結果
問題 | No.1907 DETERMINATION |
ユーザー |
👑 ![]() |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 63 |
ソースコード
#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;}