結果
| 問題 | No.1907 DETERMINATION |
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2022-02-01 02:14:05 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 10,193 bytes |
| 記録 | |
| コンパイル時間 | 1,513 ms |
| コンパイル使用メモリ | 109,684 KB |
| 実行使用メモリ | 5,760 KB |
| 最終ジャッジ日時 | 2024-12-24 12:20:49 |
| 合計ジャッジ時間 | 89,953 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 49 WA * 14 |
ソースコード
// 任意 mod での実行時間検討
#include <cassert>
#include <iostream>
#include <set>
#include <utility>
#include <vector>
using namespace std;
struct ModIntRuntime {
private:
static int md;
public:
using lint = long long;
static int mod() { return md; }
int val;
static std::vector<ModIntRuntime> &facs() {
static std::vector<ModIntRuntime> facs_;
return facs_;
}
static int &get_primitive_root() {
static int primitive_root_ = 0;
if (!primitive_root_) {
primitive_root_ = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModIntRuntime(g).power((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root_;
}
static void set_mod(const int &m) {
if (md != m) facs().clear();
md = m;
get_primitive_root() = 0;
}
ModIntRuntime &_setval(lint v) {
val = (v >= md ? v - md : v);
return *this;
}
ModIntRuntime() : val(0) {}
ModIntRuntime(lint v) { _setval(v % md + md); }
explicit operator bool() const { return val != 0; }
ModIntRuntime operator+(const ModIntRuntime &x) const {
return ModIntRuntime()._setval((lint)val + x.val);
}
ModIntRuntime operator-(const ModIntRuntime &x) const {
return ModIntRuntime()._setval((lint)val - x.val + md);
}
ModIntRuntime operator*(const ModIntRuntime &x) const {
return ModIntRuntime()._setval((lint)val * x.val % md);
}
ModIntRuntime operator/(const ModIntRuntime &x) const {
return ModIntRuntime()._setval((lint)val * x.inv() % md);
}
ModIntRuntime operator-() const { return ModIntRuntime()._setval(md - val); }
ModIntRuntime &operator+=(const ModIntRuntime &x) { return *this = *this + x; }
ModIntRuntime &operator-=(const ModIntRuntime &x) { return *this = *this - x; }
ModIntRuntime &operator*=(const ModIntRuntime &x) { return *this = *this * x; }
ModIntRuntime &operator/=(const ModIntRuntime &x) { return *this = *this / x; }
friend ModIntRuntime operator+(lint a, const ModIntRuntime &x) {
return ModIntRuntime()._setval(a % md + x.val);
}
friend ModIntRuntime operator-(lint a, const ModIntRuntime &x) {
return ModIntRuntime()._setval(a % md - x.val + md);
}
friend ModIntRuntime operator*(lint a, const ModIntRuntime &x) {
return ModIntRuntime()._setval(a % md * x.val % md);
}
friend ModIntRuntime operator/(lint a, const ModIntRuntime &x) {
return ModIntRuntime()._setval(a % md * x.inv() % md);
}
bool operator==(const ModIntRuntime &x) const { return val == x.val; }
bool operator!=(const ModIntRuntime &x) const { return val != x.val; }
bool operator<(const ModIntRuntime &x) const {
return val < x.val;
} // To use std::map<ModIntRuntime, T>
friend std::istream &operator>>(std::istream &is, ModIntRuntime &x) {
lint t;
return is >> t, x = ModIntRuntime(t), is;
}
friend std::ostream &operator<<(std::ostream &os, const ModIntRuntime &x) {
return os << x.val;
}
lint power(lint n) const {
lint ans = 1, tmp = this->val;
while (n) {
if (n & 1) ans = ans * tmp % md;
tmp = tmp * tmp % md;
n /= 2;
}
return ans;
}
ModIntRuntime pow(lint n) const { return power(n); }
lint inv() const { return this->power(md - 2); }
ModIntRuntime fac() const {
int l0 = facs().size();
if (l0 > this->val) return facs()[this->val];
facs().resize(this->val + 1);
for (int i = l0; i <= this->val; i++)
facs()[i] = (i == 0 ? ModIntRuntime(1) : facs()[i - 1] * ModIntRuntime(i));
return facs()[this->val];
}
ModIntRuntime doublefac() const {
lint k = (this->val + 1) / 2;
return (this->val & 1)
? ModIntRuntime(k * 2).fac() / (ModIntRuntime(2).pow(k) * ModIntRuntime(k).fac())
: ModIntRuntime(k).fac() * ModIntRuntime(2).pow(k);
}
ModIntRuntime nCr(const ModIntRuntime &r) const {
return (this->val < r.val) ? ModIntRuntime(0) : this->fac() / ((*this - r).fac() * r.fac());
}
ModIntRuntime sqrt() const {
if (val == 0) return 0;
if (md == 2) return val;
if (power((md - 1) / 2) != 1) return 0;
ModIntRuntime b = 1;
while (b.power((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModIntRuntime x = power((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModIntRuntime z = b.power(m);
while (y != 1) {
int j = 0;
ModIntRuntime t = y;
while (t != 1) j++, t *= t;
z = z.power(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModIntRuntime(std::min(x.val, md - x.val));
}
};
int ModIntRuntime::md = 1;
using mint = ModIntRuntime;
// Upper Hessenberg reduction of square matrices
// Complexity: O(n^3)
// Reference:
// http://www.phys.uri.edu/nigh/NumRec/bookfpdf/f11-5.pdf
template <class Tp> void hessenberg_reduction(std::vector<std::vector<Tp>> &M) {
assert(M.size() == M[0].size());
const int N = M.size();
for (int r = 0; r < N - 2; r++) {
int piv = -1;
for (int h = r + 1; h < N; ++h) {
if (M[h][r] != 0) {
piv = h;
break;
}
}
if (piv < 0) continue;
for (int i = 0; i < N; i++) std::swap(M[r + 1][i], M[piv][i]);
for (int i = 0; i < N; i++) std::swap(M[i][r + 1], M[i][piv]);
const auto rinv = Tp(1) / M[r + 1][r];
for (int i = r + 2; i < N; i++) {
const auto n = M[i][r] * rinv;
for (int j = 0; j < N; j++) M[i][j] -= M[r + 1][j] * n;
for (int j = 0; j < N; j++) M[j][r + 1] += M[j][i] * n;
}
}
}
// Characteristic polynomial of matrix M (|xI - M|)
// Complexity: O(n^3)
// R. Rehman, I. C. Ipsen, "La Budde's Method for Computing Characteristic Polynomials," 2011.
