結果
問題 | No.931 Multiplicative Convolution |
ユーザー | satanic |
提出日時 | 2019-11-23 00:17:43 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 167 ms / 2,000 ms |
コード長 | 9,586 bytes |
コンパイル時間 | 1,869 ms |
コンパイル使用メモリ | 146,344 KB |
実行使用メモリ | 22,704 KB |
最終ジャッジ日時 | 2024-10-11 06:36:44 |
合計ジャッジ時間 | 4,374 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
(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
6,816 KB |
testcase_01 | AC | 2 ms
6,816 KB |
testcase_02 | AC | 2 ms
6,816 KB |
testcase_03 | AC | 2 ms
6,816 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 | 19 ms
6,816 KB |
testcase_08 | AC | 164 ms
22,704 KB |
testcase_09 | AC | 154 ms
22,680 KB |
testcase_10 | AC | 162 ms
22,508 KB |
testcase_11 | AC | 152 ms
22,404 KB |
testcase_12 | AC | 89 ms
13,552 KB |
testcase_13 | AC | 163 ms
22,680 KB |
testcase_14 | AC | 166 ms
22,692 KB |
testcase_15 | AC | 166 ms
22,676 KB |
testcase_16 | AC | 167 ms
22,696 KB |
ソースコード
// need #include <iostream> #include <algorithm> // data structure #include <bitset> #include <map> #include <queue> #include <set> #include <stack> #include <string> #include <utility> #include <vector> #include <complex> //#include <deque> #include <valarray> #include <unordered_map> #include <unordered_set> #include <array> // etc #include <cassert> #include <cmath> #include <functional> #include <iomanip> #include <chrono> #include <random> #include <numeric> #include <fstream> // input #define INIT std::ios::sync_with_stdio(false);std::cin.tie(0); #define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__); template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; } template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest& ...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); } #define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int w_=0; w_<n; ++w_){MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);} template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); } template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest& ...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); } template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; } template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest& ...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); } #define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i; #define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& R:c)for(auto& w:R)std::cin>>w; // output template<typename T>void MACRO_OUT(const T t) { std::cout << t; } template<typename First, typename...Rest>void MACRO_OUT(const First first, const Rest...rest) { std::cout << first << " "; MACRO_OUT(rest...); } #define OUT(...) MACRO_OUT(__VA_ARGS__); #define FOUT(n, dist) std::cout<<std::fixed<<std::setprecision(n)<<(dist); #define SOUT(n, c, dist) std::cout<<std::setw(n)<<std::setfill(c)<<(dist); #define SP std::cout<<" "; #define TAB std::cout<<"\t"; #define BR std::cout<<"\n"; #define SPBR(w, n) std::cout<<(w + 1 == n ? '\n' : ' '); #define ENDL std::cout<<std::endl; #define FLUSH std::cout<<std::flush; #define SHOW(dist) {std::cerr << #dist << "\t: " << (dist) << "\n";} #define SHOWVECTOR(v) {std::cerr << #v << "\t: ";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";} #define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}} #define SHOWQUEUE(a) {auto tmp(a);std::cerr << #a << "\t: ";while(!tmp.empty()){std::cerr << tmp.front() << " ";tmp.pop();}std::cerr << "\n";} #define SHOWSTACK(a) {auto tmp(a);std::cerr << #a << "\t: ";while(!tmp.empty()){std::cerr << tmp.top() << " ";tmp.pop();}std::cerr << "\n";} // utility #define ALL(a) (a).begin(),(a).end() #define FOR(w, a, n) for(int w=(a);w<(n);++w) #define RFOR(w, a, n) for(int w=(n)-1;w>=(a);--w) #define REP(w, n) for(int w=0;w<int(n);++w) #define RREP(w, n) for(int w=int(n)-1;w>=0;--w) #define IN(a, x, b) (a<=x && x<b) template<class T> inline T CHMAX(T & a, const T b) { return a = (a < b) ? b : a; } template<class T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; } // test template<class T> using V = std::vector<T>; template<class T> using VV = V<V<T>>; template<typename S, typename T> std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; } // type/const #define int ll using ll = long long; using ull = unsigned long long; using ld = long double; using PAIR = std::pair<int, int>; using PAIRLL = std::pair<ll, ll>; constexpr int INFINT = (1 << 30) - 1; // 1.07x10^ 9 constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9 constexpr ll INFLL = 1LL << 60; // 1.15x10^18 constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18 constexpr double EPS = 1e-10; constexpr int MOD = 998244353; constexpr double PI = 