結果

問題 No.2441 行列累乗
ユーザー noya2noya2
提出日時 2023-08-25 21:35:50
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 9,655 bytes
コンパイル時間 3,988 ms
コンパイル使用メモリ 259,996 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-12-24 08:05:04
合計ジャッジ時間 4,816 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
other AC * 20
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout.hpp"
namespace noya2 {

template<typename T> concept Scanable  = requires (ifstream &is, T &a){ is >> a; };
template<typename T> concept Printable = requires (ofstream &os, T &a){ os << a; };

template <typename Scanable> istream &operator>>(istream &is, vector<Scanable> &v);
template <typename Printable> ostream &operator<<(ostream &os, const vector<Printable> &v);

template <typename T, typename U>
requires Scanable<T> && Scanable<U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}
template <typename T, typename U>
requires Printable<T> && Printable<U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}

template <typename Scanable>
istream &operator>>(istream &is, vector<Scanable> &v){
    for (auto &x : v) is >> x;
    return is;
}
template <typename Printable>
ostream &operator<<(ostream &os, const vector<Printable> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}

void in() {}
template <typename Scanable, class... U>
void in(Scanable &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename Printable, class... U, char sep = ' '>
void out(const Printable &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}
template<typename Printable>
void out(const vector<vector<Printable>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(abs(a),abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(vector<T> &v){
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/math/matrix.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/matrix.hpp"

namespace noya2{

template<typename T> struct Matrix{
    int rows, cols;
    vector<vector<T>> m;
    Matrix (int h = 0, int w = -1, T init = T(0)) : m(h,vector<T>((w == -1 ? h : w),init)){
        rows = h, cols = (w == -1 ? h : w);
    } 
    Matrix (vector<vector<T>> _init) : m(_init), rows(_init.size()), cols(_init.at(0).size()){}
    vector<T>& operator[](const int i) const {return m[i];}
    vector<T>& operator[](const int i) {return m[i];}
    Matrix &operator+= (const Matrix &r){
        assert(this->rows == r.rows && this->cols == r.cols);
        for (int i = 0; i < r.rows; ++i){
            for (int j = 0; j < r.cols; ++j){
                m[i][j] += r.m[i][j];
            }
        }
        return *this;
    }
    Matrix &operator-= (const Matrix &r){
        assert(this->rows == r.rows && this->cols == r.cols);
        for (int i = 0; i < r.rows; ++i){
            for (int j = 0; j < r.cols; ++j){
                m[i][j] -= r.m[i][j];
            }
        }
        return *this;
    }
    Matrix &operator*= (const Matrix &r){
        assert(this->cols == r.rows);
        Matrix res(rows, r.cols);
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < r.cols; ++j){
                for (int k = 0; k < r.rows; ++k){
                    res[i][j] += m[i][k] * r.m[k][j];
                }
            }
        }
        return *this = res;
    }
    Matrix operator+ (const Matrix &r) const {return Matrix(*this) += r;}
    Matrix operator- (const Matrix &r) const {return Matrix(*this) -= r;}
    Matrix operator* (const Matrix &r) const {return Matrix(*this) *= r;}
    bool operator== (const Matrix &r){
        if (rows != r.rows || cols != r.cols) return false;
        for (int i = 0; i < r.rows; ++i){
            for (int j = 0; j < r.cols; ++j){
                if (m[i][j] != r.m[i][j]) return false;
            }
        }
        return true;
    }
    Matrix& operator+=(const T &r){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                m[i][j] += r;
            }
        }
        return *this;
    }
    Matrix& operator-=(const T &r){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                m[i][j] -= r;
            }
        }
        return *this;
    }
    Matrix& operator*=(const T &r){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                m[i][j] *= r;
            }
        }
        return *this;
    }
    Matrix& operator/=(const T &r){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                m[i][j] /= r;
            }
        }
        return *this;
    }
    Matrix operator+ (const T &r) const {return Matrix(*this) += r;}
    Matrix operator- (const T &r) const {return Matrix(*this) -= r;}
    Matrix operator* (const T &r) const {return Matrix(*this) *= r;}
    Matrix operator/ (const T &r) const {return Matrix(*this) /= r;}
    Matrix e(){
        assert(this->rows == this->cols);
        Matrix res(this->rows, this->rows);
        for (int i = 0; i < rows; ++i) res[i][i] = 1;
        return res;
    }
    Matrix pow(long long n){
        assert(this->rows == this->cols);
        if (n == 0) return e();
        Matrix f = pow(n / 2);
        Matrix ans = f * f;
        if (n % 2 == 1) ans *= *this;
        return ans;
    }
    // for T = int, long long, double, long double
    void show(){
        for (int i = 0; i < rows; ++i){
            for (int j = 0; j < cols; ++j){
                cout << m[i][j] << (j+1 == this->cols ? "\n" : " ");
            }
        }
    }
    T determinant() const {
        Matrix B(*this);
        assert(rows == cols);
        T ret = 1;
        for (int i = 0; i < rows; i++) {
            int idx = -1;
            for (int j = i; j < cols; j++) {
                if (B[j][i] != 0) {
                    idx = j;
                    break;
                }
            }
            if (idx == -1) return 0;
            if (i != idx) {
                ret *= T(-1);
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T inv = T(1) / B[i][i];
            for (int j = 0; j < cols; j++) {
                B[i][j] *= inv;
            }
            for (int j = i + 1; j < rows; j++) {
                T a = B[j][i];
                if (a == 0) continue;
                for (int k = i; k < cols; k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return ret;
    }
};

} // namespace noya2
#line 4 "c.cpp"

void solve(){
    vector a(2,vector<ll>(2)); in(a);
    Matrix<ll> b(2);
    rep(i,2) rep(j,2) b[i][j] = a[i][j];
    b.pow(3).show();
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
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