結果
問題 | No.931 Multiplicative Convolution |
ユーザー | NyaanNyaan |
提出日時 | 2019-11-22 21:40:51 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 73 ms / 2,000 ms |
コード長 | 8,596 bytes |
コンパイル時間 | 2,262 ms |
コンパイル使用メモリ | 189,956 KB |
実行使用メモリ | 10,152 KB |
最終ジャッジ日時 | 2024-10-11 03:05:25 |
合計ジャッジ時間 | 4,179 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
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ファイルパターン | 結果 |
---|---|
other | AC * 17 |
ソースコード
#include <bits/stdc++.h>#define whlie while#define pb push_back#define eb emplace_back#define fi first#define se second#define rep(i,N) for(int i = 0; i < (N); i++)#define repr(i,N) for(int i = (N) - 1; i >= 0; i--)#define rep1(i,N) for(int i = 1; i <= (N) ; i++)#define repr1(i,N) for(int i = (N) ; i > 0 ; i--)#define each(x,v) for(auto& x : v)#define all(v) (v).begin(),(v).end()#define sz(v) ((int)(v).size())#define ini(...) int __VA_ARGS__; in(__VA_ARGS__)#define inl(...) ll __VA_ARGS__; in(__VA_ARGS__)#define ins(...) string __VA_ARGS__; in(__VA_ARGS__)using namespace std; void solve();using ll = long long; using vl = vector<ll>;using vi = vector<int>; using vvi = vector< vector<int> >;constexpr int inf = 1001001001;constexpr ll infLL = (1LL << 61) - 1;struct IoSetupNya {IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7);} } iosetupnya;template<typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; }template<typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; }template<typename T, typename U> ostream& operator <<(ostream& os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; }template<typename T, typename U> istream& operator >>(istream& is, pair<T, U> &p) { is >> p.first >> p.second; return is; }template<typename T> ostream& operator <<(ostream& os, const vector<T> &v) { int s = (int)v.size(); rep(i,s) os << (i ? " " : "") << v[i]; return os;}template<typename T> istream& operator >>(istream& is, vector<T> &v) { for(auto &x : v) is >> x; return is; }void in(){} template <typename T,class... U> void in(T &t,U &...u){ cin >> t; in(u...);}void out(){cout << "\n";} template <typename T,class... U> void out(const T &t,const U &...u){ cout << t; if(sizeof...(u)) cout << " "; out(u...);}template<typename T>void die(T x){out(x); exit(0);}#ifdef NyaanDebug#include "NyaanDebug.h"#define trc(...) do { cerr << #__VA_ARGS__ << " = "; dbg_out(__VA_ARGS__);} while(0)#define trca(v,N) do { cerr << #v << " = "; array_out(v , N);cout << endl;} while(0)#else#define trc(...)#define trca(...)int main(){solve();}#endif//using P = pair<ll,ll>; using vp = vector<P>;constexpr int MOD = /** 1000000007; //*/ 998244353;////////////////// 素数判定 O( sqrt(N) log log N )// 0からNに対して素数->1、それ以外->0の配列を返す関数vector<int> Primes(int N){vector<int> A(N + 1 , 1);A[0] = A[1] = 0;for(int i = 2; i * i <= N ; i++)if(A[i]==1) for(int j = i << 1 ; j <= N; j += i) A[j] = 0;return A;}// 因数 O( sqrt(N) log log N )// 0からNに対して素数->1、それ以外->最小の素数である因数、の配列を返すvector<int> Factors(int N){vector<int> A(N + 1 , 1);A[0] = A[1] = 0;for(int i = 2; i * i <= N ; i++)if(A[i]==1) for(int j = i << 1 ; j <= N; j += i) A[j] = i;return A;}// オイラーのトーシェント関数 φ(N)=(Nと互いに素なN以下の自然数の個数)vector<int> EulersTotientFunction(int N){vector<int> ret(N + 1 , 0);for(int i = 0; i <= N ; i++) ret[i] = i;for(int i = 2 ; i <= N ; i++){if(ret[i] == i)for(int j = i; j <= N; j += i) ret[j] = ret[j] / i * (i - 1);}return ret;}// 約数列挙 O(sqrt(N))// Nの約数を列挙した配列を返すvector<long long> Divisor(long long N){vector<long long> v;for(long long i = 1; i * i <= N ; i++){if(N % i == 0){v.push_back(i);if(i * i != N) v.push_back(N / i);}}return v;}// 素因数分解// 因数をkey、そのべきをvalueとするmapを返す// ex) N=12 -> m={ (2,2) , (3,1) }map<long long,int> PrimeFactors(long long N){map<long long,int> m;for(long long i=2; i * i <= N; i++)while(N % i == 0) m[i]++ , N /= i;if(N != 1) m[N]++;return m;}// 原始根 modでrが原始根かどうかを調べるbool PrimitiveRoot(long long r , long long mod){r %= mod; if(r == 0) return false;auto modpow = [](long long a,long long b,long long m)->long long{a %= m; long long ret = 1;while(b){if(b & 1) ret = a * ret % m;a = a * a % m;b >>= 1;}return ret;};map<long long,int> m = PrimeFactors(mod - 1);each(x , m){if(modpow(r , (mod - 1) / x.fi , mod ) == 1) return false;}return true;}// 拡張ユークリッド ax+by=gcd(a,b)の解// 返り値 最大公約数long long extgcd(long long a,long long b, long long &x, long long &y){if(b == 0){x = 1; y = 0; return a;}long long d = extgcd(b , a%b , y , x);y -= a / b * x;return d;}// ブール代数ライブラリ// Point. 乗法の単位元は-1 (UNIT & a = aを満たすUNITであるため)struct BA{unsigned long long x;BA(): x(0){}BA(unsigned long long y):x(y){}BA operator += (const BA &p){x = x ^ p.x;return (*this);}BA operator *= (const BA &p){x = x & p.x;return (*this);}BA operator+(const BA &p)const {return BA(*this) += p;}BA operator*(const BA &p)const {return BA(*this) *= p;}bool operator==(const BA &p) const { return x == p.x; }bool operator!=(const BA &p) const { return x != p.x; }friend ostream &operator<<(ostream &os,const BA &p){return os << p.x;}friend istream &operator>>(istream &is, BA &a){unsigned int t;is >> t;a = BA(t);return (is);}};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;}};void solve(){ini(P);vi A(P-1) , B(P-1); in(A , B);ll pr = 1;while(PrimitiveRoot(pr , P) == false) pr++;vi p(P-1);p[0] = 1;trc(p);rep1(i , P-2) p[i] = 1LL * p[i-1] * pr % P;vi inv(P);//rep(i,P-1) inv[p[i]] = i ;trc(p);vi s(P-1) , t(P-1);rep(i , P-1){s[i] = A[p[i] - 1];t[i] = B[p[i] - 1];}trc(s,t);NumberTheoreticTransform<MOD> ntt;auto u = ntt.multiply(s , t);trc(u);for(int i = P-1 ; i < u.size();i++) u[i%(P-1)] = (u[i%(P-1)] + u[i]) % MOD;trc(u);trc(inv);vi ans(P-1);rep(i,P-1) ans[p[i] - 1] = u[i];out(ans);}