結果
問題 |
No.1907 DETERMINATION
|
ユーザー |
![]() |
提出日時 | 2025-08-31 06:08:59 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 543 ms / 4,000 ms |
コード長 | 25,184 bytes |
コンパイル時間 | 3,700 ms |
コンパイル使用メモリ | 341,364 KB |
実行使用メモリ | 7,720 KB |
最終ジャッジ日時 | 2025-08-31 06:09:26 |
合計ジャッジ時間 | 25,591 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 63 |
ソースコード
// Begin include: "../../template/template.hpp" using namespace std; // intrinstic #include <immintrin.h> #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <cctype> #include <cfenv> #include <cfloat> #include <chrono> #include <cinttypes> #include <climits> #include <cmath> #include <complex> #include <cstdarg> #include <cstddef> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <fstream> #include <functional> #include <initializer_list> #include <iomanip> #include <ios> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <streambuf> #include <string> #include <tuple> #include <type_traits> #include <typeinfo> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> // utility // Begin include: "util.hpp" namespace yamada { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; using lld = long double; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; template <typename T> using VVV = vector<vector<vector<T>>>; template <typename T> using VVVV = vector<vector<vector<vector<T>>>>; using vi = vector<int>; using vl = vector<long long>; using vd = V<double>; using vs = V<string>; using vvi = vector<vector<int>>; using vvl = vector<vector<long long>>; using vvvl = vector<vector<vector<long long>>>; using vvvvl = vector<vector<vector<vector<long long>>>>; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <typename T> using maxpq = priority_queue<T, vector<T>, less<T>>; template <typename T, typename U> struct P : pair<T, U> { template <typename... Args> P(Args... args) : pair<T, U>(args...) {} using pair<T, U>::first; using pair<T, U>::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template <typename S> P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template <typename S> P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P<ll, ll>; using pi = P<int, int>; using vp = V<pl>; using vvp = VV<pl>; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template <typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template <typename T> inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); } template <typename T> inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); } template <typename T> inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), T(0)); } template <typename T> int lb(const vector<T> &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template <typename T> int ub(const vector<T> &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template <typename T, typename U> pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); } template <typename T> vector<T> mkrui(const vector<T> &v, bool rev = false) { vector<T> ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template <typename T> vector<T> mkuni(const vector<T> &v) { vector<T> ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template <typename F> vector<int> mkord(int N, F f) { vector<int> ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template <typename T> vector<int> mkinv(vector<T> &v) { int max_val = *max_element(begin(v), end(v)); vector<int> inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector<int> mkiota(int n) { vector<int> ret(n); iota(begin(ret), end(ret), 0); return ret; } template <typename T> T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template <typename T> bool nxp(T &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template <typename T> vector<vector<T>> product(const vector<T> &a) { vector<vector<T>> ret; vector<T> v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } template <typename T, typename U> vector<U> Digit(T a, const U &x, int siz = -1) { vector<U> ret; while (a > 0) { ret.emplace_back(a % x); a /= x; } if (siz >= 0) while (ret.size() < siz) ret.emplace_back(0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I, const