#994235 (C++17) No.2810 Have Another Go (Hard)

提出ソース

結果

問題	No.2810 Have Another Go (Hard)
ユーザー	Nachia
提出日時	2024-07-12 21:58:17
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	34 ms / 3,000 ms
コード長	11,670 bytes
コンパイル時間	1,684 ms
コンパイル使用メモリ	128,712 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-12 21:59:04
合計ジャッジ時間	4,567 ms
ジャッジサーバーID （参考情報）	judge6 / 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 6,816 KB
testcase_01	AC	33 ms 6,944 KB
testcase_02	AC	33 ms 6,940 KB
testcase_03	AC	33 ms 6,944 KB
testcase_04	AC	33 ms 6,944 KB
testcase_05	AC	33 ms 6,940 KB
testcase_06	AC	33 ms 6,944 KB
testcase_07	AC	34 ms 6,944 KB
testcase_08	AC	33 ms 6,940 KB
testcase_09	AC	33 ms 6,944 KB
testcase_10	AC	33 ms 6,940 KB
testcase_11	AC	2 ms 6,944 KB
testcase_12	AC	2 ms 6,944 KB
testcase_13	AC	2 ms 6,940 KB
testcase_14	AC	2 ms 6,944 KB
testcase_15	AC	2 ms 6,940 KB
testcase_16	AC	9 ms 6,940 KB
testcase_17	AC	30 ms 6,944 KB
testcase_18	AC	19 ms 6,940 KB
testcase_19	AC	28 ms 6,940 KB
testcase_20	AC	6 ms 6,944 KB
testcase_21	AC	12 ms 6,940 KB
testcase_22	AC	19 ms 6,944 KB
testcase_23	AC	14 ms 6,940 KB
testcase_24	AC	21 ms 6,940 KB
testcase_25	AC	32 ms 6,940 KB
testcase_26	AC	33 ms 6,944 KB
testcase_27	AC	33 ms 6,940 KB
testcase_28	AC	33 ms 6,940 KB
testcase_29	AC	34 ms 6,940 KB
testcase_30	AC	33 ms 6,940 KB
testcase_31	AC	33 ms 6,940 KB
testcase_32	AC	33 ms 6,944 KB
testcase_33	AC	33 ms 6,940 KB
testcase_34	AC	33 ms 6,944 KB
testcase_35	AC	33 ms 6,940 KB
testcase_36	AC	34 ms 6,944 KB
testcase_37	AC	33 ms 6,940 KB
testcase_38	AC	33 ms 6,944 KB
testcase_39	AC	34 ms 6,940 KB
testcase_40	AC	33 ms 6,944 KB
testcase_41	AC	33 ms 6,944 KB
testcase_42	AC	33 ms 6,940 KB
testcase_43	AC	33 ms 6,940 KB
testcase_44	AC	34 ms 6,944 KB
testcase_45	AC	33 ms 6,940 KB
testcase_46	AC	2 ms 6,944 KB
testcase_47	AC	2 ms 6,940 KB
testcase_48	AC	2 ms 6,944 KB
testcase_49	AC	3 ms 6,940 KB
testcase_50	AC	2 ms 6,940 KB
testcase_51	AC	6 ms 6,944 KB
testcase_52	AC	4 ms 6,944 KB
testcase_53	AC	6 ms 6,944 KB
testcase_54	AC	7 ms 6,944 KB
testcase_55	AC	4 ms 6,944 KB
testcase_56	AC	6 ms 6,944 KB
testcase_57	AC	6 ms 6,940 KB
testcase_58	AC	5 ms 6,940 KB
testcase_59	AC	9 ms 6,940 KB
testcase_60	AC	6 ms 6,940 KB

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ソースコード

raw source code

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
#define repr(i,n) for(int i=int(n)-1; i>=0; i--)
const i64 INF = 1001001001001001001;
const char* yn(bool x){ return x ? "Yes" : "No"; }
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
template<typename A> using nega_queue = std::priority_queue<A,std::vector<A>,std::greater<A>>;
template<class R> auto ComparingBy(R f){ return [g=std::move(f)](auto l, auto r) -> bool { return g(l) < g(r); }; }
#include <atcoder/modint>
using Modint = atcoder::static_modint<998244353>;

