結果
| 問題 |
No.1907 DETERMINATION
|
| コンテスト | |
| ユーザー |
 flself
|
| 提出日時 | 2023-10-09 00:16:37 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 712 ms / 4,000 ms |
| コード長 | 11,598 bytes |
| コンパイル時間 | 5,978 ms |
| コンパイル使用メモリ | 326,436 KB |
| 実行使用メモリ | 7,296 KB |
| 最終ジャッジ日時 | 2024-07-26 18:17:07 |
| 合計ジャッジ時間 | 30,572 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| 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(...)
#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>;
#include "atcoder/all"
using Z = atcoder::modint998244353;
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] != T{}) {
// 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) {
int x;
std::cin >> x;
D2[i][j] = x;
}
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
int x;
std::cin >> x;
D1[i][j] = x;
}
}
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].val() << '\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;
}