function<void(T &)> &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I = T{1}) { return Power(a, n, I, function<void(T &)>{[](T &) -> void {}}); } template <typename T> T Rev(const T &v) { T res = v; reverse(begin(res), end(res)); return res; } template <typename T> vector<T> Transpose(const vector<T> &v) { using U = typename T::value_type; if(v.empty()) return {}; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { res[j][i] = v[i][j]; } } return res; } template <typename T> vector<T> Rotate(const vector<T> &v, int clockwise = true) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { if (clockwise) { res[W - 1 - j][i] = v[i][j]; } else { res[j][H - 1 - i] = v[i][j]; } } } return res; } template <typename T, typename F> T bisect(T ok, T bad, F pred) { if (ok == bad) return ok; if (!pred(ok)) return ok; while (bad - ok > 1) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } return bad; } template <typename T, typename F> T bisect_double(T ok, T bad, F pred, int iter = 100) { if (ok == bad) return ok; if (!pred(ok)) return ok; for (int i = 0; i < iter; i++){ T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } return bad; } template <typename T> bool inLR(T L, T x, T R){ return (L <= x && x < R); } bool YESNO(bool b) { cout << (b ? "YES\n" : "NO\n"); return b; } bool YesNo(bool b) { cout << (b ? "Yes\n" : "No\n"); return b; } template <typename mint> void mout(mint a, int M = 100) { if (a == 0) { cout << 0 << "\n"; return; } for (int i = 0; i <= M; i++) for (int j = 1; j <= M; j++) { mint val = (mint)i / j; if (val == a) { if (j == 1) cout << i << "\n"; else cout << i << "/" << j << "\n"; return; } else if (val == -a) { if (j == 1) cout << -i << "\n"; else cout << -i << "/" << j << "\n"; return; } } cout << "NF\n"; } template <typename mint> void mout(std::vector<mint> A, int M = 100) { int N = A.size(); for (int pos = 0; pos < N; pos++) { if (A[pos] == 0) { cout << 0 << (pos == N - 1 ? "\n" : " "); continue; } bool fn = false; for (int i = 0; i <= M; i++) { for (int j = 1; j <= M; j++) { mint val = (mint)i / j; if (val == A[pos]) { if (j == 1) cout << i << (pos == N - 1 ? "\n" : " "); else cout << i << "/" << j << (pos == N - 1 ? "\n" : " "); fn = true; break; } else if (val == -A[pos]) { if (j == 1) cout << -i << (pos == N - 1 ? "\n" : " "); else cout << -i << "/" << j << (pos == N - 1 ? "\n" : " "); fn = true; break; } } if (fn) break; } if (!fn) cout << "NF" << (pos == N - 1 ? "\n" : " "); } } bool is_square(uint64_t n) { if (n < 2) return true; uint64_t r = static_cast<uint64_t>(sqrtl(static_cast<long double>(n))); if (r * r == n) return true; ++r; return r * r == n; } } // namespace yamada // End include: "util.hpp" // bit operation // Begin include: "bitop.hpp" namespace yamada { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return __builtin_popcountll(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template <typename T> inline int gbit(const T &a, int i) { return (a >> i) & 1; } template <typename T> inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace yamada // End include: "bitop.hpp" // inout // Begin include: "inout.hpp" namespace yamada { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template <typename T, class... U> void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupYamada { IoSetupYamada() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupyamada; } // namespace yamada // End include: "inout.hpp" // macro // Begin include: "macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define each3(x, y, z, v) for (auto&& [x, y, z] : v) #define all(v) (v).begin(), (v).end() #define rep1(a) for (long long _ = 0; _ < (long long)(a); ++_) #define rep2(i, a) for (long long i = 0; i < (long long)(a); ++i) #define rep3(i, a, b) for (long long i = a; i < (long long)(b); ++i) #define rep4(i, a, b, c) for (long long i = a; i < (long long)(b); i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rep1r(a) for (long long i = (long long)(a)-1; i >= 0LL; --i) #define rep2r(i, a) for (long long i = (long