結果
| 問題 | No.2441 行列累乗 |
| ユーザー |
 ほえい
|
| 提出日時 | 2023-08-31 18:50:10 |
| 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 | 10,367 bytes |
| コンパイル時間 | 6,111 ms |
| コンパイル使用メモリ | 332,472 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2025-01-03 04:46:40 |
| 合計ジャッジ時間 | 7,177 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 20 |
ソースコード
#include <bits/stdc++.h>#include <atcoder/all>using namespace std;using namespace atcoder;using ll = long long;using lb = long double;using ull = unsigned long long;using P = pair<ll, ll>;#define rep(i, n) for (int i = 0; i < (n); i++)#define rep1(i, n) for (int i = 1; i <= (n); i++)#define rep2(i, n) for (int i = (n)-1; i >= 0; i--)#define repp(i, m, n) for (int i = m; i < n; i++)#define elif else if#define yes cout << "Yes" << endl;#define no cout << "No" << endl;#define fi first#define se second#define r0 return 0;#define Graph map<int,vector<int>>#define ALL(a) (a).begin(),(a).end()#define RALL(a) (a).rbegin(),(a).rend()#define eb emplace_back#define pb pop_backconst int di[] = {-1,-1,-1,0,0,1,1,1};const int dj[] = {-1,0,1,-1,1,-1,0,1};const int dx[] = {1,0,-1,0};const int dy[] = {0,1,0,-1};template <class T1, class T2> bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }template <class T1, class T2> bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }const lb pi = 3.14159265358979;using mint = modint998244353;priority_queue<ll, vector<ll>, greater<ll>> pq;namespace matrix_ {struct has_id_method_impl {template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type());template <class T_> static auto check(...) -> std::false_type;};template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {};} // namespace matrix_template <typename T> struct matrix {int H, W;std::vector<T> elem;typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }inline T &at(int i, int j) { return elem[i * W + j]; }inline T get(int i, int j) const { return elem[i * W + j]; }int height() const { return H; }int width() const { return W; }std::vector<std::vector<T>> vecvec() const {std::vector<std::vector<T>> ret(H);for (int i = 0; i < H; i++) {std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));}return ret;}operator std::vector<std::vector<T>>() const { return vecvec(); }matrix() = default;matrix(int H, int W) : H(H), W(W), elem(H * W) {}matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));}template <typename T2, typename std::enable_if<matrix_::has_id<T2>::value>::type * = nullptr>static T2 _T_id() {return T2::id();}template <typename T2, typename std::enable_if<!matrix_::has_id<T2>::value>::type * = nullptr>static T2 _T_id() {return T2(1);}static matrix Identity(int N) {matrix ret(N, N);for (int i = 0; i < N; i++) ret.at(i, i) = _T_id<T>();return ret;}matrix operator-() const {matrix ret(H, W);for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];return ret;}matrix operator*(const T &v) const {matrix ret = *this;for (auto &x : ret.elem) x *= v;return ret;}matrix operator/(const T &v) const {matrix ret = *this;const T vinv = _T_id<T>() / v;for (auto &x : ret.elem) x *= vinv;return ret;}matrix operator+(const matrix &r) const {matrix ret = *this;for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];return ret;}matrix operator-(const matrix &r) const {matrix ret = *this;for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];return ret;}matrix operator*(const matrix &r) const {matrix ret(H, r.W);for (int i = 0; i < H; i++) {for (int k = 0; k < W; k++) {for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);}}return ret;}matrix &operator*=(const T &v) { return *this = *this * v; }matrix &operator/=(const T &v) { return *this = *this / v; }matrix &operator+=(const matrix &r) { return *this = *this + r; }matrix &operator-=(const matrix &r) { return *this = *this - r; }matrix &operator*=(const matrix &r) { return *this = *this * r; }bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }bool operator<(const matrix &r) const { return elem < r.elem; }matrix pow(int64_t n) const {matrix ret = Identity(H);bool ret_is_id = true;if (n == 0) return ret;for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {if (!ret_is_id) ret *= ret;if ((n >> i) & 1) ret *= (*this), ret_is_id = false;}return ret;}std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {matrix x = *this;while (n) {if (n & 1) vec = x * vec;x *= x;n >>= 1;}return vec;};matrix transpose() const {matrix ret(W, H);for (int i = 0; i < H; i++) {for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);}return ret;}// Gauss-Jordan elimination// - Require inverse for every non-zero element// - Complexity: O(H^2 W)template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {int piv = -1;for (int j = h; j < mtr.H; j++) {if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c))))piv = j;}return piv;}template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {for (int j = h; j < mtr.H; j++) {if (mtr.get(j, c) != T2()) return j;}return -1;}matrix gauss_jordan() const {int c = 0;matrix mtr(*this);std::vector<int> ws;ws.reserve(W);for (int h = 0; h < H; h++) {if (c == W) break;int piv = choose_pivot(mtr, h, c);if (piv == -1) {c++;h--;continue;}if (h != piv) {for (int w = 0; w < W; w++) {std::swap(mtr[piv][w], mtr[h][w]);mtr.at(piv, w) *= -_T_id<T>(); // To preserve sign of determinant}}ws.clear();for (int w = c; w < W; w++) {if (mtr.at(h, w) != T()) ws.emplace_back(w);}const T hcinv = _T_id<T>() / mtr.at(h, c);for (int hh = 0; hh < H; hh++)if (hh != h) {const T coeff = mtr.at(hh, c) * hcinv;for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;mtr.at(hh, c) = T();}c++;}return mtr;}int rank_of_gauss_jordan() const {for (int i = H * W - 1; i >= 0; i--) {if (elem[i] != 0) return i / W + 1;}return 0;}int rank() const { return gauss_jordan().rank_of_gauss_jordan(); }T determinant_of_upper_triangle() const {T ret = _T_id<T>();for (int i = 0; i < H; i++) ret *= get(i, i);return ret;}int inverse() {assert(H == W);std::vector<std::vector<T>> ret = Identity(H), tmp = *this;int rank = 0;for (int i = 0; i < H; i++) {int ti = i;while (ti < H and tmp[ti][i] == T()) ti++;if (ti == H) {continue;} else {rank++;}ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);T inv = _T_id<T>() / tmp[i][i];for (int j = 0; j < W; j++) ret[i][j] *= inv;for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;for (int h = 0; h < H; h++) {if (i == h) continue;const T c = -tmp[h][i];for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;}}*this = ret;return rank;}friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {assert(m.W == int(v.size()));std::vector<T> ret(m.H);for (int i = 0; i < m.H; i++) {for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];}return ret;}friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {assert(int(v.size()) == m.H);std::vector<T> ret(m.W);for (int i = 0; i < m.H; i++) {for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);}return ret;}std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; }std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); }template <class OStream> friend OStream &operator<<(OStream &os, const matrix &x) {os << "[(" << x.H << " * " << x.W << " matrix)";os << "\n[column sums: ";for (int j = 0; j < x.W; j++) {T s = T();for (int i = 0; i < x.H; i++) s += x.get(i, j);os << s << ",";}os << "]";for (int i = 0; i < x.H; i++) {os << "\n[";for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";os << "]";}os << "]\n";return os;}template <class IStream> friend IStream &operator>>(IStream &is, matrix &x) {for (auto &v : x.elem) is >> v;return is;}};int main() {matrix<ll> mat(2, 2);rep(i, 2) rep(j, 2) {int a;cin >> a;mat[i][j] = a;}mat = mat.pow(3);cout << mat[0][0] << ' ' << mat[0][1] << '\n';cout << mat[1][0] << ' ' << mat[1][1] << '\n';}