3.141592653589793238462643383279; template<class T, size_t N> void FILL(T(&a)[N], const T & val) { for (auto& x : a) x = val; } template<class ARY, size_t N, size_t M, class T> void FILL(ARY(&a)[N][M], const T & val) { for (auto& b : a) FILL(b, val); } template<class T> void FILL(std::vector<T> & a, const T & val) { for (auto& x : a) x = val; } template<class ARY, class T> void FILL(std::vector<std::vector<ARY>> & a, const T & val) { for (auto& b : a) FILL(b, val); } // ------------>8------------------------------------->8------------ ll powMod(ll n, ll p, ll mod) { n %= mod; ll res = 1; while (p) { if (p & 1) res *= n, res %= mod; n *= n, n %= mod; p >>= 1; } return res; } int generator(int p) { std::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; } // find x such that g^x == y (mod p) int BabyStepGiantStep(int p, int g, int y) { int m = std::ceil(std::sqrt(p)); std::unordered_map<int, int> mp; mp.reserve(m); ll gj = 1; for (int j = 0; j < m; ++j) { mp[gj] = j; (gj *= g) %= p; } ll gm = powMod(g, p - 1 - m, p); ll ga = y; for (int i = 0; i < m; ++i) { auto it = mp.find(ga); if (it != mp.end()) return i * m + it->second; (ga *= gm) %= p; } return -1; } // Description: 整数列a[i],b[i]から列c[k]=sum{a[i]*b[k-i]}を生成する.任意modに対応.O(NlogN). namespace NTT { std::vector<int> tmp; size_t sz = 1; inline int powMod(int n, int p, int m) { int res = 1; while (p) { if (p & 1) res = (ll)res * n % m; n = (ll)n * n % m; p >>= 1; } return (int)res; } inline int invMod(int n, int m) { return powMod(n, m - 2, m); } template <int Mod, int PrimitiveRoot> struct NTTPart { static std::vector<int> ntt(std::vector<int> a, bool inv = false) { size_t mask = sz - 1; size_t p = 0; for (size_t i = sz >> 1; i >= 1; i >>= 1) { auto& cur = (p & 1) ? tmp : a; auto& nex = (p & 1) ? a : tmp; int e = powMod(PrimitiveRoot, (Mod - 1) / sz * i, Mod); if (inv) e = invMod(e, Mod); int w = 1; for (size_t j = 0; j < sz; j += i) { for (size_t k = 0; k < i; ++k) { nex[j + k] = (cur[((j << 1) & mask) + k] + (ll)w * cur[(((j << 1) + i) & mask) + k]) % Mod; } w = (ll)w * e % Mod; } ++p; } if (p & 1) std::swap(a, tmp); if (inv) { int invSz = invMod(sz, Mod); for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * invSz % Mod; } return a; } static std::vector<int> mul(std::vector<int> a, std::vector<int> b) { a = ntt(a); b = ntt(b); for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * b[i] % Mod; a = ntt(a, true); return a; } }; constexpr int M[] = { 1224736769, 469762049, 167772161 }; constexpr int PR[] = { 3, 3, 3 }; constexpr int NTT_CONVOLUTION_TIME = 3; /* X := max(a)*max(b)*min(|a|, |b|) のとき, NTT_CONVOLUTION_TIME <- 1: X < 1224736769 = 1.2*10^ 9 ~ 2^30 NTT_CONVOLUTION_TIME <- 2: X < 575334854091079681 = 5.8*10^17 ~ 2^59 NTT_CONVOLUTION_TIME <- 3: X < 2^86 (32bit * 32bit * 10^7くらいまで) */ inline void garner(std::vector<int> * c, int mod) { if (NTT_CONVOLUTION_TIME == 1) { for (auto& x : c[0]) x %= mod; } else if (NTT_CONVOLUTION_TIME == 2) { const int r01 = invMod(M[0], M[1]); for (size_t i = 0; i < sz; ++i) { c[1][i] = (c[1][i] - c[0][i]) * (ll)r01 % M[1]; if (c[1][i] < 0) c[1][i] += M[1]; c[0][i] = (c[0][i] + (ll)c[1][i] * M[0]) % mod; } } else if (NTT_CONVOLUTION_TIME == 3) { const int R01 = invMod(M[0], M[1]); const int R02 = invMod(M[0], M[2]); const int R12 = invMod(M[1], M[2]); const int M01 = (ll)M[0] * M[1] % mod; for (size_t i = 0; i < sz; ++i) { c[1][i] = (c[1][i] - c[0][i]) * (ll)R01 % M[1]; if (c[1][i] < 0) c[1][i] += M[1]; c[2][i] = ((c[2][i] - c[0][i]) * (ll)R02 % M[2] - c[1][i]) * R12 % M[2]; if (c[2][i] < 0) c[2][i] += M[2]; c[0][i] = (c[0][i] + (ll)c[1][i] * M[0] + (ll)c[2][i] * M01) % mod; } } } std::vector<int> mul(std::vector<int> a, std::vector<int> b, int mod) { for (auto& x : a) x %= mod; for (auto& x : b) x %= mod; size_t m = a.size() + b.size() - 1; sz = 1; while (m > sz) sz <<= 1; tmp.resize(sz); a.resize(sz, 0); b.resize(sz, 0); std::vector<int> c[NTT_CONVOLUTION_TIME]; if (NTT_CONVOLUTION_TIME >= 1) c[0] = NTTPart<M[0], PR[0]>::mul(a, b); if (NTT_CONVOLUTION_TIME >= 2) c[1] = NTTPart<M[1], PR[1]>::mul(a, b); if (NTT_CONVOLUTION_TIME >= 3) c[2] = NTTPart<M[2], PR[2]>::mul(a, b); for (auto& v : c) v.resize(m); garner(c, mod); return c[0]; } }; // !!! CHECK NTT_CONVOLUTION_TIME !!! signed main() { INIT; VAR(int, p); VEC(int, a, p - 1); VEC(int, b, p - 1); a.insert(a.begin(), 0); b.insert(b.begin(), 0); int g = generator(p); V<int> A(p - 1), B(p - 1); { int t = 1; REP(i, p - 1) { A[i] = a[t]; B[i] = b[t]; (t *= g) %= p; } } auto C = NTT::mul(A, B, MOD); { FOR(i, p - 1, C.size()) { (C[i % (p - 1)] += C[i]) %= MOD; C[i] = 0; } } V<int> c(p, 0); { int t = 1; REP(i, p - 1) { c[t] = C[i]; (t *= g) %= p; } } FOR(i, 1, p) { OUT(c[i])SPBR(i, p) } return 0; }