結果
問題 | No.1907 DETERMINATION |
ユーザー |
|
提出日時 | 2023-10-09 00:08:11 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,829 ms / 4,000 ms |
コード長 | 18,169 bytes |
コンパイル時間 | 3,640 ms |
コンパイル使用メモリ | 272,116 KB |
実行使用メモリ | 7,168 KB |
最終ジャッジ日時 | 2024-07-26 18:16:36 |
合計ジャッジ時間 | 58,777 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
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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
#include<bits/stdc++.h>#ifdef LOCAL#include "debugger.hpp"#else#define dbg(...)#endifusing i64 = long long;template<class T>constexpr T power(T a, i64 b) {T res = 1;for (; b; b /= 2, a *= a) {if (b % 2) {res *= a;}}return res;}constexpr i64 mul(i64 a, i64 b, i64 p) {i64 res = a * b - i64(1.L * a * b / p) * p;res %= p;if (res < 0) {res += p;}return res;}template<i64 P>struct MLong {i64 x;constexpr MLong() : x{} {}constexpr MLong(i64 x) : x{norm(x % getMod())} {}static i64 Mod;constexpr static i64 getMod() {if (P > 0) {return P;} else {return Mod;}}constexpr static int getRoot() {if (getMod() == 1231453023109121) return 3;assert(false);}constexpr static void setMod(i64 Mod_) {Mod = Mod_;}constexpr i64 norm(i64 x) const {if (x < 0) {x += getMod();}if (x >= getMod()) {x -= getMod();}return x;}constexpr i64 val() const { return x; }explicit constexpr operator i64() const { return x; }explicit constexpr operator bool() const { return x != 0;}constexpr MLong operator-() const { MLong res; res.x = norm(getMod() - x); return res; }constexpr MLong inv() const {i64 a = getMod(), b = x;i64 y = 0, z = 1;for (; b; ) {i64 k = a / b;std::swap(a -= k * b, b);std::swap(y -= k * z, z);}assert(a == 1);return MLong(y);}constexpr MLong &operator*=(MLong rhs) & { x = mul(x, rhs.x, getMod()); return *this; }constexpr MLong &operator+=(MLong rhs) & { x = norm(x + rhs.x); return *this; }constexpr MLong &operator-=(MLong rhs) & { x = norm(x - rhs.x); return *this; }constexpr MLong &operator/=(MLong rhs) & { return *this *= rhs.inv(); }friend constexpr MLong operator*(MLong lhs, MLong rhs) { MLong res = lhs; res *= rhs; return res; }friend constexpr MLong operator+(MLong lhs, MLong rhs) { MLong res = lhs; res += rhs; return res; }friend constexpr MLong operator-(MLong lhs, MLong rhs) { MLong res = lhs; res -= rhs; return res; }friend constexpr MLong operator/(MLong lhs, MLong rhs) { MLong res = lhs; res /= rhs; return res; }friend constexpr std::istream &operator>>(std::istream &is, MLong &a) { i64 v; is >> v; a = MLong(v); return is; }friend constexpr std::ostream &operator<<(std::ostream &os, const MLong &a) { return os << a.val(); }friend constexpr bool operator==(MLong lhs, MLong rhs) { return lhs.val() == rhs.val(); }friend constexpr bool operator!=(MLong lhs, MLong rhs) { return lhs.val() != rhs.val(); }};template<>i64 MLong<0LL>::Mod = i64(1E18) + 9;template<int P>struct MInt {int x;constexpr MInt() : x{} {}constexpr MInt(i64 x) : x{norm(x % getMod())} {}static int Mod;constexpr static int getMod() {if (P > 0) {return P;} else {return Mod;}}constexpr static int getRoot() {if (getMod() == 998244353) return 3;assert(false);}constexpr static void setMod(int Mod_) { Mod = Mod_; }constexpr int norm(int x) const {if (x < 0) {x += getMod();}if (x >= getMod()) {x -= getMod();}return x;}constexpr int val() const { return x; }explicit operator MLong<P>() const { return MLong<P>(x); }explicit constexpr operator int() const { return x; }explicit constexpr operator bool() const { return x != 0;}constexpr MInt operator-() const { MInt res; res.x = norm(getMod() - x); return res; }constexpr MInt inv() const {unsigned a = getMod(), b = x;int y = 0, z = 1;for (; b; ) {int k = a / b;std::swap(a -= k * b, b);std::swap(y -= k * z, z);}assert(a == 1U);return MInt(y);}constexpr MInt &operator*=(MInt rhs) & { x = 1LL * x * rhs.x % getMod(); return *this; }constexpr MInt &operator+=(MInt rhs) & { x = norm(x + rhs.x); return *this; }constexpr MInt &operator-=(MInt rhs) & { x = norm(x - rhs.x); return *this; }constexpr MInt &operator/=(MInt rhs) & { return *this *= rhs.inv(); }friend constexpr MInt operator*(MInt lhs, MInt rhs) { MInt res = lhs; res *= rhs; return res; }friend constexpr MInt operator+(MInt lhs, MInt rhs) { MInt res = lhs; res += rhs; return res; }friend constexpr MInt operator-(MInt lhs, MInt rhs) { MInt res = lhs; res -= rhs; return res; }friend constexpr MInt operator/(MInt lhs, MInt rhs) { MInt res = lhs; res /= rhs; return res; }friend constexpr std::istream &operator>>(std::istream &is, MInt &a) { i64 v; is >> v; a = MInt(v); return is; }friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) { return os << a.val(); }friend constexpr bool operator==(MInt lhs, MInt rhs) { return lhs.val() == rhs.val(); }friend constexpr bool operator!=(MInt lhs, MInt rhs) { return lhs.val() != rhs.val(); }};template<>int MInt<0>::Mod = 998244353;template<int V, int P>constexpr MInt<P> CInv = MInt<P>(V).inv();constexpr int P = 998244353;using Z = MInt<P>;std::vector<int> rev;std::vector<Z> roots{0, 1};void dft(std::vector<Z> &a) {int n = a.size();if ((int)(rev.size()) != n) {int k = __builtin_ctz(n) - 1;rev.resize(n);for (int i = 0; i < n; i++) {rev[i] = rev[i >> 1] >> 1 | (i & 1) << k;}}for (int i = 0; i < n; i++) {if (rev[i] < i) {std::swap(a[i], a[rev[i]]);}}if ((int)(roots.size()) < n) {int k = __builtin_ctz(roots.size());roots.resize(n);while ((1 << k) < n) {Z e = power(Z(Z::getRoot()), (Z::getMod() - 1) >> (k + 1));for (int i = 1 << (k - 1); i < (1 << k); i++) {roots[2 * i] = roots[i];roots[2 * i + 1] = roots[i] * e;}k++;}}for (int k = 1; k < n; k *= 2) {for (int i = 0; i < n; i += 2 * k) {for (int j = 0; j < k; j++) {Z u = a[i + j];Z v = a[i + j + k] * roots[k + j];a[i + j] = u + v;a[i + j + k] = u - v;}}}}void idft(std::vector<Z> &a) {int n = a.size();std::reverse(a.begin() + 1, a.end());dft(a);Z inv = (1 - Z::getMod()) / n;for (int i = 0; i < n; i++) {a[i] *= inv;}}template<typename T>struct Poly {std::vector<T> a;Poly() {}Poly(const std::vector<T> &a) : a(a) {}Poly(const std::initializer_list<T> &a) : a(a) {}int size() const {return a.size();}void resize(int n) {a.resize(n);}T operator[](int idx) const {if (idx < size()) {return a[idx];} else {return 0;}}T &operator[](int idx) {return a[idx];}Poly mulxk(int k) const {auto b = a;b.insert(b.begin(), k, 0);return Poly(b);}Poly modxk(int k) const {k = std::min(k, size());return Poly(std::vector<T>(a.begin(), a.begin() + k));}Poly divxk(int k) const {if (size() <= k) {return Poly();}return Poly(std::vector<T>(a.begin() + k, a.end()));}friend Poly operator+(const Poly &a, const Poly &b) {std::vector<T> res(std::max(a.size(), b.size()));for (int i = 0; i < (int)(res.size()); i++) {res[i] = a[i] + b[i];}return Poly(res);}friend Poly operator-(const Poly &a, const Poly &b) {std::vector<T> res(std::max(a.size(), b.size()));for (int i = 0; i < (int)(res.size()); i++) {res[i] = a[i] - b[i];}return Poly(res);}friend Poly operator*(Poly a, Poly b) {if (a.size() == 0 || b.size() == 0) {return Poly();}int sz = 1, tot = a.size() + b.size() - 1;while (sz < tot) {sz *= 2;}a.a.resize(sz);b.a.resize(sz);dft(a.a);dft(b.a);for (int i = 0; i < sz; ++i) {a.a[i] = a[i] * b[i];}idft(a.a);a.resize(tot);return a;}friend Poly operator*(T a, Poly b) {for (int i = 0; i < (int)(b.size()); i++) {b[i] *= a;}return b;}friend Poly operator*(Poly a, T b) {for (int i = 0; i < (int)(a.size()); i++) {a[i] *= b;}return a;}Poly &operator+=(Poly b) {return (*this) = (*this) + b;}Poly &operator-=(Poly b) {return (*this) = (*this) - b;}Poly &operator*=(Poly b) {return (*this) = (*this) * b;}Poly deriv() const {if (a.empty()) {return Poly();}std::vector<T> res(size() - 1);for (int i = 0; i < size() - 1; ++i) {res[i] = (i + 1) * a[i + 1];}return Poly(res);}Poly integr() const {std::vector<T> res(size() + 1);for (int i = 0; i < size(); ++i) {res[i + 1] = a[i] / (i + 1);}return Poly(res);}Poly inv(int m) const {Poly x{a[0].inv()};int k = 1;while (k < m) {k *= 2;x = (x * (Poly{2} - modxk(k) * x)).modxk(k);}return x.modxk(m);}Poly log(int m) const {return (deriv() * inv(m)).integr().modxk(m);}Poly exp(int m) const {Poly x{1};int k = 1;while (k < m) {k *= 2;x = (x * (Poly{1} - x.log(k) + modxk(k))).modxk(k);}return x.modxk(m);}Poly pow(int k, int m) const {int i = 0;while (i < size() && a[i].val() == 0) {i++;}if (i == size() || 1LL * i * k >= m) {return Poly(std::vector<T>(m));}T v = a[i];auto f = divxk(i) * v.inv();return (f.log(m - i * k) * k).exp(m - i * k).mulxk(i * k) * power(v, k);}Poly sqrt(int m) const {Poly x{1};int k = 1;while (k < m) {k *= 2;x = (x + (modxk(k) * x.inv(k)).modxk(k)) * ((T::getMod() + 1) / 2);}return x.modxk(m);}Poly mulT(Poly b) const {if (b.size() == 0) {return Poly();}int n = b.size();std::reverse(b.a.begin(), b.a.end());return ((*this) * b).divxk(n - 1);}std::vector<T> eval(std::vector<T> x) const {if (size() == 0) {return std::vector<T>(x.size(), 0);}const int n = std::max((int)(x.size()), size());std::vector<Poly> q(4 * n);std::vector<T> ans(x.size());x.resize(n);std::function<void(int, int, int)> build = [&](int p, int l, int r) {if (r - l == 1) {q[p] = Poly{1, -x[l]};} else {int m = (l + r) / 2;build(2 * p, l, m);build(2 * p + 1, m, r);q[p] = q[2 * p] * q[2 * p + 1];}};build(1, 0, n);std::function<void(int, int, int, const Poly &)> work = [&](int p, int l, int r, const Poly &num) {if (r - l == 1) {if (l < (int)(ans.size())) {ans[l] = num[0];}} else {int m = (l + r) / 2;work(2 * p, l, m, num.mulT(q[2 * p + 1]).modxk(m - l));work(2 * p + 1, m, r, num.mulT(q[2 * p]).modxk(r - m));}};work(1, 0, n, mulT(q[1].inv(n)));return ans;}};template<typename T>T count_minor(const std::vector<std::vector<int>> matrix, int idx = 0, int idy = 0) {assert(matrix.size() == matrix[0].size());int n = matrix.size();assert(idx < n && idy < n);if (n == 1) {return 0;}std::vector minor(n-1, std::vector<T>(n-1));for (int i = 0; i < n; ++i) {if (i == idx) continue;for (int j = 0; j < n; ++j) {if (j == idy) continue;minor[i - (i > idx)][j - (j > idy)] = matrix[i][j];}}n--;auto gauss=[&]()->T {for (int i = 0; i < n; ++i) {if (minor[i][i] == 0) {for (int j = i + 1; j < n; ++j) {if (minor[j][i]) {// for (int k = 0; k < n; ++k) {// std::swap(minor[i][k], minor[j][k]);// }std::swap(minor[i], minor[j]);break;}}}if (minor[i][i] == 0) {return 0;}for (int j = i + 1; j < n; ++j) {if (i == j) continue;T mul = minor[j][i] / minor[i][i];for (int k = i; k < n; ++k) {minor[j][k] -= mul * minor[i][k];}}}T res = 1;for (int i = 0; i < n; ++i) {res *= minor[i][i];}return res;};return gauss();}// KirchhoffZ Kirchhoff(const std::vector<std::vector<int>> &G) {int n = G.size();std::vector<std::vector<int>> L(n, std::vector<int>(n));for (int i = 0; i < n; ++i) {L[i][i] = G[i].size();for (auto &j : G[i]) {L[i][j]--;}}return count_minor<Z>(L);}/// @param A square matrix of size n/// @return characteristic polynomial of A, which is `det(xI - M)`template <typename T>std::vector<T> char_poly(std::vector<std::vector<T>> M) {int N = M.size();assert(N == M[0].size());// Hessenberg Reductionfor (int i = 0; i < N - 2; i++) {int p = -1;for (int j = i + 1; j < N; j++) {if (M[j][i] != T(0)) {p = j;break;}}if (p == -1) {continue;}M[i + 1].swap(M[p]);for (int j = 0; j < N; j++) {std::swap(M[j][i + 1], M[j][p]);}T r = T(1) / M[i + 1][i];for (int j = i + 2; j < N; j++) {T c = M[j][i] * r;for (int k = 0; k < N; k++) M[j][k] -= M[i + 1][k] * c;for (int k = 0; k < N; k++) M[k][i + 1] += M[k][j] * c;}}// La Budde's Methodstd::vector<std::vector<T>> P = {{T(1)}};for (int i = 0; i < N; i++) {std::vector<T> f(i + 2, 0);for (int j = 0; j <= i; j++) f[j + 1] += P[i][j];for (int j = 0; j <= i; j++) f[j] -= P[i][j] * M[i][i];T b = 1;for (int j = i - 1; j >= 0; j--) {b *= M[j + 1][j];T h = -M[j][i] * b;for (int k = 0; k <= j; k++) f[k] += h * P[j][k];}P.push_back(f);}return P.back();}/// @brief calculate `det(Ax + B)`, where A and B are square matrices of size n/// @tparam T usually Z/// @tparam Matrix usually std::vector<std::vector<T>>, or custom matrix class/// @param A/// @param B/// @return `det(Ax + B)`template <typename T>std::vector<T> det_linear(std::vector<std::vector<T>> A, std::vector<std::vector<T>> B) {int N = A.size(), nu = 0;T det = 1;for (int i = 0; i < N; i++) {// do normal gaussian eliminationint p = -1;for (int j = i; j < N; j++) {if (A[j][i] != T(0)) {p = j;break;}}// replace B with Aif (p == -1) {// Increase nullity by 1if (++nu > N) {return std::vector<T>(N + 1, 0);}// i-th column is emptyfor (int j = 0; j < i; j++) {for (int k = 0; k < N; k++) {B[k][i] -= B[k][j] * A[j][i];}A[j][i] = 0;}for (int j = 0; j < N; j++) {std::swap(A[j][i], B[j][i]);}// retry--i;continue;}if (p != i) {A[i].swap(A[p]);B[i].swap(B[p]);det = -det;}det *= A[i][i];T c = T(1) / A[i][i];for (int j = 0; j < N; j++) {A[i][j] *= c, B[i][j] *= c;}for (int j = 0; j < N; j++) {if (j != i) {T c = A[j][i];for (int k = 0; k < N; k++) {A[j][k] -= A[i][k] * c, B[j][k] -= B[i][k] * c;}}}}for (auto &y : B) {for (T &x : y) {x = -x;}}auto f = char_poly(B);for (T &x : f) {x *= det;}f.erase(f.begin(), f.begin() + nu);f.resize(N + 1);return f;}void solv() {int n;std::cin >> n;std::vector<std::vector<Z>> D1(n, std::vector<Z>(n));auto D2 = D1;for (int i = 0; i < n; ++i) {for (int j = 0; j < n; ++j) {std::cin >> D2[i][j];}}for (int i = 0; i < n; ++i) {for (int j = 0; j < n; ++j) {std::cin >> D1[i][j];}}auto poly = det_linear(D1, D2);for (int i = 0; i <= n; ++i) {if (i >= poly.size()) {std::cout << "0\n";} else {std::cout << poly[i] << '\n';}}}signed main() {std::ios::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr);int tt = 1;// std::cin >> tt;while (tt--) {solv();}return 0;}