結果
| 問題 | No.2272 多項式乗算 mod 258280327 |
| ユーザー |
 milanis48663220
|
| 提出日時 | 2023-04-14 22:42:35 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 554 ms / 2,000 ms |
| コード長 | 6,342 bytes |
| コンパイル時間 | 2,664 ms |
| コンパイル使用メモリ | 155,308 KB |
| 最終ジャッジ日時 | 2025-02-12 07:27:49 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 33 |
ソースコード
#include <iostream>#include <algorithm>#include <iomanip>#include <vector>#include <queue>#include <deque>#include <set>#include <map>#include <tuple>#include <cmath>#include <numeric>#include <functional>#include <cassert>#include <atcoder/modint>#include <atcoder/convolution>#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }using namespace std;typedef long long ll;template<typename T>vector<vector<T>> vec2d(int n, int m, T v){return vector<vector<T>>(n, vector<T>(m, v));}template<typename T>vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));}template<typename T>void print_vector(vector<T> v, char delimiter=' '){if(v.empty()) {cout << endl;return;}for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;cout << v.back() << endl;}// https://math314.hateblo.jp/entry/2015/05/07/014908typedef pair<int, int> Pii;#define FOR(i,n) for(int i = 0; i < (n); i++)#define sz(c) ((int)(c).size())#define ten(x) ((int)1e##x)template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b-= q * a, a); } return b; }template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }ll mod_pow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }template<int mod, int primitive_root>class NTT {public:int get_mod() const { return mod; }void _ntt(vector<ll>& a, int sign) {const int n = sz(a);assert((n ^ (n&-n)) == 0); //n = 2^kconst int g = 3; //g is primitive root of modint h = (int)mod_pow(g, (mod - 1) / n, mod); // h^n = 1if (sign == -1) h = (int)mod_inv(h, mod); //h = h^-1 % mod//bit reverseint i = 0;for (int j = 1; j < n - 1; ++j) {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) {const int m2 = 2 * m;const ll base = mod_pow(h, n / m2, mod);ll w = 1;FOR(x, m) {for (int s = x; s < n; s += m2) {ll u = a[s];ll d = a[s + m] * w % mod;a[s] = u + d;if (a[s] >= mod) a[s] -= mod;a[s + m] = u - d;if (a[s + m] < 0) a[s + m] += mod;}w = w * base % mod;}}for (auto& x : a) if (x < 0) x += mod;}void ntt(vector<ll>& input) {_ntt(input, 1);}void intt(vector<ll>& input) {_ntt(input, -1);const int n_inv = mod_inv(sz(input), mod);for (auto& x : input) x = x * n_inv % mod;}// 畳み込み演算を行うvector<ll> convolution(const vector<ll>& a, const vector<ll>& b){int ntt_size = 1;while (ntt_size < sz(a) + sz(b)) ntt_size *= 2;vector<ll> _a = a, _b = b;_a.resize(ntt_size); _b.resize(ntt_size);ntt(_a);ntt(_b);FOR(i, ntt_size){(_a[i] *= _b[i]) %= mod;}intt(_a);return _a;}};ll garner(vector<Pii> mr, int mod){mr.emplace_back(mod, 0);vector<ll> coffs(sz(mr), 1);vector<ll> constants(sz(mr), 0);FOR(i, sz(mr) - 1){// coffs[i] * v + constants[i] == mr[i].second (mod mr[i].first) を解くll v = (mr[i].second - constants[i]) * mod_inv<ll>(coffs[i], mr[i].first) % mr[i].first;if (v < 0) v += mr[i].first;for (int j = i + 1; j < sz(mr); j++) {(constants[j] += coffs[j] * v) %= mr[j].first;(coffs[j] *= mr[i].first) %= mr[j].first;}}return constants[sz(mr) - 1];}typedef NTT<167772161, 3> NTT_1;typedef NTT<469762049, 3> NTT_2;typedef NTT<1224736769, 3> NTT_3;//任意のmodで畳み込み演算 O(n log n)vector<ll> int32mod_convolution(vector<ll> a, vector<ll> b,int mod){for (auto& x : a) x %= mod;for (auto& x : b) x %= mod;NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;auto x = ntt1.convolution(a, b);auto y = ntt2.convolution(a, b);auto z = ntt3.convolution(a, b);vector<ll> ret(sz(x));vector<Pii> mr(3);FOR(i, sz(x)){mr[0].first = ntt1.get_mod(), mr[0].second = (int)x[i];mr[1].first = ntt2.get_mod(), mr[1].second = (int)y[i];mr[2].first = ntt3.get_mod(), mr[2].second = (int)z[i];ret[i] = garner(mr, mod);}return ret;}// garnerのアルゴリズムを直書きしたversion，速いvector<ll> fast_int32mod_convolution(vector<ll> a, vector<ll> b,int mod){for (auto& x : a) x %= mod;for (auto& x : b) x %= mod;NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;assert(ntt1.get_mod() < ntt2.get_mod() && ntt2.get_mod() < ntt3.get_mod());auto x = ntt1.convolution(a, b);auto y = ntt2.convolution(a, b);auto z = ntt3.convolution(a, b);// garnerのアルゴリズムを極力高速化したconst ll m1 = ntt1.get_mod(), m2 = ntt2.get_mod(), m3 = ntt3.get_mod();const ll m1_inv_m2 = mod_inv<ll>(m1, m2);const ll m12_inv_m3 = mod_inv<ll>(m1 * m2, m3);const ll m12_mod = m1 * m2 % mod;vector<ll> ret(sz(x));FOR(i, sz(x)){ll v1 = (y[i] - x[i]) * m1_inv_m2 % m2;if (v1 < 0) v1 += m2;ll v2 = (z[i] - (x[i] + m1 * v1) % m3) * m12_inv_m3 % m3;if (v2 < 0) v2 += m3;ll constants3 = (x[i] + m1 * v1 + m12_mod * v2) % mod;if (constants3 < 0) constants3 += mod;ret[i] = constants3;}return ret;}const ll mod = 258280327;int main(){ios::sync_with_stdio(false);cin.tie(0);cout << setprecision(10) << fixed;int n; cin >> n;vector<ll> f(n+1);for(int i = 0; i <= n; i++){cin >> f[i];}int m; cin >> m;vector<ll> g(m+1);for(int i = 0; i <= m; i++){cin >> g[i];}if(n == 0 && f[0] == 0){cout << 0 << endl;cout << 0 << endl;return 0;}if(m == 0 && g[0] == 0){cout << 0 << endl;cout << 0 << endl;return 0;}for(int i = 0; i <= n; i++) f[i] %= mod;for(int i = 0; i <= m; i++) g[i] %= mod;auto h = fast_int32mod_convolution(f, g, mod);while(h.size() > n+m+1) h.pop_back();cout << h.size()-1 << endl;print_vector(h);}