結果
問題 | No.1907 DETERMINATION |
ユーザー |
👑 |
提出日時 | 2022-04-15 21:22:23 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 663 ms / 4,000 ms |
コード長 | 6,533 bytes |
コンパイル時間 | 1,604 ms |
コンパイル使用メモリ | 113,748 KB |
実行使用メモリ | 7,296 KB |
最終ジャッジ日時 | 2024-12-24 23:20:13 |
合計ジャッジ時間 | 25,905 ms |
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
#include <cassert>#include <cmath>#include <cstdint>#include <cstdio>#include <cstdlib>#include <cstring>#include <algorithm>#include <bitset>#include <complex>#include <deque>#include <functional>#include <iostream>#include <map>#include <numeric>#include <queue>#include <set>#include <sstream>#include <string>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using Int = long long;template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }////////////////////////////////////////////////////////////////////////////////template <unsigned M_> struct ModInt {static constexpr unsigned M = M_;unsigned x;constexpr ModInt() : x(0U) {}constexpr ModInt(unsigned x_) : x(x_ % M) {}constexpr ModInt(unsigned long long x_) : x(x_ % M) {}constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }ModInt pow(long long e) const {if (e < 0) return inv().pow(-e);ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;}ModInt inv() const {unsigned a = M, b = x; int y = 0, z = 1;for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }assert(a == 1U); return ModInt(y);}ModInt operator+() const { return *this; }ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }explicit operator bool() const { return x; }bool operator==(const ModInt &a) const { return (x == a.x); }bool operator!=(const ModInt &a) const { return (x != a.x); }friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }};////////////////////////////////////////////////////////////////////////////////constexpr unsigned MO = 998244353;using Mint = ModInt<MO>;// det(a + x I)// O(n^3)// Call by value: Modifies a (Watch out when using C-style array!)template <class T> vector<T> charPoly(vector<vector<T>> a) {const int n = a.size();// upper Hessenbergfor (int j = 0; j < n - 2; ++j) {for (int i = j + 1; i < n; ++i) {if (a[i][j]) {swap(a[j + 1], a[i]);for (int ii = 0; ii < n; ++ii) swap(a[ii][j + 1], a[ii][i]);break;}}if (a[j + 1][j]) {const T s = 1 / a[j + 1][j];for (int i = j + 2; i < n; ++i) {const T t = s * a[i][j];for (int jj = j; jj < n; ++jj) a[i][jj] -= t * a[j + 1][jj];for (int ii = 0; ii < n; ++ii) a[ii][j + 1] += t * a[ii][i];}}}// fss[i] := det(a[0..i][0..i] + x I_i)vector<vector<T>> fss(n + 1);fss[0] = {1};for (int i = 0; i < n; ++i) {fss[i + 1].assign(i + 2, 0);for (int k = 0; k <= i; ++k) fss[i + 1][k + 1] = fss[i][k];for (int k = 0; k <= i; ++k) fss[i + 1][k] += a[i][i] * fss[i][k];T prod = 1;for (int j = i - 1; j >= 0; --j) {prod *= -a[j + 1][j];const T t = prod * a[j][i];for (int k = 0; k <= j; ++k) fss[i + 1][k] += t * fss[j][k];}}return fss[n];}// det(a + x b)// O(n^3)// Call by value: Modifies a, b (Watch out when using C-style array!)template <class T> vector<T> detPoly(vector<vector<T>> a, vector<vector<T>> b) {const int n = a.size();T prod = 1;int off = 0;for (int h = 0; h < n; ++h) {for (; ; ) {if (b[h][h]) break;for (int j = h + 1; j < n; ++j) {if (b[h][j]) {prod *= -1;for (int i = 0; i < n; ++i) {swap(a[i][h], a[i][j]);swap(b[i][h], b[i][j]);}break;}}if (b[h][h]) break;if (++off > n) return vector<T>(n + 1, 0);for (int j = 0; j < n; ++j) {b[h][j] = a[h][j];a[h][j] = 0;}for (int i = 0; i < h; ++i) {const T t = b[h][i];for (int j = 0; j < n; ++j) {a[h][j] -= t * a[i][j];b[h][j] -= t * b[i][j];}}}prod *= b[h][h];const T s = 1 / b[h][h];for (int j = 0; j < n; ++j) {a[h][j] *= s;b[h][j] *= s;}for (int i = 0; i < n; ++i) if (h != i) {const T t = b[i][h];for (int j = 0; j < n; ++j) {a[i][j] -= t * a[h][j];b[i][j] -= t * b[h][j];}}}const vector<T> fs = charPoly(a);vector<T> gs(n + 1, 0);for (int i = 0; off + i <= n; ++i) gs[i] = prod * fs[off + i];return gs;}int N;vector<vector<Mint>> A, B;int main() {for (; ~scanf("%d", &N); ) {A.assign(N, vector<Mint>(N)); for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) scanf("%u", &A[i][j].x);B.assign(N, vector<Mint>(N)); for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) scanf("%u", &B[i][j].x);const auto ans = detPoly(A, B);for (int i = 0; i <= N; ++i) {printf("%u\n", ans[i].x);}#ifdef LOCALcerr<<"========"<<endl;#endif}return 0;}