結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
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提出日時 | 2019-11-22 23:18:27 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
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 |
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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
// >>> 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)#endifusing ll = long long;using ld = long double;#define int ll#define double ldtemplate <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>::typeoutput_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;elsea = 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 modintusing 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.htmltemplate< 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;}