結果
| 問題 |
No.3224 2×2行列入門
|
| ユーザー |
 iiljj
|
| 提出日時 | 2025-08-08 21:30:19 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 14,409 bytes |
| コンパイル時間 | 1,322 ms |
| コンパイル使用メモリ | 168,100 KB |
| 実行使用メモリ | 7,716 KB |
| 最終ジャッジ日時 | 2025-08-08 21:30:21 |
| 合計ジャッジ時間 | 2,259 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 |
|---|---|
| sample | AC * 3 |
| other | AC * 23 |
ソースコード
/* #region Head */
// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert> // assert.h
#include <cmath> // math.h
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;
#define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))
#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))
#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))
#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))
#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))
#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define ISIZE(x) ((int)(x).size())
#define PERM(c) \
sort(ALL(c)); \
for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define CEIL(a, b) (((a) + (b) - 1) / (b))
#define endl '\n'
constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;
// 前方宣言
template <typename T> istream &operator>>(istream &is, vc<T> &vec);
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec);
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec);
template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr);
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr);
template <typename T, size_t _Nm> ostream &operator>>(ostream &os, const array<T, _Nm> &arr);
template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var);
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var);
template <class T> ostream &out_iter(ostream &os, const T &map_var);
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var);
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var);
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var);
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var);
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var);
template <typename T> ostream &operator<<(ostream &os, const queue<T> &queue_var);
template <typename T> ostream &operator<<(ostream &os, const stack<T> &stk_var);
template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
for (T &x : vec) is >> x;
return is;
}
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)
os << "{";
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
return os;
}
template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
REP(i, 0, SIZE(arr)) is >> arr[i];
return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
os << "{";
REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
is >> pair_var.first >> pair_var.second;
return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力
os << "(" << pair_var.first << ", " << pair_var.second << ")";
return os;
}
// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, const T &map_var) {
os << "{";
REPI(itr, map_var) {
os << *itr;
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {
return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {
os << "{";
REPI(itr, map_var) {
auto [key, value] = *itr;
os << "(" << key << ", " << value << ")";
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
os << "}";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {
pq<T> pq_cp(pq_var);
os << "{";
if (!pq_cp.empty()) {
os << pq_cp.top(), pq_cp.pop();
while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
}
return os << "}";
}
// tuple 出力
template <size_t N = 0, bool end_line = false, typename... Args> ostream &operator<<(ostream &os, tuple<Args...> &a) {
if constexpr (N < std::tuple_size_v<tuple<Args...>>) {
os << get<N>(a);
if constexpr (N + 1 < std::tuple_size_v<tuple<Args...>>) {
os << ' ';
} else if constexpr (end_line) {
os << '\n';
}
return operator<< <N + 1, end_line>(os, a);
}
return os;
}
template <typename... Args> void print_tuple(tuple<Args...> &a) { operator<< <0, true>(std::cout, a); }
void pprint() { std::cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
std::cout << head;
if (sizeof...(Tail) > 0) std::cout << ' ';
pprint(move(tail)...);
}
// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&...tail) {
DUMPOUT << head;
if (sizeof...(Tail) > 0) DUMPOUT << ", ";
dump_func(move(tail)...);
}
// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
if (comp(xmax, x)) {
xmax = x;
return true;
}
return false;
}
// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
