結果
| 問題 | No.1907 DETERMINATION |
| コンテスト | |
| ユーザー |
 Misuki
|
| 提出日時 | 2026-03-12 15:43:14 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 1,498 ms / 4,000 ms |
| コード長 | 18,449 bytes |
| 記録 | |
| コンパイル時間 | 7,586 ms |
| コンパイル使用メモリ | 314,984 KB |
| 実行使用メモリ | 11,392 KB |
| 最終ジャッジ日時 | 2026-03-12 15:44:29 |
| 合計ジャッジ時間 | 72,689 ms |
|
ジャッジサーバーID （参考情報） |
judge3_0 / judge1_0 |
（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
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>
#define int ll
#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)
#define pb push_back
#define eb emplace_back
#define clock chrono::steady_clock::now().time_since_epoch().count()
using namespace std;
template<size_t I = 0, typename... args>
ostream& print_tuple(ostream& os, const tuple<args...> tu) {
os << get<I>(tu);
if constexpr (I + 1 != sizeof...(args)) {
os << ' ';
print_tuple<I + 1>(os, tu);
}
return os;
}
template<typename... args>
ostream& operator<<(ostream& os, const tuple<args...> tu) {
return print_tuple(os, tu);
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
for(size_t i = 0; T x : arr) {
os << x;
if (++i != N) os << ' ';
}
return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
for(size_t i = 0; T x : vec) {
os << x;
if (++i != size(vec)) os << ' ';
}
return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
for(size_t i = 0; T x : s) {
os << x;
if (++i != size(s)) os << ' ';
}
return os;
}
template<class T>
ostream& operator<<(ostream& os, const multiset<T> &s) {
for(size_t i = 0; T x : s) {
os << x;
if (++i != size(s)) os << ' ';
}
return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
for(size_t i = 0; pair<T1, T2> x : m) {
os << x.first << " : " << x.second;
if (++i != size(m)) os << ", ";
}
return os;
}
#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif
using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
//#define double ldb
template<typename T> using vc = vector<T>;
template<typename T> using vvc = vc<vc<T>>;
template<typename T> using vvvc = vc<vvc<T>>;
using vi = vc<int>;
using vll = vc<ll>;
using vvi = vvc<int>;
using vvll = vvc<ll>;
template<typename T> using min_heap = priority_queue<T, vc<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;
template<typename R, typename F, typename... Args>
concept R_invocable = requires(F&& f, Args&&... args) {
{ std::invoke(std::forward<F>(f), std::forward<Args>(args)...) } -> std::same_as<R>;
};
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, typename F>
requires R_invocable<T, F, T, T>
void pSum(rng &&v, F f) {
if (!v.empty())
for(T p = *v.begin(); T &x : v | views::drop(1))
x = p = f(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>>
void pSum(rng &&v) {
if (!v.empty())
for(T p = *v.begin(); T &x : v | views::drop(1))
x = p = p + x;
}
template<ranges::forward_range rng>
void Unique(rng &v) {
ranges::sort(v);
v.resize(unique(v.begin(), v.end()) - v.begin());
}
template<ranges::random_access_range rng>
rng invPerm(rng p) {
rng ret = p;
for(int i = 0; i < ssize(p); i++)
ret[p[i]] = i;
return ret;
}
template<ranges::random_access_range rng>
vi argSort(rng p) {
vi id(size(p));
iota(id.begin(), id.end(), 0);
ranges::sort(id, {}, [&](int i) { return pair(p[i], i); });
return id;
}
template<ranges::random_access_range rng, class T = ranges::range_value_t<rng>, typename F>
requires invocable<F, T&>
vi argSort(rng p, F proj) {
vi id(size(p));
iota(id.begin(), id.end(), 0);
ranges::sort(id, {}, [&](int i) { return pair(proj(p[i]), i); });
return id;
}
template<bool directed>
vvi read_graph(int n, int m, int base) {
vvi g(n);
for(int i = 0; i < m; i++) {
int u, v; cin >> u >> v;
u -= base, v -= base;
g[u].emplace_back(v);
if constexpr (!directed)
g[v].emplace_back(u);
}
return g;
}
template<bool directed>
vvi adjacency_list(int n, vc<pii> e, int base) {
vvi g(n);
for(auto [u, v] : e) {
u -= base, v -= base;
g[u].emplace_back(v);
if constexpr (!directed)
g[v].emplace_back(u);
}
return g;
}
template<class T>
vc<pii> equal_subarrays(vc<T> &v) {
vc<pii> lr;
for(int i = 0, j = 0; i < ssize(v); i = j) {
while(j < ssize(v) and v[i] == v[j]) j++;
lr.eb(i, j);
}
return lr;
}
template<class T, typename F>
requires invocable<F, T&>
vc<pii> equal_subarrays(vc<T> &v, F proj) {
vc<pii> lr;
for(int i = 0, j = 0; i < ssize(v); i = j) {
while(j < ssize(v) and proj(v[i]) == proj(v[j])) j++;
lr.eb(i, j);
}
return lr;
}
template<class T>
void setBit(T &msk, int bit, bool x) { (msk &= ~(T(1) << bit)) |= T(x) << bit; }
template<class T> void onBit(T &msk, int bit) { setBit(msk, bit, true); }
template<class T> void offBit(T &msk, int bit) { setBit(msk, bit, false); }
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }
template<class T>
T floorDiv(T a, T b) {
if (b < 0) a *= -1, b *= -1;
return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
if (b < 0) a *= -1, b *= -1;
return a >= 0 ? (a + b - 1) / b : a / b;
}
template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
//reference: https://github.com/NyaanNyaan/library/blob/master/modint/montgomery-modint.hpp#L10
//note: mod should be an odd prime less than 2^30.