long)(a)-1; i >= 0LL; --i) #define rep3r(i, a, b) for (long long i = (long long)(b)-1; i >= (long long)(a); --i) #define overload3(a, b, c, d, ...) d #define repr(...) overload3(__VA_ARGS__, rep3r, rep2r, rep1r)(__VA_ARGS__) #define eb emplace_back #define mkp make_pair #define mkt make_tuple #define fi first #define se second #define vv(type, name, h, ...) \ vector<vector<type> > name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector<vector<vector<type>>> name( \ h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name( \ a, vector<vector<vector<type>>>( \ b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ yamada::out(__VA_ARGS__);\ return; \ } while (0) // End include: "macro.hpp" namespace yamada { void solve(); } int main() { yamada::solve(); } // End include: "../../template/template.hpp" // Begin include: "../../matrix/first-degree-matrix-determinant.hpp" // Begin include: "characteristric-polynomial.hpp" // calculate det(a - xI) template <typename mint> vector<mint> CharacteristicPolynomial(vector<vector<mint>> a) { int N = a.size(); for (int j = 0; j < N - 2; j++) { for (int i = j + 1; i < N; i++) { if (a[i][j] != 0) { swap(a[j + 1], a[i]); for (int k = 0; k < N; k++) swap(a[k][j + 1], a[k][i]); break; } } if (a[j + 1][j] != 0) { mint inv = mint(1) / a[j + 1][j]; for (int i = j + 2; i < N; i++) { if (a[i][j] == 0) continue; mint coe = inv * a[i][j]; for (int l = j; l < N; l++) a[i][l] -= coe * a[j + 1][l]; for (int k = 0; k < N; k++) a[k][j + 1] += coe * a[k][i]; } } } vector<vector<mint>> p(N + 1); p[0] = {mint(1)}; for (int i = 1; i <= N; i++) { p[i].resize(i + 1); for (int j = 0; j < i; j++) { p[i][j + 1] -= p[i - 1][j]; p[i][j] += p[i - 1][j] * a[i - 1][i - 1]; } mint x = 1; for (int m = 1; m < i; m++) { x *= -a[i - m][i - m - 1]; mint coe = x * a[i - m - 1][i - 1]; for (int j = 0; j < i - m; j++) p[i][j] += coe * p[i - m - 1][j]; } } return p[N]; } // End include: "characteristric-polynomial.hpp" // det(M0 + xM1) template <typename mint> vector<mint> FirstDegreeMatrixDeterminant(vector<vector<mint>>& M0, vector<vector<mint>>& M1) { const int N = M0.size(); int multiply_by_x = 0; mint detAdetBinv = 1; for (int p = 0; p < N; ++p) { int pivot = -1; for (int r = p; r < N; ++r) if (M1[r][p] != mint()) { pivot = r; break; } if (pivot < 0) { ++multiply_by_x; if (multiply_by_x > N) return std::vector<mint>(N + 1); for (int r = 0; r < p; ++r) { mint v = M1[r][p]; M1[r][p] = 0; for (int i = 0; i < N; ++i) M0[i][p] -= v * M0[i][r]; } for (int i = 0; i < N; ++i) swap(M0[i][p], M1[i][p]); --p; continue; } if (pivot != p) { M1[pivot].swap(M1[p]); M0[pivot].swap(M0[p]); detAdetBinv *= -1; } mint v = M1[p][p], vinv = v.inverse(); detAdetBinv *= v; for (int c = 0; c < N; ++c) { M0[p][c] *= vinv; M1[p][c] *= vinv; } for (int r = 0; r < N; ++r) { if (r == p) continue; mint v = M1[r][p]; for (int c = 0; c < N; ++c) { M0[r][c] -= M0[p][c] * v; M1[r][c] -= M1[p][c] * v; } } } for (auto &vec : M0) for (auto &x : vec) x = -x; auto poly = CharacteristicPolynomial(M0); for (auto &x : poly) x *= detAdetBinv * (N % 2 ? -1 : 1); poly.erase(poly.begin(), poly.begin() + multiply_by_x); poly.resize(N + 1); return poly; } // End include: "../../matrix/first-degree-matrix-determinant.hpp" // Begin include: "../../modint/montgomery-modint.hpp" template <uint32_t mod> struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); static_assert(r * mod == 1, "this code has bugs."); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint operator+() const { return mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0; while (y > 0) { t = x / y; x -= t * y, u -= t * v; tmp = x, x = y, y = tmp; tmp = u, u = v, v = tmp; } return mint{u}; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt<mod>(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; // End include: "../../modint/montgomery-modint.hpp" // Begin include: "../../matrix/matrix.hpp" // Begin include: "inverse-matrix.hpp" // Begin include: "gauss-elimination.hpp" #include <utility> #include <vector> using namespace std; // {rank, det(非正方行列の場合は未定義)} を返す // 型が double や Rational でも動くはず?