結果
問題 | No.1783 Remix Sum |
ユーザー | 👑 hitonanode |
提出日時 | 2021-12-12 02:54:51 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 9,519 ms / 10,000 ms |
コード長 | 12,271 bytes |
コンパイル時間 | 3,391 ms |
コンパイル使用メモリ | 192,880 KB |
実行使用メモリ | 23,572 KB |
最終ジャッジ日時 | 2023-09-27 17:24:01 |
合計ジャッジ時間 | 92,165 ms |
ジャッジサーバーID (参考情報) |
judge12 / judge11 |
(要ログイン)
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 | 1 ms
4,380 KB |
testcase_01 | AC | 1 ms
4,376 KB |
testcase_02 | AC | 1 ms
4,380 KB |
testcase_03 | AC | 2 ms
4,376 KB |
testcase_04 | AC | 54 ms
4,676 KB |
testcase_05 | AC | 53 ms
4,464 KB |
testcase_06 | AC | 83 ms
4,636 KB |
testcase_07 | AC | 313 ms
6,236 KB |
testcase_08 | AC | 102 ms
4,592 KB |
testcase_09 | AC | 101 ms
4,496 KB |
testcase_10 | AC | 53 ms
4,624 KB |
testcase_11 | AC | 53 ms
4,508 KB |
testcase_12 | AC | 387 ms
6,112 KB |
testcase_13 | AC | 176 ms
6,148 KB |
testcase_14 | AC | 85 ms
4,444 KB |
testcase_15 | AC | 297 ms
22,596 KB |
testcase_16 | AC | 309 ms
6,356 KB |
testcase_17 | AC | 389 ms
6,160 KB |
testcase_18 | AC | 51 ms
4,452 KB |
testcase_19 | AC | 122 ms
4,448 KB |
testcase_20 | AC | 132 ms
4,684 KB |
testcase_21 | AC | 117 ms
4,516 KB |
testcase_22 | AC | 122 ms
4,504 KB |
testcase_23 | AC | 150 ms
4,704 KB |
testcase_24 | AC | 80 ms
4,592 KB |
testcase_25 | AC | 81 ms
4,484 KB |
testcase_26 | AC | 385 ms
6,116 KB |
testcase_27 | AC | 81 ms
4,628 KB |
testcase_28 | AC | 68 ms
4,572 KB |
testcase_29 | AC | 129 ms
4,524 KB |
testcase_30 | AC | 128 ms
4,792 KB |
testcase_31 | AC | 120 ms
4,500 KB |
testcase_32 | AC | 448 ms
23,224 KB |
testcase_33 | AC | 130 ms
4,540 KB |
testcase_34 | AC | 89 ms
5,008 KB |
testcase_35 | AC | 185 ms
6,480 KB |
testcase_36 | AC | 220 ms
23,004 KB |
testcase_37 | AC | 218 ms
22,852 KB |
testcase_38 | AC | 185 ms
6,568 KB |
testcase_39 | AC | 90 ms
4,932 KB |
testcase_40 | AC | 65 ms
5,100 KB |
testcase_41 | AC | 90 ms
5,076 KB |
testcase_42 | AC | 88 ms
4,980 KB |
testcase_43 | AC | 184 ms
6,572 KB |
testcase_44 | AC | 145 ms
4,932 KB |
testcase_45 | AC | 766 ms
5,020 KB |
testcase_46 | AC | 1,453 ms
5,044 KB |
testcase_47 | AC | 2,170 ms
5,232 KB |
testcase_48 | AC | 5,749 ms
6,612 KB |
testcase_49 | AC | 6,820 ms
23,528 KB |
testcase_50 | AC | 145 ms
4,864 KB |
testcase_51 | AC | 772 ms
4,892 KB |
testcase_52 | AC | 1,456 ms
4,964 KB |
testcase_53 | AC | 2,089 ms
4,940 KB |
testcase_54 | AC | 5,735 ms
6,496 KB |
testcase_55 | AC | 6,834 ms
23,356 KB |
testcase_56 | AC | 229 ms
4,844 KB |
testcase_57 | AC | 1,087 ms
5,028 KB |
testcase_58 | AC | 2,034 ms
4,920 KB |
testcase_59 | AC | 2,952 ms
5,080 KB |
testcase_60 | AC | 8,058 ms
6,500 KB |
testcase_61 | AC | 9,519 ms
23,564 KB |
testcase_62 | AC | 147 ms
5,020 KB |
testcase_63 | AC | 772 ms
5,032 KB |
testcase_64 | AC | 1,447 ms
4,920 KB |
testcase_65 | AC | 2,123 ms
4,936 KB |
testcase_66 | AC | 5,677 ms
6,488 KB |
testcase_67 | AC | 5,939 ms
23,164 KB |
testcase_68 | AC | 68 ms
5,004 KB |
testcase_69 | AC | 125 ms
4,888 KB |
testcase_70 | AC | 199 ms
4,892 KB |
testcase_71 | AC | 280 ms
4,936 KB |
testcase_72 | AC | 757 ms
6,520 KB |
testcase_73 | AC | 794 ms
23,368 KB |
testcase_74 | AC | 67 ms
4,852 KB |
testcase_75 | AC | 141 ms
4,880 KB |
testcase_76 | AC | 201 ms
4,972 KB |
testcase_77 | AC | 143 ms
5,008 KB |
testcase_78 | AC | 522 ms
