long long e) noexcept { if(e < 0) e = e % (mod - 1) + mod - 1; modint res{1}; while(e) { if(e & 1) res *= other; other *= other, e >>= 1; } return res; } friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; } friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; } }; // class modint class zeta_calc { static constexpr size_t n = __builtin_ctz(mod - 1); modint _zeta[n + 1]; public: constexpr zeta_calc() : _zeta{} { _zeta[n] = modint::pow(modint(primitive), (mod - 1) / (1 << n)); for(size_t i{n}; i; --i) _zeta[i - 1] = _zeta[i] * _zeta[i]; } constexpr modint operator[](size_t k) const { return _zeta[k]; } }; // class zeta_calc constexpr zeta_calc zeta; class inv_calc { static constexpr size_t n = __builtin_ctz(mod - 1); modint _inv[n + 1]; public: constexpr inv_calc() : _inv{1, (mod + 1) / 2} { for(size_t i{1}; i < n; ++i) _inv[i + 1] = _inv[i] * _inv[1]; } constexpr modint operator[](size_t k) const { return _inv[k]; } }; // class inv_calc constexpr inv_calc inv; using poly_t = std::vector<modint>; void discrete_Fourier_transform(poly_t &f) { const size_t n{f.size()}, mask{n - 1}; assert(__builtin_popcount(n) == 1); // degree of f must be a power of two. static poly_t g; g.resize(n); for(size_t i{n >> 1}, ii{1}; i; i >>= 1, ++ii, swap(f, g)) { modint powzeta{1}; for(size_t j{}; j < n; powzeta *= zeta[ii]) { for(size_t k{}, x{mask & j << 1}, y{mask & (i + (j << 1))}; k < i; ++k, ++j, ++x, ++y) { g[j] = f[x] + powzeta * f[y]; } } } } void inverse_discrete_Fourier_transform(poly_t &f) { discrete_Fourier_transform(f), reverse(next(f.begin()), f.end()); const size_t k = __builtin_ctz(f.size()); for(modint &e : f) e *= inv[k]; } poly_t convolute(poly_t f, poly_t g) { if(f.empty() || g.empty()) return poly_t(); const size_t deg_f{f.size() - 1}, deg_g{g.size() - 1}, deg_h{deg_f + deg_g}, n(1u << (32 - __builtin_clz(deg_h))); static poly_t h; f.resize(n, 0), g.resize(n, 0), h.resize(n); discrete_Fourier_transform(f), discrete_Fourier_transform(g); for(size_t i{}; i < n; ++i) h[i] = f[i] * g[i]; inverse_discrete_Fourier_transform(h); h.resize(deg_h + 1); return h; } } // namespace Number_theoretic_transform #endif // number_theoretic_transform_hpp #include <bits/stdc++.h> using namespace std; using i64=int64_t; i64 modpow(i64 x, i64 y, i64 p) { i64 res=1; while(y) { if(y&1) res=res*x%p; x=x*x%p; y>>=1; } return res; } main() { int P; cin>>P; i64 pr=1; for(;;) { int ord=P-1; for(int d=1; d*d<P; d++) { if((P-1)%d) continue; if(modpow(pr,d,P)==1) ord=min(ord,d); if(modpow(pr,(P-1)/d,P)==1) ord=min(ord,(P-1)/d); } if(ord==P-1) break; pr++; } // cerr<<pr<<endl; vector<int> e(P); for(i64 i=0,x=1; i<P-1; i++) { e[x]=i; x=x*pr%P; } using namespace number_theoretic_transform; poly_t a(P-1),b(P-1); for(int i=1;i<P;i++) { cin>>a[e[i]]; } for(int i=1;i<P;i++) { cin>>b[e[i]]; } poly_t c=convolute(a,b); for(int i=P-1;i<(int)c.size();i++) c[i-P+1]+=c[i]; poly_t res(P); for(i64 i=0,j=1;i<P-1;i++) { res[j]=c[i]; j=j*pr%P; } for(int i=1;i<P;i++) cout<<res[i]<<" "; cout<<endl; }