#907891 (C++17) No.2441 行列累乗

提出ソース

結果

問題	No.2441 行列累乗
ユーザー	dyktr_06
提出日時	2023-08-25 22:27:34
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	9,278 bytes
コンパイル時間	4,265 ms
コンパイル使用メモリ	266,668 KB
実行使用メモリ	4,380 KB
最終ジャッジ日時	2023-08-25 22:27:43
合計ジャッジ時間	5,304 ms
ジャッジサーバーID （参考情報）	judge13 / judge14

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 4,380 KB
testcase_01	AC	1 ms 4,376 KB
testcase_02	AC	1 ms 4,376 KB
testcase_03	AC	1 ms 4,380 KB
testcase_04	AC	2 ms 4,376 KB
testcase_05	AC	2 ms 4,380 KB
testcase_06	AC	2 ms 4,380 KB
testcase_07	AC	2 ms 4,376 KB
testcase_08	AC	1 ms 4,376 KB
testcase_09	AC	1 ms 4,376 KB
testcase_10	AC	1 ms 4,376 KB
testcase_11	AC	1 ms 4,376 KB
testcase_12	AC	1 ms 4,376 KB
testcase_13	AC	1 ms 4,376 KB
testcase_14	AC	2 ms 4,380 KB
testcase_15	AC	1 ms 4,376 KB
testcase_16	AC	2 ms 4,376 KB
testcase_17	AC	1 ms 4,376 KB
testcase_18	AC	1 ms 4,376 KB
testcase_19	AC	2 ms 4,376 KB

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

raw source code

#include <bits/stdc++.h>
#include <atcoder/all>

using namespace std;
using namespace atcoder;

#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))

typedef long long int ll;
typedef unsigned long long ul;
typedef long double ld;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector<char> vc;
typedef vector<string> vst;
typedef vector<double> vd;
typedef vector<long double> vld;
typedef pair<long long, long long> P;

template<class T> long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T& a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T& a){ return *max_element(a.begin(), a.end()); }

const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);
 
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; }

template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }

template<class T, class U> inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T, class U> void inGraph(vector<vector<T>>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } }

template <typename T>
struct Matrix{
    int n, m;
    vector<T> val;
    Matrix(int _n, int _m): n(_n), m(_m), val(_n * _m){}
    Matrix(const vector<vector<T>>& mat){
        n = mat.size();
        m = mat[0].size();
        val.resize(n * m);
        for(int i = 0; i < n; ++i){
            for(int j = 0; j < m; ++j){
                val[i * m + j] = mat[i][j];
            }
        }
    }
    static Matrix e(int _n){
        Matrix res(_n, _n);
        for(int i = 0; i < _n; ++i){
            res[i][i] = T{1};
        }
        return res;
    }
    auto operator[](int i){ return val.begin() + i * m; }
    auto operator[](int i) const { return val.begin() + i * m; }
    inline Matrix& operator+=(const Matrix &rhs){
        for(int i = 0; i < n * m; ++i){
            val[i] += rhs[i];
        }
        return *this;
    }
    inline Matrix& operator-=(const Matrix &rhs){
        for(int i = 0; i < n * m; ++i){
            val[i] -= rhs[i];
        }
        return *this;
    }
    inline Matrix operator*(const Matrix &rhs){
        assert(m == rhs.n);
        const int l = rhs.m;
        Matrix res(n, l);
        for(int i = 0; i < n; ++i){
            for(int j = 0; j < m; ++j){
                for(int k = 0; k < l; ++k){
                    res[i][k] += val[i * m + j] * rhs[j][k];
                }
            }
        }
        return res;
    }
    inline Matrix& operator*=(const Matrix &rhs){
        return *this = *this * rhs;
    }
    friend inline Matrix operator+(const Matrix& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) += rhs; }
    friend inline Matrix operator-(const Matrix& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) -= rhs; }
    friend inline bool operator==(const Matrix& lhs, const Matrix& rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const Matrix& lhs, const Matrix& rhs) noexcept { return lhs.val != rhs.val; }
    friend inline ostream& operator<<(ostream& os, const Matrix& mat) noexcept {
        const int _n = mat.n;
        const int _m = mat.m;
        for(int i = 0; i < _n; ++i){
            for(int j = 0; j < _m; ++j){
                os << mat[i][j] << " \n"[j == _m - 1];
            }
        }
        return os;
    }
    Matrix inv() const {
        Matrix a = *this, b = e(n);
        for(int i = 0; i < n; ++i){
            if(a[i][i] == 0){
                for(int j = i + 1; j < n; ++j){
                    if(a[j][i] != 0){
                        for(int k = i; k < n; ++k) swap(a[i][k], a[j][k]);
                        for(int k = 0; k < n; ++k) swap(b[i][k], b[j][k]);
                        break;
                    }
                }
            }
            if(a[i][i] == 0) throw "Inverse does not exist.";
            const T x = T{1} / a[i][i];
            for(int k = i; k < n; ++k) a[i][k] *= x;
            for(int k = 0; k < n; ++k) b[i][k] *= x;
            for(int j = 0; j < n; ++j){
                if(i != j){
                    const T x = a[j][i];
                    for(int k = i; k < n; ++k) a[j][k] -= a[i][k] * x;
                    for(int k = 0; k < n; ++k) b[j][k] -= b[i][k] * x;
                }
            }
        }
        return b;
    }
    Matrix pow(long long r) const {
        if(r == 0) return e(n);
        if(r < 0) return inv().pow(-r);
        Matrix res = e(n), a = *this;
        while(r > 0){
            if(r & 1) res *= a;
            a *= a;
            r >>= 1;
        }
        return res;
    }
    Matrix pow2(string &r) const {
        if(r == "0") return e(n);
        Matrix res = e(n), a = *this;
        int siz = r.size();
        for(int i = siz - 1; i >= 0; i--){
            if(r[i] == '1') res *= a;
            a *= a;
        }
        return res;
    }
    T det() const {
        Matrix a = *this;
        T res = 1;
        for(int i = 0; i < n; ++i){
            if(a[i][i] == 0){
                for(int j = i + 1; j < n; ++j){
                    if(a[j][i] != 0){
                        for(int k = i; k < n; ++k){
                            swap(a[i][k], a[j][k]);
                        }
                        res = -res;
                        break;
                    }
                }
            }
            if(a[i][i] == 0) return 0;
            res *= a[i][i];
            const T x = T{1} / a[i][i];
            for(int k = i; k < n; ++k){
                a[i][k] *= x;
            }
            for(int j = i + 1; j < n; ++j){
                const T x = a[j][i];
                for(int k = i; k < n; ++k){
                    a[j][k] -= a[i][k] * x;
                }
            }
        }
        return res;
    }
    // Rotate 90 degrees clockwise
    Matrix rotate() const {
        Matrix res(m, n), a = *this;
        for(int i = 0; i < m; ++i){
            for(int j = 0; j < n; ++j){
                res[i][j] = a[n - j - 1][i];
            }
        }
        return res;
    }
};

void input(){
}
 
void solve(){
    Matrix<ll> mat(2, 2);
    rep(i, 2) rep(j, 2){
        in(mat[i][j]);
    }
    cout << mat.pow(3);
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);
    
    input();
    solve();
}

yukicoder

結果

テストケース

ソースコード