#include <iterator>
#include <functional>

template<class Elem> struct vec;

template<class Iter>
struct seq_view{
    using Ref = typename std::iterator_traits<Iter>::reference;
    using Elem = typename std::iterator_traits<Iter>::value_type;
    Iter a, b;
    Iter begin() const { return a; }
    Iter end() const { return b; }
    int size() const { return (int)(b-a); }
    seq_view(Iter first, Iter last) : a(first), b(last) {}
    seq_view sort() const { std::sort(a, b); return *this; }
    Ref& operator[](int x){ return *(a+x); }
    template<class F = std::less<Elem>, class ret = vec<int>> ret sorti(F f = F()) const {
        ret x(size()); for(int i=0; i<size(); i++) x[i] = i;
        x().sort([&](int l, int r){ return f(a[l],a[r]); });
        return x;
    }
    template<class ret = vec<Elem>> ret col() const { return ret(begin(), end()); }
    template<class F = std::equal_to<Elem>, class ret = vec<std::pair<Elem, int>>>
    ret rle(F eq = F()) const {
        auto x = ret();
        for(auto& a : (*this)){
            if(x.size() == 0 || !eq(x[x.size()-1].first, a)) x.emp(a, 1); else x[x.size()-1].second++;
        } return x;
    }
    template<class F> seq_view sort(F f) const { std::sort(a, b, f); return *this; }
    Iter uni() const { return std::unique(a, b); }
    Iter lb(const Elem& x) const { return std::lower_bound(a, b, x); }
    Iter ub(const Elem& x) const { return std::upper_bound(a, b, x); }
    int lbi(const Elem& x) const { return lb(x) - a; }
    int ubi(const Elem& x) const { return ub(x) - a; }
    seq_view bound(const Elem& l, const Elem& r) const { return { lb(l), lb(r) }; }
    template<class F> Iter lb(const Elem& x, F f) const { return std::lower_bound(a, b, x, f); }
    template<class F> Iter ub(const Elem& x, F f) const { return std::upper_bound(a, b, x, f); }
    template<class F> Iter when_true_to_false(F f) const {
        if(a == b) return a;
        return std::lower_bound(a, b, *a,
            [&](const Elem& x, const Elem&){ return f(x); });
    }
    seq_view same(Elem x) const { return { lb(x), ub(x) }; }
    template<class F> auto map(F f) const {
        vec<typename Iter::value_type> r;
        for(auto& x : *this) r.emp(f(x));
        return r;
    }
    Iter max() const { return std::max_element(a, b); }
    Iter min() const { return std::min_element(a, b); }
    template<class F = std::less<Elem>>
    Iter min(F f) const { return std::min_element(a, b, f); }
    seq_view rev() const { std::reverse(a, b); return *this; }
};

template<class Elem>
struct vec {
    using Base = typename std::vector<Elem>;
    using Iter = typename Base::iterator;
    using CIter = typename Base::const_iterator;
    using View = seq_view<Iter>;
    using CView = seq_view<CIter>;

    vec(){}
    explicit vec(int n, const Elem& value = Elem()) : a(0<n?n:0, value) {}
    template <class I2> vec(I2 first, I2 last) : a(first, last) {}
    vec(std::initializer_list<Elem> il) : a(std::move(il)) {}
    vec(Base b) : a(std::move(b)) {}
    operator Base() const { return a; }

