結果
問題 | No.931 Multiplicative Convolution |
ユーザー | haruki_K |
提出日時 | 2019-11-22 23:18:27 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 80 ms / 2,000 ms |
コード長 | 9,126 bytes |
コンパイル時間 | 2,061 ms |
コンパイル使用メモリ | 177,460 KB |
実行使用メモリ | 16,204 KB |
最終ジャッジ日時 | 2024-10-11 04:52:54 |
合計ジャッジ時間 | 3,885 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
(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 | 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 | 3 ms
5,248 KB |
testcase_07 | AC | 10 ms
5,248 KB |
testcase_08 | AC | 78 ms
16,204 KB |
testcase_09 | AC | 65 ms
15,988 KB |
testcase_10 | AC | 75 ms
15,916 KB |
testcase_11 | AC | 66 ms
15,740 KB |
testcase_12 | AC | 46 ms
10,372 KB |
testcase_13 | AC | 76 ms
15,928 KB |
testcase_14 | AC | 79 ms
16,164 KB |
testcase_15 | AC | 80 ms
16,180 KB |
testcase_16 | AC | 76 ms
16,008 KB |
ソースコード
// >>> TEMPLATES #include <bits/stdc++.h> using namespace std; #define rep(i,n) for (int i = 0; i < int(n); i++) #define rep1(i,n) for (int i = 1; i <= int(n); i++) #define repR(i,n) for (int i = int(n)-1; i >= 0; i--) #define rep1R(i,n) for (int i = int(n); i >= 1; i--) #define loop(i,a,B) for (int i = a; i B; i++) #define loopR(i,a,B) for (int i = a; i B; i--) #define all(x) (x).begin(), (x).end() #define allR(x) (x).rbegin(), (x).rend() #define eb emplace_back #define mp make_pair #define fst first #define snd second #ifdef LOCAL #define dump(...) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__) #define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl; #define debug if (1) void dump_impl(const char*) { cerr << endl; } template <class T, class... U> void dump_impl(const char *s, T const& x, U const& ...y) { const char *o = "({[", *e = "]})"; for (int i = 0; *s != '\0'; cerr << *s++) { if (count(o,o+3,*s)) i++; if (count(e,e+3,*s)) i--; if (!i && *s == ',') break; } cerr << " = " << x; if (*s == ',') cerr << ", ", s++; dump_impl(s, y...); } #else #define dump(...) #define say(x) #define debug if (0) #endif using ll = long long; using ld = long double; #define int ll #define double ld template <class T> using pque_max = priority_queue<T>; template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >; template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type> ostream& operator<<(ostream& os, T const& v) { os << "{"; for (auto const& x : v) os << " " << x; return os << " }"; } template <class T> istream& operator>>(istream& is, vector<T>& v) { for (auto& x : v) is >> x; return is; } template <class T, class S> ostream& operator<<(ostream& os, pair<T,S> const& p) { return os << "(" << p.first << ", " << p.second << ")"; } template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; } template <size_t i, class T> typename enable_if<i >= tuple_size<T>::value>::type output_tuple(ostream&, T const&) { } template <size_t i = 0, class T> typename enable_if<i < tuple_size<T>::value>::type output_tuple(ostream& os, T const& t) { os << (i ? " " : "") << get<i>(t); output_tuple<i+1,T>(os,t); } template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t) { return output_tuple(os,t), os; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template <class T, size_t d> struct vec_impl { using type = vector<typename vec_impl<T,d-1>::type>; template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); } }; template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } }; template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type; template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); } template <class T> void quit(T const& x) { cout << x << endl; exit(0); } template <class T> constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; } template <class T> constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; } template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); } const ll INF = (1LL<<62)-1; // ~ 4.6e18 // <<< int powmod (int a, int b, int p) { int res = 1; while (b) if (b & 1) res = int (res * 1ll * a % p), --b; else a = int (a * 1ll * a % p), b >>= 1; return res; } int generator (int p) { vector<int> fact; int phi = p-1, n = phi; for (int i=2; i*i<=n; ++i) if (n % i == 0) { fact.push_back (i); while (n % i == 0) n /= i; } if (n > 1) fact.push_back (n); for (int res=2; res<=p; ++res) { bool ok = true; for (size_t i=0; i<fact.size() && ok; ++i) ok &= powmod (res, phi / fact[i], p) != 1; if (ok) return res; } return -1; } // >>> runtime modint using ll = long long; class runtime_modint { using M = runtime_modint; ll x; public: static ll& mod() { static int mod = 0; return mod; } runtime_modint(ll x = 0) { assert(mod() > 0); this->x = ((x%=mod()) < 0 ? x+mod() : x); } ll val() const { return x; } bool operator==(M r) const { return x == r.x; } bool operator!=(M r) const { return x != r.x; } M operator+() const { return *this; } M operator-() const { return {mod()-x}; } M& operator+=(M r) { if ((x += r.x) >= mod()) x -= mod(); return *this; } M& operator-=(M r) { if ((x += mod()-r.x) >= mod()) x -= mod(); return *this; } M& operator*=(M r) { (x *= r.x) %= mod(); return *this; } M operator+(M r) const { return M(*this) += r; } M operator-(M r) const { return M(*this) -= r; } M operator*(M r) const { return M(*this) *= r; } M& operator/=(M r) { return *this *= r.inv(); } M operator/(M r) const { return *this * r.inv(); } M pow(ll n) const { if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } M inv() const { assert(x != 0); ll t = 1, v = x, q, r; while (v != 1) { q = mod() / v; r = mod() % v; if (r * 2 < v) { t *= -q; t %= mod(); v = r; } else { t *= q + 1; t %= mod(); v -= r; } } return t; } }; ostream& operator<<(ostream& os, runtime_modint r) { return os << r.val(); } istream& operator>>(istream& is, runtime_modint &r) { ll x; is >> x; r = x; return is; } using mint = runtime_modint; // <<< // https://ei1333.github.io/luzhiled/snippets/math/fast-fourier-transform.html template< int mod > struct NumberTheoreticTransform { vector< int > rev, rts; int base, max_base, root; NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} { assert(mod >= 3 && mod % 2 == 1); auto tmp = mod - 1; max_base = 0; while(tmp % 2 == 0) tmp >>= 1, max_base++; root = 2; while(mod_pow(root, (mod - 1) >> 1) == 1) ++root; assert(mod_pow(root, mod - 1) == 1); root = mod_pow(root, (mod - 1) >> max_base); } inline int mod_pow(int x, int n) { int ret = 1; while(n > 0) { if(n & 1) ret = mul(ret, x); x = mul(x, x); n >>= 1; } return ret; } inline int inverse(int x) { return mod_pow(x, mod - 2); } inline unsigned add(unsigned x, unsigned y) { x += y; if(x >= mod) x -= mod; return x; } inline unsigned mul(unsigned a, unsigned b) { return 1ull * a * b % (unsigned long long) mod; } 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)); } assert(nbase <= max_base); while(base < nbase) { int z = mod_pow(root, 1 << (max_base - 1 - base)); for(int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; rts[(i << 1) + 1] = mul(rts[i], z); } ++base; } } void ntt(vector< int > &a) { const int n = (int) a.size(); 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++) { int z = mul(a[i + j + k], rts[j + k]); a[i + j + k] = add(a[i + j], mod - z); a[i + j] = add(a[i + j], z); } } } } vector< int > multiply(vector< int > a, vector< int > b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; a.resize(sz, 0); b.resize(sz, 0); ntt(a); ntt(b); int inv_sz = inverse(sz); for(int i = 0; i < sz; i++) { a[i] = mul(a[i], mul(b[i], inv_sz)); } reverse(a.begin() + 1, a.end()); ntt(a); a.resize(need); return a; } }; int32_t main() { int p; cin >> p; mint::mod() = p; int g = generator(p); vector<int> a(p),b(p); rep1 (i,p-1) cin >> a[i]; rep1 (i,p-1) cin >> b[i]; vector<int> idx(p-1); idx[0] = 1; rep (i,p-2) idx[i+1] = (idx[i]*g) % p; vector<int> aa(p-1),bb(p-1); rep (i,p-1) aa[i] = a[idx[i]], bb[i] = b[idx[i]]; NumberTheoreticTransform< 998244353 > ntt; auto cc = ntt.multiply(aa,bb); dump(cc); vector<int> c(p); rep (i,cc.size()) c[idx[i%(p-1)]] += cc[i]; rep1 (i,p-1) cout << c[i]%998244353 << " "; cout << endl; }