結果

問題 No.1907 DETERMINATION
ユーザー 👑 NachiaNachia
提出日時 2023-10-07 22:58:53
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 778 ms / 4,000 ms
コード長 7,329 bytes
コンパイル時間 1,318 ms
コンパイル使用メモリ 93,136 KB
最終ジャッジ日時 2025-02-17 06:14:01
ジャッジサーバーID
(参考情報)
judge2 / judge3
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

#line 1 "..\\Main.cpp"
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <atcoder/modint>
#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\linear-modulo\\matrix-modulo.hpp"
#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\linear-modulo\\matrix-modulo.hpp"
#include <cassert>
#include <utility>
namespace nachia{
template<class Elem>
struct MatrixModulo{
private:
int h;
int w;
std::vector<Elem> elems;
public:
MatrixModulo(int new_h=0, int new_w=0){ h = new_h; w = new_w; elems.assign(h * w, 0); }
MatrixModulo(const MatrixModulo &) = default;
int numRow() const { return h; }
int numColumn() const { return w; }
int height() const { return numRow(); }
int width() const { return numColumn(); }
typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y * w); }
typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y * w); }
static MatrixModulo Identity(int idx){ auto res = MatrixModulo(idx, idx); for(int i = 0; i < idx; i++) res[i][i] = 1; return res; }
void swapColumns(int x1, int x2){
assert(0 <= x1 && x1 < numColumn());
assert(0 <= x2 && x2 < numColumn());
for(int y=0; y<numRow(); y++) std::swap((*this)[y][x1], (*this)[y][x2]);
}
void swapRows(int y1, int y2){
assert(0 <= y1 && y1 < numRow());
assert(0 <= y2 && y2 < numRow());
for(int x=0; x<numColumn(); x++) std::swap((*this)[y1][x], (*this)[y2][x]);
}
MatrixModulo operator*(const MatrixModulo& r) const {
assert(width() == r.height());
auto res = MatrixModulo(h, r.w);
for (int i=0; i<h; i++) for (int j=0; j<w; j++) for (int k=0; k<r.w; k++) res[i][k] += (*this)[i][j] * r[j][k];
return res;
}
Elem det() const {
assert(height() == width());
MatrixModulo g = *this;
Elem ans = 1;
for (int i=0; i<h; i++) {
int tg = -1;
for (int j=i; j<h; j++) { if (g[j][i].val() != 0) tg = j; }
if (tg == -1) return 0;
if (tg != i) ans = -ans;
for (int j=0; j<h; j++) std::swap(g[i][j], g[tg][j]);
tg = i;
ans *= g[i][i];
Elem const_coeff = g[i][i].inv();
for (int j=0; j<h; j++) g[i][j] *= const_coeff;
for (int j=i+1; j<h; j++) for(int k=h-1; k>=i; k--) g[j][k] -= g[j][i] * g[i][k];
}
return ans;
}
int rank() const {
MatrixModulo g = *this;
int y = 0;
for (int d=0; d<w; d++) {
if(y == h) break;
int tg = -1;
for (int i=y; i<h; i++) { if (g[i][d].val() != 0){ tg = i; break; } }
if (tg == -1) continue;
for (int j=d; j<w; j++) std::swap(g[y][j], g[tg][j]);
tg = y;
Elem const_coeff = g[y][d].inv();
for (int j=d; j<w; j++) g[y][j] *= const_coeff;
for (int i=y+1; i<h; i++) for(int j=w-1; j>=d; j--) g[i][j] -= g[i][d] * g[y][j];
y++;
}
return y;
}
MatrixModulo pow(unsigned long long i){
auto a = *this;
auto res = Identity(height());
while(i){
if(i % 2 == 1) res = res * a;
a = a * a;
i /= 2;
}
return res;
}
};
} // namespace nachia
#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\linear-modulo\\characteristic-polynomial.hpp"
