結果
問題 |
No.3175 転移迷宮 (Easy)
|
ユーザー |
👑 |
提出日時 | 2025-06-06 23:12:33 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 406 ms / 3,000 ms |
コード長 | 6,567 bytes |
コンパイル時間 | 4,359 ms |
コンパイル使用メモリ | 260,024 KB |
実行使用メモリ | 7,844 KB |
最終ジャッジ日時 | 2025-06-06 23:12:49 |
合計ジャッジ時間 | 16,257 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 44 |
ソースコード
#include<bits/stdc++.h> #include<atcoder/all> #define rep(i,n) for(int i=0;i<n;i++) using namespace std; using namespace atcoder; typedef long long ll; typedef pair<int, int> P; template <int m> ostream& operator<<(ostream& os, const static_modint<m>& a) {os << a.val(); return os;} template <int m> ostream& operator<<(ostream& os, const dynamic_modint<m>& a) {os << a.val(); return os;} template <int m> istream& operator>>(istream& is, static_modint<m>& a) {long long x; is >> x; a = x; return is;} template <int m> istream& operator>>(istream& is, dynamic_modint<m>& a) {long long x; is >> x; a = x; return is;} template<typename T> istream& operator>>(istream& is, vector<T>& v){int n = v.size(); assert(n > 0); rep(i, n) is >> v[i]; return is;} template<typename U, typename T> ostream& operator<<(ostream& os, const pair<U, T>& p){os << p.first << ' ' << p.second; return os;} template<typename T> ostream& operator<<(ostream& os, const vector<T>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : " "); return os;} template<typename T> ostream& operator<<(ostream& os, const vector<vector<T>>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : ""); return os;} template<typename T> ostream& operator<<(ostream& os, const set<T>& se){for(T x : se) os << x << " "; os << "\n"; return os;} template<typename T> ostream& operator<<(ostream& os, const unordered_set<T>& se){for(T x : se) os << x << " "; os << "\n"; return os;} template<typename S, auto op, auto e> ostream& operator<<(ostream& os, const atcoder::segtree<S, op, e>& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;} template<typename S, auto op, auto e, typename F, auto mapping, auto composition, auto id> ostream& operator<<(ostream& os, const atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;} template<typename T> void chmin(T& a, T b){a = min(a, b);} template<typename T> void chmax(T& a, T b){a = max(a, b);} // https://youtu.be/ylWYSurx10A?t=2352 template<typename T> struct Matrix : vector<vector<T>> { int h, w; Matrix(int h, int w, T val=0): vector<vector<T>>(h, vector<T>(w, val)), h(h), w(w) {} Matrix(initializer_list<initializer_list<T>> a) : vector<vector<T>>(a.begin(), a.end()){ assert(int(this->size()) >= 1); assert(int((*this)[0].size()) >= 1); h = this->size(); w = (*this)[0].size(); rep(i, h) assert(int((*this)[i].size()) == w); } Matrix& unit() { assert(h == w); rep(i,h) (*this)[i][i] = 1; return *this; } Matrix operator*=(const Matrix& M){ assert(w == M.h); Matrix r(h, M.w); rep(i,h) rep(k,w) rep(j, M.w){ r[i][j] += (*this)[i][k] * M[k][j]; } swap(*this, r); return *this; } Matrix operator*(const Matrix& M) const {return (Matrix(*this) *= M);} Matrix operator*=(const T& a) { for(int i = 0; i < h; i++) for(int j = 0; j < w; j++) (*this)[i][j] *= a; return *this; } Matrix operator*(const T& a) const {return (Matrix(*this) *= a);} Matrix operator+=(const Matrix& M){ assert(h == M.h and w == M.w); for(int i = 0; i < h; i++) for(int j = 0; j < w; j++) (*this)[i][j] += M[i][j]; return *this; } Matrix operator+(const Matrix& M) const {return (Matrix(*this) += M);} Matrix pow(long long t) const { assert(h == w); if (!t) return Matrix(h,h).unit(); if (t == 1) return *this; Matrix r = pow(t>>1);r = r*r; if (t&1) r = r*(*this); return r; } }; template<typename T> pair<int, Matrix<T>> eliminate(Matrix<T> a){ int h = a.h; int w = a.w; int ny = 0; rep(x, w){ for(int y = ny; y < h; y++){ if(a[y][x] != T(0)){ swap(a[y], a[ny]); break; } } if(a[ny][x] == T(0)) continue; rep(y, h){ if(y != ny and a[y][x] != T(0)){ T c = a[y][x] / a[ny][x]; rep(x, w){ a[y][x] -= a[ny][x] * c; } } } ny++; if(ny == h) break; } return make_pair(ny, a); }; // O(HW + W(W - rank)) // solve aM = b // a = a_0 + Sum_{i=1,...,w - rank} c_i a_i // c_i is arbitrary constant template<typename T> tuple<int, vector<T>, vector<vector<T>>> solve(Matrix<T> mat, vector<T> b){ int h = mat.h; int w = mat.w; assert(h == int(b.size())); { Matrix<T> mat_new(h, w + 1); rep(y, h) rep(x, w) mat_new[y][x] = mat[y][x]; rep(y, h) mat_new[y][w] = b[y]; swap(mat, mat_new); } int rank; { auto res = eliminate(mat); rank = res.first; mat = res.second; } vector<int> fixed; vector<int> unfixed; { int y = 0; rep(x, w){ if(y == h){ unfixed.push_back(x); continue; } if(mat[y][x] == T(0)){ unfixed.push_back(x); }else{ fixed.push_back(x); y++; } } for(; y < h; y++){ if(mat[y][w] != T(0)){ return make_tuple(-1, vector<T>(0), vector<vector<T>>(0)); } } } int freedom = w - rank; vector<T> a_0(w); vector<vector<T>> a_vec(freedom); rep(i, freedom) a_vec[i].resize(w); { rep(y, rank) a_0[fixed[y]] = mat[y][w] / mat[y][fixed[y]]; } rep(i, freedom){ a_vec[i][unfixed[i]] = 1; rep(y, rank) a_vec[i][fixed[y]] = -(mat[y][unfixed[i]]) / mat[y][fixed[y]]; } return make_tuple(freedom, a_0, a_vec); } // (detA, invA) // O(n^3) // Thanks for maspy-san's submission https://atcoder.jp/contests/abc323/submissions/46293806 template <typename T> pair<T, Matrix<T>> mat_inv(Matrix<T> A) { assert(A.size() == A[0].size()); T det = 1; int n = A.size(); Matrix<T> B(n, n); for(int r = 0; r < n; r++) B[r][r] = 1; for(int r = 0; r < n; r++){ if(A[r][r] == 0){ int pivot = -1; for(int h = r; h < n; h++){ if(A[h][r] != 0){pivot = h; break;} } if(pivot == -1) return {T(0), Matrix<T>(1, 1)}; swap(A[r], A[pivot]); swap(B[r], B[pivot]); det *= -1; } T c = T(1) / A[r][r]; det *= A[r][r]; for(int i = r; i < n; i++) A[r][i] *= c; for(int i = 0; i < n; i++) B[r][i] *= c; for(int h = 0; h < n; h++){ if(h == r) continue; T c = A[h][r]; for(int i = r; i < n; i++) A[h][i] -= A[r][i] * c; for(int i = 0; i < n; i++) B[h][i] -= B[r][i] * c; } } return {det, B}; } using mint = modint998244353; int solve(){ int n, k; cin >> n >> k; Matrix<mint> mat(n, n); rep(i, n) mat[i][i]++; rep(i, n) for(int j = max(0, i - k); j <= min(n - 1, i + k); j++){ mat[i][j] -= mint(1) / (2 * k + 1); } auto [det, inv] = mat_inv(mat); vector<mint> ans(n); rep(i, n) rep(j, n) ans[i] += inv[i][j]; cout << ans; return 0; } int main(){ int t; cin >> t; rep(_, t) solve(); return 0; }