if (comp(x, xmin)) {
xmin = x;
return true;
}
return false;
}
// ローカル用
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif
#ifndef MYLOCAL
#undef DEBUG_
#endif
#ifdef DEBUG_
#define DEB
#define dump(...) \
DUMPOUT << " " << string(#__VA_ARGS__) << ": " << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" \
<< endl \
<< " ", \
dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif
#define VAR(type, ...) \
type __VA_ARGS__; \
assert((std::cin >> __VA_ARGS__));
template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }
struct AtCoderInitialize {
static constexpr int IOS_PREC = 15;
static constexpr bool AUTOFLUSH = false;
AtCoderInitialize() {
ios_base::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr);
std::cout << fixed << setprecision(IOS_PREC);
if (AUTOFLUSH) std::cout << unitbuf;
}
} ATCODER_INITIALIZE;
void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { std::cout << (p ? "YES" : "NO") << endl; }
template <typename T> constexpr void operator--(vc<T> &v, int) noexcept {
for (int i = 0; i < ISIZE(v); ++i) v[i]--;
}
template <typename T> constexpr void operator++(vc<T> &v, int) noexcept {
for (int i = 0; i < ISIZE(v); ++i) v[i]++;
}
/* #endregion */
/* #region Mat */
template <typename T> constexpr bool false_v = false;
// 行列，==, !=, [] あたりは array と一緒
template <class Num, size_t H, size_t W> class Mat : public array<array<Num, W>, H> {
public:
Mat() : array<array<Num, W>, H>() { fill(0); }
Mat(const Num value) : array<array<Num, W>, H>() { fill(value); }
Mat(std::initializer_list<array<Num, W>> init) : array<array<Num, W>, H>() {
int i = 0;
for (auto iter = init.begin(); iter != init.end(); ++iter) (*this)[i++] = array<Num, W>(*iter);
}
Mat(array<array<Num, W>, H> ar) : array<array<Num, W>, H>(ar) {}
// 行列に別の行列を足す
Mat<Num, H, W> &operator+=(const Mat<Num, H, W> &another) {
REP(i, 0, H) REP(j, 0, W)(*this)[i][j] += another[i][j];
return *this;
}
// 行列から別の行列を引く
Mat<Num, H, W> &operator-=(const Mat<Num, H, W> &another) {
REP(i, 0, H) REP(j, 0, W)(*this)[i][j] -= another[i][j];
return *this;
}
// 行列に別の行列を右から掛ける
// template <size_t AW> Mat<Num, H, AW> &operator*=(const Mat<Num, W, AW> &another) {
// Mat<Num, H, AW> ret = {};
// REP(i, 0, H) REP(j, 0, AW) REP(k, 0, W) ret[i][j] += (*this)[i][k] * another[k][j];
// *this = ret;
// return *this;
// }
// this を更新する場合，行列サイズが変わらない乗算のみ許容する（型が変わってしまうため）
Mat<Num, H, W> &operator*=(const Mat<Num, W, W> &another) {
Mat<Num, H, W> ret = (*this) * another;
*this = ret;
return *this;
}
// 行列に別の行列を足す
Mat<Num, H, W> operator+(const Mat<Num, H, W> &another) const {
Mat<Num, H, W> ret(*this);
return ret += another;
}
// 行列から別の行列を引く
Mat<Num, H, W> operator-(const Mat<Num, H, W> &another) const {
Mat<Num, H, W> ret(*this);
return ret -= another;
}
// 行列に別の行列を右から掛ける
template <size_t AW> Mat<Num, H, AW> operator*(const Mat<Num, W, AW> &another) const {
// Mat<Num, H, AW> ret(*this);
// return ret *= another;
Mat<Num, H, AW> ret = {};
REP(i, 0, H) REP(j, 0, AW) REP(k, 0, W) ret[i][j] += (*this)[i][k] * another[k][j];
return ret;
}
// 行列の n 乗を計算する
Mat<Num, H, W> pow(ll n) const {
assert(H == W);
Mat<Num, H, W> ret = {};
Mat<Num, H, W> a(*this);
REP(i, 0, H) ret[i][i] = 1;
while (n) {
if (n & 1) ret = a * ret;
a = a * a, n >>= 1;
}
return ret;
}
// 列和が 1 になるよう正規化する
Mat<Num, H, W> norm() const {
array<Num, W> s = {};
Mat<Num, H, W> a(*this);
REP(i, 0, H) REP(j, 0, W) s[j] += a[i][j];
REP(i, 0, H) REP(j, 0, W) a[i][j] /= s[j];
return a;
}
// 行列の n 乗を計算する（列和が常に 1 になるよう正規化する）
Mat<Num, H, W> pow_norm(ll n) const {
assert(H == W);
Mat<Num, H, W> ret = {};
Mat<Num, H, W> a(*this);
REP(i, 0, H) ret[i][i] = 1;
while (n) {
if (n & 1) ret = (a * ret).norm();
a = (a * a).norm(), n >>= 1;
}
return ret;
}
template <class... T> Mat<Num, H, W> assign(T... nums) {
vc<Num> num_list = vc<Num>{nums...};
assert(SIZE(num_list) == H * W);
REP(i, 0, H) REP(j, 0, W)(*this)[i][j] = num_list[W * i + j];
return *this;
}
void fill(Num num) { REP(i, 0, H) REP(j, 0, W)(*this)[i][j] = num; }
void print() { REP(i, 0, H) REP(j, 0, W) cout << (*this)[i][j] << (j == W - 1 ? '\n' : ' '); }
void dump_col(ll j) { REP(i, 0, H) cout << (*this)[i][j] << (i == H - 1 ? '\n' : ' '); }
};
/* #endregion */
// Problem
void solve() {
using mat = Mat<ll, 2, 2>;
array<array<ll, 2>, 2> m, mp;
cin >> m, mp;
const mat M = m;
const mat MP = mp;
const mat ans = M * MP * M * MP;
pprint(ans[0][0], ans[0][1]);
pprint(ans[1][0], ans[1][1]);
}
// entry point
int main() {
solve();
return 0;
}