結果

問題 No.1907 DETERMINATION
ユーザー flselfflself
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
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 4
other AC * 63
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

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
#ifdef LOCAL
#include "debugger.hpp"
#else
#define dbg(...)
#endif
using 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();
}
// Kirchhoff
Z 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 Reduction
for (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 Method
std::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 elimination
int p = -1;
for (int j = i; j < N; j++) {
if (A[j][i] != T(0)) {
p = j;
break;
}
}
// replace B with A
if (p == -1) {
// Increase nullity by 1
if (++nu > N) {
return std::vector<T>(N + 1, 0);
}
// i-th column is empty
for (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;
}
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