結果
| 問題 |
No.1907 DETERMINATION
|
| コンテスト | |
| ユーザー |
 rniya
|
| 提出日時 | 2022-04-16 17:50:44 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 664 ms / 4,000 ms |
| コード長 | 9,333 bytes |
| コンパイル時間 | 2,337 ms |
| コンパイル使用メモリ | 210,416 KB |
| 最終ジャッジ日時 | 2025-01-28 18:54:01 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（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
#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()
template <typename T> istream& operator>>(istream& is, vector<T>& v) {
for (T& x : v) is >> x;
return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
for (size_t i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 == v.size() ? "" : " ");
}
return os;
}
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> ostream& operator<<(ostream& os, const map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
for (size_t i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 == v.size() ? "" : " ");
}
return os;
}
template <typename T, size_t N> ostream& operator<<(ostream& os, const array<T, N>& v) {
for (size_t i = 0; i < N; i++) {
os << v[i] << (i + 1 == N ? "" : " ");
}
return os;
}
template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
if (i) os << ',';
os << get<i>(t);
print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
os << '{';
print_tuple<0, tuple<Args...>, Args...>(os, t);
return os << '}';
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
cerr << head;
if (sizeof...(Tail) > 0) cerr << ", ";
debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) \
cerr << " "; \
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
cerr << " "; \
debug_out(__VA_ARGS__)
#else
#define debug(...) void(0)
#endif
template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }
template <class T> T ceil(T x, T y) {
assert(y >= 1);
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
assert(y >= 1);
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <typename T> void mkuni(vector<T>& v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }
#pragma endregion
#include <iostream>
#include "atcoder/modint"
namespace atcoder {
template <int MOD> std::istream& operator>>(std::istream& is, static_modint<MOD>& x) {
int64_t v;
x = static_modint<MOD>{(is >> v, v)};
return is;
}
template <int MOD> std::ostream& operator<<(std::ostream& os, const static_modint<MOD>& x) { return os << x.val(); }
template <int ID> std::ostream& operator<<(std::ostream& os, const dynamic_modint<ID>& x) { return os << x.val(); }
} // namespace atcoder
#include <algorithm>
#include <cassert>
#include <vector>
template <typename T> std::vector<T> characteristic_polynomial(std::vector<std::vector<T>> M) {
assert(M.empty() or M.size() == M[0].size());
int n = M.size();
// reduce M to upper Hessenberg form
for (int j = 0; j < n - 2; j++) {
for (int i = j + 2; i < n; i++) {
if (M[i][j] != 0) {
std::swap(M[j + 1], M[i]);
for (int k = 0; k < n; k++) std::swap(M[k][j + 1], M[k][i]);
break;
}
}
if (M[j + 1][j] == 0) continue;
auto inv = T(1) / M[j + 1][j];
for (int i = j + 2; i < n; i++) {
auto coef = M[i][j] * inv;
for (int k = j; k < n; k++) M[i][k] -= coef * M[j + 1][k];
for (int k = 0; k < n; k++) M[k][j + 1] += coef * M[k][i];
}
}
// compute the characteristic polynomial of upper Hessenberg matrix M
std::vector<std::vector<T>> p(n + 1);
p[0] = {T(1)};
for (int i = 0; i < n; i++) {
p[i + 1].resize(i + 2);
for (int j = 0; j <= i; j++) {
p[i + 1][j + 1] += p[i][j];
p[i + 1][j] -= p[i][j] * M[i][i];
}
T betas = 1;
for (int j = i - 1; j >= 0; j--) {
betas *= M[j + 1][j];
T coef = -betas * M[j][i];
for (int k = 0; k <= j; k++) p[i + 1][k] += coef * p[j][k];
}
}
return p[n];
}
template <typename T>
std::vector<T> determinant_polynomial(std::vector<std::vector<T>> M0, std::vector<std::vector<T>> M1) {
assert(M0.size() == M1.size());
assert(M0.size() == M0[0].size());
assert(M1.size() == M1[0].size());
int n = M0.size(), off = 0;
T prod = 1;
for (int p = 0; p < n; p++) {
int pivot = -1;
for (int i = p; i < n; i++) {
if (M1[i][p] != 0) {
pivot = i;
break;
}
}
if (pivot == -1) {
if (++off > n) return std::vector<T>(n + 1, 0);
for (int i = 0; i < p; i++) {
for (int k = 0; k < n; k++) M0[k][p] -= M1[i][p] * M0[k][i];
M1[i][p] = 0;
}
for (int i = 0; i < n; i++) std::swap(M0[i][p], M1[i][p]);
p--;
continue;
}
if (pivot != p) {
std::swap(M0[p], M0[pivot]);
std::swap(M1[p], M1[pivot]);
prod *= -1;
}
prod *= M1[p][p];
auto inv = T(1) / M1[p][p];
for (int j = 0; j < n; j++) {
M0[p][j] *= inv;
M1[p][j] *= inv;
}
for (int i = 0; i < n; i++) {
if (i == p) continue;
auto coef = M1[i][p];
for (int j = 0; j < n; j++) {
M0[i][j] -= M0[p][j] * coef;
M1[i][j] -= M1[p][j] * coef;
}
}
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
M0[i][j] *= -1;
}
}
auto poly = characteristic_polynomial(M0);
std::vector<T> res(n + 1, 0);
for (int i = 0; i + off <= n; i++) res[i] = prod * poly[i + off];
return res;
}
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;
using mint = atcoder::modint998244353;
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
int N;
cin >> N;
vector<vector<mint>> M0(N, vector<mint>(N)), M1(N, vector<mint>(N));
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
cin >> M0[i][j];
}
}
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
cin >> M1[i][j];
}
}
auto ans = determinant_polynomial(M0, M1);
for (auto& x : ans) cout << x << '\n';
return 0;
}