template <class Tp> std::vector<Tp> characteristic_poly(std::vector<std::vector<Tp>> M) {
hessenberg_reduction(M);
const int N = M.size();
// p[i + 1] = (Characteristic polynomial of i-th leading principal minor)
std::vector<std::vector<Tp>> p(N + 1);
p[0] = {1};
for (int i = 0; i < N; i++) {
p[i + 1].assign(i + 2, 0);
for (int j = 0; j < i + 1; j++) p[i + 1][j + 1] += p[i][j];
for (int j = 0; j < i + 1; j++) p[i + 1][j] -= p[i][j] * M[i][i];
Tp betas = 1;
for (int j = i - 1; j >= 0; j--) {
betas *= M[j + 1][j];
Tp hb = -M[j][i] * betas;
for (int k = 0; k < j + 1; k++) p[i + 1][k] += hb * p[j][k];
}
}
return p[N];
}
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
mint::set_mod(998244353);
int N;
cin >> N;
vector M0(N, vector<mint>(N)), M1(N, vector<mint>(N));
for (auto &vec : M0) {
for (auto &x : vec) {
int v;
cin >> v;
x = v;
}
}
for (auto &vec : M1) {
for (auto &x : vec) {
int v;
cin >> v;
x = v;
}
}
int multiply_by_x = 0; // 基本変形の最中に M0 + M1x に x をかけた回数
mint detAdetBinv = 1;
for (int p = 0; p < N; ++p) {
// M1[p][p] に nonzero を持ってきて、M1 の第 p 行と第 p 列を全て掃き出す
int piv = -1;
for (int r = p; r < N; ++r) {
if (M1[r][p] != 0) {
piv = r;
break;
}
}
if (piv < 0) {
++multiply_by_x;
if (multiply_by_x > N) break;
for (int i = 0; i < N; ++i) {
swap(M1[i][p], M0[i][p]);
}
--p;
continue;
}
if (piv != p) {
M1[piv].swap(M1[p]);
M0[piv].swap(M0[p]);
detAdetBinv *= -1;
}
mint v = M1[p][p], vinv = v.inv();
detAdetBinv *= v;
// p 行目を定数倍して M1[p][p] == 1 にする
for (int j = 0; j < N; ++j) {
M0[p][j] *= vinv;
M1[p][j] *= vinv;
}
assert(M1[p][p] == 1);
// p 行目を使用して M1 の p 列目を p 行目以外ゼロにする
for (int r = 0; r < N; ++r) {
if (r == p) continue;
if (M1[r][p] != 0) {
auto v = M1[r][p];
for (int j = 0; j < N; ++j) {
M0[r][j] -= M0[p][j] * v;
M1[r][j] -= M1[p][j] * v;
}
}
}
// p 列目を使用して M1 の p 行目を p 列目以外ゼロにする
for (int j = p + 1; j < N; ++j) {
if (M1[p][j] != 0) {
auto v = M1[p][j];
for (int r = 0; r < N; ++r) {
M0[r][j] -= M0[r][p] * v;
M1[r][j] -= M1[r][p] * v;
}
}
}
}
if (multiply_by_x > N) {
// 行列式がゼロであることが確定
for (int i = 0; i <= N; ++i) cout << 0 << '\n';
return 0;
}
// この時点で M1 = I なので det(x + M0) を求める
for (auto &vec : M0) {
for (auto &x : vec) x = -x;
}
auto poly = characteristic_poly(M0);
for (auto &x : poly) x *= detAdetBinv;
for (int i = 0; i < multiply_by_x; ++i) poly.erase(poly.begin());
poly.resize(N + 1);
for (auto a : poly) cout << a << '\n';
}