    Iter begin(){ return a.begin(); }
    CIter begin() const { return a.begin(); }
    Iter end(){ return a.end(); }
    CIter end() const { return a.end(); }
    int size() const { return a.size(); }
    bool empty() const { return a.empty(); }
    Elem& back(){ return a.back(); }
    const Elem& back() const { return a.back(); }
    vec sortunied(){ vec x = *this; x().sort(); x.a.erase(x().uni(), x.end()); return x; }
    Iter operator()(int x){ return a.begin() + x; }
    CIter operator()(int x) const { return a.begin() + x; }
    View operator()(int l, int r){ return { (*this)(l), (*this)(r) }; }
    CView operator()(int l, int r) const { return { (*this)(l), (*this)(r) }; }
    View operator()(){ return (*this)(0,size()); }
    CView operator()() const { return (*this)(0,size()); }
    Elem& operator[](int x){ return a[x]; }
    const Elem& operator[](int x) const { return a[x]; }
    Base& operator*(){ return a; }
    const Base& operator*() const { return a; }
    vec& push(Elem args){
        a.push_back(std::move(args));
        return *this;
    }
    template<class... Args>
    vec& emp(Args &&... args){
        a.emplace_back(std::forward<Args>(args) ...);
        return *this;
    }
    template<class Range>
    vec& app(Range& x){ for(auto& v : a) emp(v); }
    Elem pop(){
        Elem x = std::move(a.back());
        a.pop_back(); return x;
    }
    bool operator==(const vec& r) const { return a == r.a; }
    bool operator!=(const vec& r) const { return a != r.a; }
    bool operator<(const vec& r) const { return a < r.a; }
    bool operator<=(const vec& r) const { return a <= r.a; }
    bool operator>(const vec& r) const { return a > r.a; }
    bool operator>=(const vec& r) const { return a >= r.a; }
    vec<vec<Elem>> pile(int n) const { return vec<vec<Elem>>(n, *this); }
    template<class F> vec& filter(F f){
        int p = 0;
        for(int q=0; q<size(); q++) if(f(a[q])) std::swap(a[p++],a[q]);
        a.resize(p); return *this;
    }
private: Base a;
};

template<class IStr, class U, class T>
IStr& operator>>(IStr& is, vec<std::pair<U,T>>& v){ for(auto& x:v){ is >> x.first >> x.second; } return is; }
template<class IStr, class T>
IStr& operator>>(IStr& is, vec<T>& v){ for(auto& x:v){ is >> x; } return is; }
template<class OStr, class T>
OStr& operator<<(OStr& os, const vec<T>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << v[i];
    } return os;
}
template<class OStr, class U, class T>
OStr& operator<<(OStr& os, const vec<std::pair<U,T>>& v){
    for(int i=0; i<v.size(); i++){
        if(i){ os << ' '; } os << '(' << v[i].first << ',' << v[i].second << ')';
    } return os;
}
#include <cassert>

namespace nachia{

template<class Elem>
struct MatrixModulo{
private:
    int h;
    int w;
    std::vector<Elem> elems;
public:
    
