結果
問題 | No.931 Multiplicative Convolution |
ユーザー | hitonanode |
提出日時 | 2019-11-22 23:30:47 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
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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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
5,248 KB |
testcase_01 | AC | 2 ms
5,248 KB |
testcase_02 | AC | 2 ms
5,248 KB |
testcase_03 | AC | 2 ms
5,248 KB |
testcase_04 | AC | 3 ms
5,248 KB |
testcase_05 | AC | 3 ms
5,248 KB |
testcase_06 | AC | 4 ms
5,248 KB |
testcase_07 | AC | 28 ms
5,248 KB |
testcase_08 | AC | 273 ms
12,752 KB |
testcase_09 | AC | 255 ms
12,504 KB |
testcase_10 | AC | 267 ms
12,544 KB |
testcase_11 | AC | 260 ms
12,376 KB |
testcase_12 | AC | 259 ms
10,876 KB |
testcase_13 | AC | 269 ms
12,504 KB |
testcase_14 | AC | 270 ms
12,744 KB |
testcase_15 | AC | 271 ms
12,728 KB |
testcase_16 | AC | 289 ms
12,532 KB |
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 << "}"; return os; } 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 << ")"; return os; } 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]); }