template<uint32_t mod>
struct MontgomeryModInt {
using mint = MontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 res = 1, base = mod;
for(i32 i = 0; i < 31; i++)
res *= base, base *= base;
return -res;
}
static constexpr u32 get_mod() {
return mod;
}
static constexpr u32 n2 = -u64(mod) % mod; //2^64 % mod
static constexpr u32 r = get_r(); //-P^{-1} % 2^32
u32 a;
static u32 reduce(const u64 &b) {
return (b + u64(u32(b) * r) * mod) >> 32;
}
static u32 transform(const u64 &b) {
return reduce(u64(b) * n2);
}
MontgomeryModInt() : a(0) {}
MontgomeryModInt(const int64_t &b)
: a(transform(b % mod + mod)) {}
mint pow(u64 k) const {
mint res(1), base(*this);
while(k) {
if (k & 1)
res *= base;
base *= base, k >>= 1;
}
return res;
}
mint inverse() const { return (*this).pow(mod - 2); }
u32 get() const {
u32 res = reduce(a);
return res >= mod ? res - mod : res;
}
mint& operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint& operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint& operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
mint& operator/=(const mint &b) {
a = reduce(u64(a) * b.inverse().a);
return *this;
}
mint operator-() { return mint() - mint(*this); }
bool operator==(mint b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(mint b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
friend mint operator+(mint c, mint d) { return c += d; }
friend mint operator-(mint c, mint d) { return c -= d; }
friend mint operator*(mint c, mint d) { return c *= d; }
friend mint operator/(mint c, mint d) { return c /= d; }
friend ostream& operator<<(ostream& os, const mint& b) {
return os << b.get();
}
friend istream& operator>>(istream& is, mint& b) {
int64_t val;
is >> val;
b = mint(val);
return is;
}
};
//using mint = MontgomeryModInt<1'000'000'007>;
using mint = MontgomeryModInt<998'244'353>;
//#include<modint/MontgomeryModInt.cpp>
template<class Mint>
struct binomial {
vector<Mint> _fac, _facInv;
binomial(int size) : _fac(size), _facInv(size) {
assert(size <= (int)Mint::get_mod());
_fac[0] = 1;
for(int i = 1; i < size; i++)
_fac[i] = _fac[i - 1] * i;
if (size > 0)
_facInv.back() = 1 / _fac.back();
for(int i = size - 2; i >= 0; i--)
_facInv[i] = _facInv[i + 1] * (i + 1);
}
Mint fac(int i) { return i < 0 ? 0 : _fac[i]; }
Mint faci(int i) { return i < 0 ? 0 : _facInv[i]; }
Mint inv(int i) { return _facInv[i] * _fac[i - 1]; }
Mint binom(int n, int r) { return r < 0 or n < r ? 0 : fac(n) * faci(r) * faci(n - r); }
Mint catalan(int i) { return binom(2 * i, i) - binom(2 * i, i + 1); }
Mint excatalan(int n, int m, int k) { //(+1) * n, (-1) * m, prefix sum > -k
if (k > m) return binom(n + m, m);
else if (k > m - n) return binom(n + m, m) - binom(n + m, m - k);
else return Mint(0);
}
};
template<class Mint>
struct matrix : vector<vector<Mint>> {
matrix(int n, int m) : vector<vector<Mint>>(n, vector<Mint>(m, 0)) {}
matrix(int n) : vector<vector<Mint>>(n, vector<Mint>(n, 0)) {}
matrix(vvc<Mint> M) : vvc<Mint>(M) {}
int n() const { return ssize(*this); }
int m() const { return n() == 0 ? 0 : ssize((*this)[0]); }
static matrix I(int n) {
auto res = matrix(n, n);
for(int i = 0; i < n; i++)
res[i][i] = 1;
return res;
}
matrix& operator+=(const matrix &b) {
assert(n() == b.n());
assert(m() == b.m());
for(int i = 0; i < n(); i++)
for(int j = 0; j < m(); j++)
(*this)[i][j] += b[i][j];
return *this;
}
matrix& operator-=(const matrix &b) {
assert(n() == b.n());
assert(m() == b.m());
for(int i = 0; i < n(); i++)
for(int j = 0; j < m(); j++)
(*this)[i][j] -= b[i][j];
return *this;
}