6,560 KB |
testcase_79 | AC | 521 ms
23,572 KB |
ソースコード
// #pragma GCC optimize("unroll-loops") // #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt") #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <chrono> #include <cmath> #include <complex> #include <deque> #include <forward_list> #include <fstream> #include <functional> #include <iomanip> #include <ios> #include <iostream> #include <limits> #include <list> #include <map> #include <numeric> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <string> #include <tuple> #include <type_traits> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> using namespace std; using lint = long long; using pint = pair<int, int>; using plint = pair<lint, lint>; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #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, typename V> void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); } template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } 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> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif 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, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &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, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif constexpr int md = (115 << 20) + 1; #include <atcoder/modint> using mint = atcoder::static_modint<md>; #include <atcoder/convolution> // Multivariate convolution (Linear, overflow cutoff) // Complexity: (kN \log N + k^2 N)$ // Note that the vectors store the infomation in **column-major order** // Implementation idea: https://rushcheyo.blog.uoj.ac/blog/6547 // Details of my implementation: https://hitonanode.github.io/cplib-cpp/convolution/multivar_ntt.hpp template <typename MODINT> struct multivar_ntt { int K, N, fftlen; std::vector<int> dim; std::vector<int> chi; MODINT invfftlen; vector<MODINT> g; std::vector<std::vector<MODINT>> gex; private: void _initialize(const std::vector<int> &dim_) { dim = dim_; K = dim_.size(); N = std::accumulate(dim_.begin(), dim_.end(), 1, [&](int l, int r) { return l * r; }); fftlen = 1; while (fftlen < N * 2) fftlen <<= 1; invfftlen = MODINT(fftlen).inv(); chi.resize(fftlen); int t = 1; for (auto d : dim_) { t *= d; for (int s = t; s < fftlen; s += t) chi[s] += 1; } for (int i = 0; i + 1 < fftlen; i++) { chi[i + 1] += chi[i]; if (chi[i + 1] >= K) chi[i + 1] -= K; } } std::vector<MODINT> _convolve(const std::vector<MODINT> &f) const { assert(int(f.size()) == N); assert(int(g.size()) == N); if (dim.empty()) return {f[0] * g[0]}; std::vector<std::vector<MODINT>> hex(K, std::vector<MODINT>(fftlen)); if (f == g) { for (int df = 0; df < K; df++) { for (int dg = 0; dg <= df; dg++) { int dh = (df + dg < K) ? df + dg : df + dg - K; for (int i = 0; i < fftlen; i++) hex[dh][i] += gex[df][i] * gex[dg][i] * (df == dg ? 