結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
|
提出日時 | 2019-11-23 00:17:43 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
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;// outputtemplate<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; }// testtemplate<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 llusing 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^ 9constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9constexpr ll INFLL = 1LL << 60; // 1.15x10^18constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18constexpr 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 ~ 2^30NTT_CONVOLUTION_TIME <- 2: X < 575334854091079681 = 5.8*10^17 ~ 2^59NTT_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;}