    MatrixModulo(int new_h=0, int new_w=0)
        : h(new_h), w(new_w), elems(h*w, Elem(0)){}
    MatrixModulo(const MatrixModulo &) = default;
    int numRow() const { return h; }
    int numColumn() const { return w; }
    int height() const { return numRow(); }
    int width() const { return numColumn(); }
    typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y*w); }
    typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y*w); }
    static MatrixModulo Identity(int n){
        auto res = MatrixModulo(n,n);
        for(int i=0; i<n; i++) res[i][i]=Elem(1);
        return res;
    }
    MatrixModulo transposed() const {
        auto res = MatrixModulo(w,h);
        for(int i=0; i<h; i++) for(int j=0; j<w; j++) res[j][i] = elems[i*w+j];
        return res;
    }
    void swapColumns(int x1, int x2){
        assert(0 <= x1 && x1 < numColumn());
        assert(0 <= x2 && x2 < numColumn());
        for(int y=0; y<numRow(); y++) std::swap((*this)[y][x1], (*this)[y][x2]);
    }
    void swapRows(int y1, int y2){
        assert(0 <= y1 && y1 < numRow());
        assert(0 <= y2 && y2 < numRow());
        for(int x=0; x<numColumn(); x++) std::swap((*this)[y1][x], (*this)[y2][x]);
    }
    MatrixModulo operator*(const MatrixModulo& r) const {
        assert(width() == r.height());
        auto res = MatrixModulo(h, r.w);
        for(int i=0; i<h; i++) for(int j=0; j<w; j++) for(int k=0; k<r.w; k++){
            res[i][k] += (*this)[i][j] * r[j][k];
        }
        return res;
    }
    std::vector<Elem> operator*(const std::vector<Elem>& r) const {
        assert(width() == int(r.size()));
        auto res = std::vector<Elem>(h);
        for(int i=0; i<h; i++) for(int j=0; j<w; j++){
            res[i] += (*this)[i][j] * r[j];
        }
        return res;
    }
    Elem det() const {
        assert(height() == width());
        MatrixModulo g = *this;
        Elem ans = 1;
        for(int i=0; i<h; i++){
            int tg = -1;
            for(int j=i; j<h; j++){ if(g[j][i].val() != 0) tg = j; }
            if(tg == -1) return 0;
            if(tg != i) ans = -ans;
            for(int j=0; j<h; j++) std::swap(g[i][j], g[tg][j]);
            tg = i;
            ans *= g[i][i];
            Elem const_coeff = g[i][i].inv();
            for(int j=0; j<h; j++) g[i][j] *= const_coeff;
            for(int j=i+1; j<h; j++) for(int k=h-1; k>=i; k--) g[j][k] -= g[j][i] * g[i][k];
        }
        return ans;
    }
    int rank() const {
        if(height() == 0 || width() == 0) return 0;
        MatrixModulo g = *this;
        int y = 0;
        for(int d=0; d<w; d++){
            if(y == h) break;
            int tg = -1;
            for(int i=y; i<h; i++){ if(g[i][d].val() != 0){ tg = i; break; } }
            if(tg == -1) continue;
            for(int j=d; j<w; j++) std::swap(g[y][j], g[tg][j]);
            tg = y;
            Elem const_coeff = g[y][d].inv();
            for(int j=d; j<w; j++) g[y][j] *= const_coeff;
            for(int i=y+1; i<h; i++) for(int j=w-1; j>=d; j--) g[i][j] -= g[i][d] * g[y][j];
            y++;
        }
        return y;
    }
    MatrixModulo pow(unsigned long long i){
        auto a = *this;
        auto res = Identity(height());
        while(i){
            if(i%2) res = res * a;
            a = a * a; i /= 2;
        }
        return res;
    }
};


} // namespace nachia
using namespace std;

void testcase(){
    using Mat = nachia::MatrixModulo<Modint>;
    Mat X(6,6);
    rep(i,5) X[i][i+1] += 1;
    rep(i,6) X[i][0] += 1;
    vec<Mat> G; G.push(X);
    rep(i,60) G.push(G.back() * G.back());

    auto Gpow = [&](i64 n) -> Mat {
        auto cy = Mat::Identity(6);
        rep(b,60) if(n & (1ll << b)) cy = cy * G[b];
        return cy;
    };

    auto GpowV = [&](i64 n, vector<Modint> v) -> vector<Modint> {
        rep(b,60) if(n & (1ll << b)) v = G[b].transposed() * v;
        return v;
    };

    i64 N, M; cin >> N >> M;
    i64 K; cin >> K;
    vec<i64> C(K); cin >> C;
    auto cy = Gpow(N);

    auto cy2 = Mat(12, 12);
    rep(i,6) rep(j,6) cy2[i+6][j+6] += cy[i][j];
    rep(i,6) rep(j,5) cy2[i][j+1] += cy[i][j+1];
    rep(i,6) cy2[i][6] += cy[i][0];
    cy2 = cy2.pow(M-1);

    for(i64 c : C){
        vector<Modint> A(12);
        vector<Modint> sa(6); sa[0] = 1;
        sa = GpowV(c, sa);
        //for(auto a : sa) cout << a.val() << " ";
        //cout << endl;
        rep(i,6) A[i] = sa[i];
        swap(A[0], A[6]);
        A = cy2.transposed() * A;
        sa = vector<Modint>(A.begin() + 6, A.begin() + 12);
        //for(auto a : sa) cout << a.val() << " ";
        //cout << endl;
        sa = GpowV(N-c-1, sa);
        Modint ans = 0;
        rep(i,6) ans += sa[i] * (6-i);
        cout << ans.val() << '\n';
    }

}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}

yukicoder

結果

テストケース

ソースコード