1 : 2); } } } else { std::vector<std::vector<MODINT>> fex(K, std::vector<MODINT>(fftlen)); for (int i = 0; i < N; i++) fex[chi[i]][i] = f[i]; for (auto &vec : fex) atcoder::internal::butterfly(vec); for (int df = 0; df < K; df++) { for (int dg = 0; dg < K; dg++) { int dh = (df + dg < K) ? df + dg : df + dg - K; for (int i = 0; i < fftlen; i++) hex[dh][i] += fex[df][i] * gex[dg][i]; } } } for (auto &vec : hex) atcoder::internal::butterfly_inv(vec); std::vector<MODINT> ret(N); for (int i = 0; i < N; i++) ret[i] = hex[chi[i]][i] * invfftlen; return ret; } public: multivar_ntt(const std::vector<int> &dim_) { _initialize(dim_); } void set_g(const vector<MODINT> &g_) { g = g_; gex.assign(K, vector<MODINT>(fftlen)); if (dim.empty()) return; for (int i = 0; i < N; i++) gex[chi[i]][i] = g[i]; for (auto &vec : gex) atcoder::internal::butterfly(vec); } void double_g() { if (!K) { g[0] *= g[0]; return; } vector hex(K, vector<MODINT>(fftlen)); for (int df = 0; df < K; df++) { for (int dg = 0; dg <= df; dg++) { int dh = (df + dg < K) ? df + dg : df + dg - K; for (int i = 0; i < fftlen; i++) hex[dh][i] += gex[df][i] * gex[dg][i] * (df == dg ? 1 : 2); } } for (auto &vec : hex) atcoder::internal::butterfly_inv(vec); for (int i = 0; i < N; ++i) g[i] = hex[chi[i]][i] * invfftlen; gex.assign(K, vector<MODINT>(fftlen)); for (int i = 0; i < N; i++) gex[chi[i]][i] = g[i]; for (auto &vec : gex) atcoder::internal::butterfly(vec); } std::vector<MODINT> operator()(const std::vector<MODINT> &f) const { return _convolve(f); } }; // 元ネタが分からないんですが,OpenCup の 7 乗根のやつですか? int main() { constexpr int E = 10; const mint r10 = 9142366; int N, K; lint M; int T; cin >> N >> K >> M >> T; int K10 = 1; REP(t, K) K10 *= 10; vector<int> A(N); cin >> A; vector<int> diminfo(T, E); // T 桁切捨,K - T 桁周期 multivar_ntt<mint> mntt(diminfo); vector nttmat(E, vector<mint>(E)); REP(i, nttmat.size()) REP(j, nttmat[i].size()) nttmat[i][j] = r10.pow(i * j); auto inttmat = nttmat; for (auto &vec : inttmat) for (auto &x : vec) x = x.inv() / mint(10); auto ntt10 = [&](const array<mint, 10> &v) { array<mint, 10> ret; ret.fill(0); REP(i, E) REP(j, E) ret[i] += nttmat[i][j] * v[j]; return ret; }; auto intt10 = [&](const array<mint, 10> &v) { array<mint, 10> ret; ret.fill(0); REP(i, E) REP(j, E) ret[i] += inttmat[i][j] * v[j]; return ret; }; auto circular_ntt = [&](vector<mint> &f) { for (int di = mntt.N; di < K10; di *= 10) { for (int l = 0; l < K10; l += di * 10) { for (int i = l; i < l + di; ++i) { // [i, i + di, i + 2di, ..., i + 9di] を NTT auto impose_ntt = [&](vector<mint> &v) { static array<mint, 10> ntttmp; ntttmp.fill(0); REP(k, E) ntttmp[k] = v[i + k * di]; ntttmp = ntt10(ntttmp); REP(k, E) v[i + k * di] = ntttmp[k]; }; impose_ntt(f); } } } }; auto circular_intt = [&](vector<mint> &g) { for (int di = mntt.N; di < K10; di *= 10) { for (int l = 0; l < K10; l += di * 10) { for (int i = l; i < l + di; ++i) { // [i, i + di, i + 2di, ..., i + 9di] を NTT auto impose_intt = [&](vector<mint> &v) { static array<mint, 10> ntttmp; REP(k, E) ntttmp[k] = v[i + k * di]; ntttmp = intt10(ntttmp); REP(k, E) v[i + k * di] = ntttmp[k]; }; impose_intt(g); } } } }; vector<mint> dp(K10), trans(K10); dp[0] = 1; for (auto a : A) trans[a] += 1; circular_ntt(dp); circular_ntt(trans); vector<mint> ret; for (int l = 0; l < K10; l += mntt.N) { vector<mint> fsub(dp.begin() + l, dp.begin() + l + mntt.N); vector<mint> gsub(trans.begin() + l, trans.begin() + l + mntt.N); lint p = M; // Multivar pow なにもわからない...... mntt.set_g(gsub); while (p) { if (p & 1) fsub = mntt(fsub); p /= 2; if (!p) break; // gsub = mntt(gsub); mntt.double_g(); } ret.insert(ret.end(), fsub.begin(), fsub.end()); } dp = ret; circular_intt(dp); for (auto x : dp) cout << x.val() << '\n'; }