#723655 (C++17) No.1783 Remix Sum

提出ソース

結果

問題	No.1783 Remix Sum
ユーザー	hitonanode
提出日時	2021-12-12 03:36:29
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	9,296 ms / 10,000 ms
コード長	12,130 bytes
コンパイル時間	5,246 ms
コンパイル使用メモリ	233,592 KB
実行使用メモリ	28,200 KB
最終ジャッジ日時	2024-07-20 12:32:09
合計ジャッジ時間	86,400 ms
ジャッジサーバーID （参考情報）	judge1 / judge3

このコードへのチャレンジ
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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 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	51 ms 5,376 KB
testcase_05	AC	51 ms 5,376 KB
testcase_06	AC	76 ms 5,376 KB
testcase_07	AC	302 ms 7,032 KB
testcase_08	AC	96 ms 5,376 KB
testcase_09	AC	97 ms 5,376 KB
testcase_10	AC	50 ms 5,376 KB
testcase_11	AC	49 ms 5,376 KB
testcase_12	AC	362 ms 7,028 KB
testcase_13	AC	169 ms 6,904 KB
testcase_14	AC	81 ms 5,376 KB
testcase_15	AC	285 ms 21,920 KB
testcase_16	AC	302 ms 6,908 KB
testcase_17	AC	361 ms 7,028 KB
testcase_18	AC	49 ms 5,376 KB
testcase_19	AC	110 ms 5,376 KB
testcase_20	AC	130 ms 5,376 KB
testcase_21	AC	111 ms 5,376 KB
testcase_22	AC	110 ms 5,376 KB
testcase_23	AC	158 ms 5,376 KB
testcase_24	AC	81 ms 5,376 KB
testcase_25	AC	76 ms 5,376 KB
testcase_26	AC	369 ms 7,028 KB
testcase_27	AC	76 ms 5,376 KB
testcase_28	AC	61 ms 5,376 KB
testcase_29	AC	131 ms 5,376 KB
testcase_30	AC	135 ms 5,376 KB
testcase_31	AC	116 ms 5,376 KB
testcase_32	AC	458 ms 27,680 KB
testcase_33	AC	137 ms 5,376 KB
testcase_34	AC	98 ms 5,376 KB
testcase_35	AC	185 ms 7,428 KB
testcase_36	AC	211 ms 22,324 KB
testcase_37	AC	240 ms 22,316 KB
testcase_38	AC	180 ms 7,300 KB
testcase_39	AC	87 ms 5,376 KB
testcase_40	AC	62 ms 5,376 KB
testcase_41	AC	88 ms 5,376 KB
testcase_42	AC	91 ms 5,376 KB
testcase_43	AC	177 ms 7,300 KB
testcase_44	AC	137 ms 5,376 KB
testcase_45	AC	692 ms 5,376 KB
testcase_46	AC	1,412 ms 5,376 KB
testcase_47	AC	2,063 ms 5,376 KB
testcase_48	AC	6,099 ms 7,296 KB
testcase_49	AC	6,768 ms 28,200 KB
testcase_50	AC	155 ms 5,376 KB
testcase_51	AC	722 ms 5,376 KB
testcase_52	AC	1,341 ms 5,376 KB
testcase_53	AC	2,188 ms 5,376 KB
testcase_54	AC	5,471 ms 7,300 KB
testcase_55	AC	6,690 ms 28,076 KB
testcase_56	AC	206 ms 5,376 KB
testcase_57	AC	1,014 ms 5,376 KB
testcase_58	AC	1,847 ms 5,376 KB
testcase_59	AC	3,079 ms 5,376 KB
testcase_60	AC	7,075 ms 7,428 KB
testcase_61	AC	9,296 ms 28,196 KB
testcase_62	AC	145 ms 5,376 KB
testcase_63	AC	733 ms 5,376 KB
testcase_64	AC	1,352 ms 5,376 KB
testcase_65	AC	2,155 ms 5,376 KB
testcase_66	AC	5,440 ms 7,304 KB
testcase_67	AC	1,794 ms 28,076 KB
testcase_68	AC	65 ms 5,376 KB
testcase_69	AC	115 ms 5,376 KB
testcase_70	AC	181 ms 5,376 KB
testcase_71	AC	269 ms 5,376 KB
testcase_72	AC	625 ms 7,300 KB
testcase_73	AC	753 ms 28,068 KB
testcase_74	AC	66 ms 5,376 KB
testcase_75	AC	120 ms 5,376 KB
testcase_76	AC	181 ms 5,376 KB
testcase_77	AC	142 ms 5,376 KB
testcase_78	AC	440 ms 7,424 KB
testcase_79	AC	447 ms 28,076 KB

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ソースコード

raw source code

#pragma GCC optimize("O3,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<char> chi;
    MODINT invfftlen;
    vector<MODINT> g;
    std::vector<std::vector<MODINT>> fex, gex, hex;

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) {
        assert(int(f.size()) == N);
        assert(int(g.size()) == N);
        if (dim.empty()) return {f[0] * g[0]};
        hex.assign(K, std::vector<MODINT>(fftlen));
        fex.assign(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) { 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() {
    auto START = std::chrono::system_clock::now();
    
    constexpr int E = 10;
    const mint r10 = 9142366;
    int N, K;
    lint M;
    int T;
    cin >> N >> K >> M >> T;
    // M %= mint::mod() - 1;
    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;
        if (gsub[0] == 0) chmin(p, 100000LL);
        // 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);
#ifndef HITONANODE_LOCAL
    for (auto x : dp) cout << x.val() << '\n';
#endif
    int64_t spent_ms = std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now() - START).count();
    dbg(spent_ms);
}

yukicoder

結果

テストケース

ソースコード