(未検証) // // pivot 候補 : [0, pivot_end) template <typename T> std::pair<int, T> GaussElimination(vector<vector<T>> &a, int pivot_end = -1, bool diagonalize = false) { if (a.empty()) return {0, 1}; int H = a.size(), W = a[0].size(), rank = 0; if (pivot_end == -1) pivot_end = W; T det = 1; for (int j = 0; j < pivot_end; j++) { int idx = -1; for (int i = rank; i < H; i++) { if (a[i][j] != T(0)) { idx = i; break; } } if (idx == -1) { det = 0; continue; } if (rank != idx) det = -det, swap(a[rank], a[idx]); det *= a[rank][j]; if (diagonalize && a[rank][j] != T(1)) { T coeff = T(1) / a[rank][j]; for (int k = j; k < W; k++) a[rank][k] *= coeff; } int is = diagonalize ? 0 : rank + 1; for (int i = is; i < H; i++) { if (i == rank) continue; if (a[i][j] != T(0)) { T coeff = a[i][j] / a[rank][j]; for (int k = j; k < W; k++) a[i][k] -= a[rank][k] * coeff; } } rank++; } return make_pair(rank, det); } // End include: "gauss-elimination.hpp" template <typename mint> vector<vector<mint>> inverse_matrix(const vector<vector<mint>>& a) { int N = a.size(); assert(N > 0); assert(N == (int)a[0].size()); vector<vector<mint>> m(N, vector<mint>(2 * N)); for (int i = 0; i < N; i++) { copy(begin(a[i]), end(a[i]), begin(m[i])); m[i][N + i] = 1; } auto [rank, det] = GaussElimination(m, N, true); if (rank != N) return {}; vector<vector<mint>> b(N); for (int i = 0; i < N; i++) { copy(begin(m[i]) + N, end(m[i]), back_inserter(b[i])); } return b; } // End include: "inverse-matrix.hpp" template <class T> struct Matrix { vector<vector<T> > A; Matrix() = default; Matrix(int n, int m) : A(n, vector<T>(m, T())) {} Matrix(int n) : A(n, vector<T>(n, T())){}; int H() const { return A.size(); } int W() const { return A[0].size(); } int size() const { return A.size(); } inline const vector<T> &operator[](int k) const { return A[k]; } inline vector<T> &operator[](int k) { return A[k]; } static Matrix I(int n) { Matrix mat(n); for (int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { int n = H(), m = W(); assert(n == B.H() && m == B.W()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { int n = H(), m = W(); assert(n == B.H() && m == B.W()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { int n = H(), m = B.W(), p = W(); assert(p == B.H()); vector<vector<T> > C(n, vector<T>(m, T{})); for (int i = 0; i < n; i++) for (int k = 0; k < p; k++) for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j]; A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(H()); while (k > 0) { if (k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } bool operator==(const Matrix &B) const { assert(H() == B.H() && W() == B.W()); for (int i = 0; i < H(); i++) for (int j = 0; j < W(); j++) if (A[i][j] != B[i][j]) return false; return true; } bool operator!=(const Matrix &B) const { assert(H() == B.H() && W() == B.W()); for (int i = 0; i < H(); i++) for (int j = 0; j < W(); j++) if (A[i][j] != B[i][j]) return true; return false; } Matrix inverse() const { assert(H() == W()); Matrix B(H()); B.A = inverse_matrix(A); return B; } Matrix transpose() const { Matrix B(W(), H()); for (int i = 0; i < W(); ++i) for (int j = 0; j < H(); ++j) B[i][j] = A[j][i]; return B; } friend ostream &operator<<(ostream &os, const Matrix &p) { int n = p.H(), m = p.W(); for (int i = 0; i < n; i++) { os << (i ? " " : "") << "["; for (int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() const { Matrix B(*this); assert(H() == W()); T ret = 1; for (int i = 0; i < H(); i++) { int idx = -1; for (int j = i; j < W(); 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 < W(); j++) { B[i][j] *= inv; } for (int j = i + 1; j < H(); j++) { T a = B[j][i]; if (a == 0) continue; for (int k = i; k < W(); k++) { B[j][k] -= B[i][k] * a; } } } return ret; } }; /** * @brief 行列ライブラリ */ // End include: "../../matrix/matrix.hpp" using mint = LazyMontgomeryModInt<998244353>; using mat = Matrix<mint>; void yamada::solve() { inl(N); vv(mint,A,N,N); vv(mint,B,N,N); in(A,B); auto ans=FirstDegreeMatrixDeterminant(A,B); each(a,ans)out(a); }