結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
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提出日時 | 2019-11-22 23:30:47 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 289 ms / 2,000 ms |
コード長 | 8,384 bytes |
コンパイル時間 | 1,878 ms |
コンパイル使用メモリ | 183,200 KB |
実行使用メモリ | 12,752 KB |
最終ジャッジ日時 | 2024-10-11 05:00:58 |
合計ジャッジ時間 | 5,841 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
コンパイルメッセージ
main.cpp: In function 'int find_primitive_root(int)': main.cpp:224:1: warning: control reaches end of non-void function [-Wreturn-type] 224 | } | ^
ソースコード
#include <bits/stdc++.h>using namespace std;using lint = long long int;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define SZ(x) ((lint)(x).size())#define POW2(n) (1LL << (n))#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }template<typename T> bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }template<typename T> bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }///// This part below is only for debug, not used /////template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; returnos; }template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}";return os; }template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; returnos; }template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;///// END //////*#include <ext/pb_ds/assoc_container.hpp>#include <ext/pb_ds/tree_policy.hpp>#include <ext/pb_ds/tag_and_trait.hpp>using namespace __gnu_pbds; // find_by_order(), order_of_key()template<typename TK> using pbds_set = tree<TK, null_type, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;template<typename TK, typename TV> using pbds_map = tree<TK, TV, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;*/lint power(lint x, lint n, lint MOD){lint ans = 1;while (n>0){if (n & 1) (ans *= x) %= MOD;(x *= x) %= MOD;n >>= 1;}return ans %= MOD;}// Solve ax+by=gcd(a, b)lint extgcd(lint a, lint b, lint &x, lint &y){lint d = a;if (b != 0) d = extgcd(b, a % b, y, x), y -= (a / b) * x;else x = 1, y = 0;return d;}// Calc a^(-1) (MOD m)lint mod_inverse(lint a, lint m){lint x, y;extgcd(a, m, x, y);return (m + x % m) % m;}// mod: 素数, primitive_root: modの原始根 is_inverse: trueならば逆変換void fft_mod(vector<lint> &a, lint mod, lint primitive_root, bool is_inverse=false){int n = a.size();lint h = power(primitive_root, (mod - 1) / n, mod);if (is_inverse) h = mod_inverse(h, mod);int i = 0;FOR(j, 1, n - 1) {for (int k = n >> 1; k > (i ^= k); k >>= 1);if (j < i) swap(a[i], a[j]);}for (int m = 1; m < n; m *= 2) {int m2 = 2 * m;lint base = power(h, n / m2, mod);lint w = 1;REP(x, m) {for (int s = x; s < n; s += m2) {lint u = a[s], d = a[s + m] * w % mod;a[s] = u + d - (u + d >= mod ? mod : 0), a[s + m] = u - d + (u - d < 0 ? mod : 0);}w = w * base % mod;}}for (auto &v : a) v = (v < 0 ? v + mod : v);if (is_inverse){lint n_inv = mod_inverse(n, mod);for (auto &v : a) v = v * n_inv % mod;}}// MOD modにおける畳み込み演算 retval[i] = \sum_j a[j] b[i - j]vector<lint> convolution_mod(vector<lint> a, vector<lint> b, lint mod, lint primitive_root){int sz = 1;while (sz < a.size() + b.size()) sz <<= 1;a.resize(sz), b.resize(sz);fft_mod(a, mod, primitive_root, false), fft_mod(b, mod, primitive_root, false);REP(i, sz) a[i] = a[i] * b[i] % mod;fft_mod(a, mod, primitive_root, true);return a;}constexpr lint MOD = 998244353;struct babystep_giantstep_modlog{lint M, sqrtM;lint a, biga;inline lint power(lint x, lint n){lint ans = 1;while (n>0){if (n & 1) (ans *= x) %= M;(x *= x) %= M;n >>= 1;}return ans;}inline lint inverse(lint a){lint b = M, u = 1, v = 0;while (b){lint t = a / b;a -= t * b; swap(a, b);u -= t * v; swap(u, v);}return u >= 0 ? u % M : u % M + M;}babystep_giantstep_modlog(lint mod) : M(mod), a(-1){lint l = -1, r = M;while (r - l > 1){lint c = (l + r) / 2;(c * c >= M ? r : l) = c;}sqrtM = r;}map<lint, lint> a_power;void set_base(lint a_new){if (a_new == a) return;a = a_new;biga = power(inverse(a), sqrtM);{a_power.clear();lint now = 1;for (lint n = 0; n < sqrtM; n++){a_power[now] = n;(now *= a_new) %= M;}}}map<lint, lint> biga_power;lint query(lint b){biga_power.clear();lint now = b;for (lint q = 0; q <= sqrtM; q++){if (a_power.count(now)){lint res = q * sqrtM + a_power[now];if (res > 0)return res;}(now *= biga) %= M;}return -1;}};int find_primitive_root(int p){vector<int> fac;lint pp = 2;int v = p - 1;while (v >= pp * pp){int e = 0;while (v % pp == 0){e++;v /= pp;}if (e) fac.push_back(pp);pp++;}if (v > 1) fac.push_back(v);int g = 2;while (g < p){if (power(g, p - 1, p) != 1) exit(8);bool ok = true;for (auto pp : fac){if (power(g, (p - 1) / pp, p) == 1){ok = false;break;}}if (ok) return g;g++;}}int main(){int P;cin >> P;vector<lint> A(P - 1), B(P - 1);cin >> A >> B;if (P == 2){cout << A[0] * B[0] % MOD << endl;return 0;}lint b = find_primitive_root(P);vector<lint> pp(P, 1), ppinv(P);FOR(i, 1, P) pp[i] = pp[i - 1] * b % P;REP(i, P) ppinv[pp[i]] = i;vector<lint> AS(P), BS(P);REP(i, P - 1) AS[ppinv[i + 1]] = A[i];REP(i, P - 1) BS[ppinv[i + 1]] = B[i];vector<lint> v = convolution_mod(AS, BS, MOD, 3);vector<lint> ret(P + 1);FOR(i, 1, v.size()){(ret[power(b, i, P)] += v[i]) %= MOD;}FOR(i, 1, P) printf("%lld ", ret[i]);}