namespace nachia{
template<class Elem>
std::vector<Elem> CharacteristicPolynomial(MatrixModulo<Elem> mat){
assert(mat.numRow() == mat.numColumn());
int n = mat.numRow();
if(n == 0){ return {1}; }
std::vector<Elem> T(n);
for(int y=1; y<n; y++){
int y1=y; while(y1<n && mat[y1][y-1].val() == 0) y1++;
if(y1 == n) continue;
if(y != y1){ mat.swapRows(y, y1); mat.swapColumns(y, y1); }
T[y] = mat[y][y-1].inv();
for(int y2=y+1; y2<n; y2++) T[y2] = T[y] * mat[y2][y-1];
for(int y2=y+1; y2<n; y2++) for(int x=y-1; x<n; x++) mat[y2][x] -= mat[y][x] * T[y2];
for(int y2=0; y2<n; y2++) for(int x=y+1; x<n; x++) mat[y2][y] += mat[y2][x] * T[x];
}
for(int y=0; y<n; y++){ Elem tmp = 1; for(int x=y+1; x<n; x++) mat[y][x] *= (tmp *= -mat[x][x-1]); }
MatrixModulo<Elem> dp(n+1, n+1);
dp[0][0] = 1;
for(int y=0; y<n; y++){
for(int x=0; x<=y; x++) dp[y+1][x+1] -= dp[y][x];
for(int x=0; x<=y; x++) dp[y+1][x] += dp[y][x] * mat[y][y];
for(int y2=0; y2<y; y2++) for(int x=0; x<=y2; x++) dp[y+1][x] += dp[y2][x] * mat[y2][y];
}
std::vector<Elem> res(n+1);
for(int i=0; i<=n; i++) res[i] = ((n%2 == 1) ? -dp[n][i] : dp[n][i]);
return res;
}
} // namespace nachia
#line 8 "..\\Main.cpp"
using Modint = atcoder::static_modint<998244353>;
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;
struct ModintX{
Modint x;
Modint c;
ModintX& operator+=(ModintX a){ x += a.x; c += a.c; return *this; }
ModintX& operator-=(ModintX a){ x -= a.x; c -= a.c; return *this; }
ModintX& operator*=(Modint a){ x *= a; c *= a; return *this; }
ModintX operator*(Modint a) const { return { x*a, c*a }; }
void sh(){ x = c; c = 0; }
};
void testcase(){
int n; cin >> n;
vector<vector<ModintX>> Mt(n, vector<ModintX>(n));
rep(i,n) rep(j,n){
int x; cin >> x;
Mt[i][j].c = x;
}
rep(i,n) rep(j,n){
int x; cin >> x;
Mt[i][j].x = x;
}
int shifted = 0;
Modint times = 1;
rep(y,n){
if(shifted == n+1){
rep(i,n+1) cout << "0\n";
return;
}
int p = y;
while(p < n && Mt[p][y].x.val() == 0) p++;
if(p == n){
shifted++;
rep(q,n) Mt[q][y].sh();
p = y;
vector<Modint> t(y);
rep(y2,y) t[y2] = -Mt[y2][y].x;
rep(y2,n) rep(x,y) Mt[y2][y] += Mt[y2][x] * t[x];
y--; continue;
}
swap(Mt[p], Mt[y]); if(p != y) times = -times;
{
Modint t = Mt[y][y].x;
times *= t; t = t.inv();
rep(i,n) Mt[y][i] *= t;
}
for(int y2=y+1; y2<n; y2++){
Modint t = -Mt[y2][y].x;
rep(x,n) Mt[y2][x] += Mt[y][x] * t;
}
{
vector<Modint> t(n);
for(int x=y+1; x<n; x++) t[x] = -Mt[y][x].x;
rep(y2,n) for(int x=y+1; x<n; x++) Mt[y2][x] += Mt[y2][y] * t[x];
}
rep(i,n) rep(j,n){
if(i > y && j > y) continue;
if(i == j) assert(Mt[i][j].x.val() == 1);
else assert(Mt[i][j].x.val() == 0);
}
}
rep(i,n) rep(j,n){
if(i == j) assert(Mt[i][j].x.val() == 1);
else assert(Mt[i][j].x.val() == 0);
}
using Matrix = nachia::MatrixModulo<Modint>;
auto matc = Matrix(n,n);
rep(i,n) rep(j,n) matc[i][j] = -Mt[i][j].c;
auto poly = nachia::CharacteristicPolynomial(matc);
rep(i,n+1) poly[i] *= times;
poly.resize(n*2+2);
rep(i,n+1) cout << poly[i+shifted].val() << '\n';
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
testcase();
return 0;
}
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