matrix& operator*=(const matrix &b) {
assert(m() == b.n());
auto res = matrix(n(), b.m());
for(int i = 0; i < n(); i++)
for(int k = 0; k < m(); k++)
for(int j = 0; j < b.m(); j++)
res[i][j] += (*this)[i][k] * b[k][j];
this -> swap(res);
return *this;
}
matrix pow(ll k) const {
assert(n() == m());
auto res = I(n()), base = *this;
while(k) {
if (k & 1) res *= base;
base *= base, k >>= 1;
}
return res;
}
tuple<matrix, vector<int>, int> eliminate() {
int sgn = 1;
matrix M = *this;
vector<int> pivot_row;
for(int row = 0, col = 0; row < n() and col < m(); col++) {
int p_row = -1;
for(int i = row; i < n() and p_row == -1; i++)
if (M[i][col] != 0)
p_row = i;
if (p_row == -1) continue;
pivot_row.emplace_back(row);
if (row != p_row) {
for(int j = col; j < m(); j++)
swap(M[row][j], M[p_row][j]);
sgn *= -1;
}
for(int i = 0; i < n(); i++) {
if (i == row or M[i][col] == 0) continue;
Mint s = M[i][col] / M[row][col];
for(int j = col; j < m(); j++)
M[i][j] -= M[row][j] * s;
}
row++;
}
return {M, pivot_row, sgn};
}
Mint det() {
assert(n() == m());
auto [M, pr, sgn] = eliminate();
if (ssize(pr) != n()) {
return Mint(0);
} else {
Mint d = sgn;
for(int i = 0; i < n(); i++)
d *= M[i][i];
return d;
}
}
int rank() {
return get<1>(eliminate()).size();
}
pair<bool, matrix> inv() {
assert(n() == m());
matrix M(n(), 2 * n());
for(int i = 0; i < n(); i++) {
for(int j = 0; j < n(); j++)
M[i][j] = (*this)[i][j];
M[i][n() + i] = 1;
}
matrix tmp = get<0>(M.eliminate());
matrix MI(n(), n());
for(int i = 0; i < n(); i++) {
if (tmp[i][i] == 0) return {false, matrix(0, 0)};
Mint r = tmp[i][i].inverse();
for(int j = 0; j < n(); j++)
MI[i][j] = tmp[i][j + n()] * r;
}
return {true, MI};
}
pair<vector<Mint>, matrix> solve_linear(vector<Mint> b) {
assert(n() == ssize(b));
matrix M(n(), m() + 1);
for(int i = 0; i < n(); i++) {
for(int j = 0; j < m(); j++)
M[i][j] = (*this)[i][j];
M[i][m()] = b[i];
}
auto [N, pr, _] = M.eliminate();
vector<Mint> x(m());
vector<int> where(m(), -1), inv_where(m(), -1);
for(int row : pr) {
int col = 0;
while(N[row][col] == 0) col++;
if (col < m())
where[col] = row, inv_where[row] = col;
}
for(int i = 0; i < m(); i++)
if (where[i] != -1)
x[i] = N[where[i]][m()] / N[where[i]][i];
for(int i = 0; i < n(); i++) {
Mint s = -N[i][m()];
for(int j = 0; j < m(); j++)
s += x[j] * N[i][j];
if (s != Mint(0))
return {vector<Mint>(), matrix(0)};
}
matrix basis(m() - ssize(pr), m());
for(int col = 0, last_row = 0, k = 0; col < m(); col++) {
if (where[col] != -1) {
last_row = where[col];
} else {
basis[k][col] = 1;
for(int i = 0; i <= last_row; i++)
basis[k][inv_where[i]] = -N[i][col] / N[i][inv_where[i]];
k++;
}
}
return {x, basis};
}
matrix operator-() { return matrix(n(), m()) - (*this); }
friend matrix operator+(matrix a, matrix b) { return a += b; }
friend matrix operator-(matrix a, matrix b) { return a -= b; }
friend matrix operator*(matrix a, matrix b) { return a *= b; }
friend ostream& operator<<(ostream& os, const matrix& b) {
for(int i = 0; i < b.n(); i++) {
os << '\n';
for(int j = 0; j < b.m(); j++)
os << b[i][j] << ' ';
}
return os;
}
friend istream& operator>>(istream& is, matrix& b) {
for(int i = 0; i < b.n(); i++)
for(int j = 0; j < b.m(); j++)
is >> b[i][j];
return is;
}
};
template<class Mint>
array<Mint, 2> operator+(array<Mint, 2> a, array<Mint, 2> b) {
return {a[0] + b[0], a[1] + b[1]};
}
template<class Mint>
array<Mint, 2> operator-(array<Mint, 2> a, array<Mint, 2> b) {
return {a[0] - b[0], a[1] - b[1]};
}
template<class Mint>
array<Mint, 2> operator*(Mint m, array<Mint, 2> b) {
return {m * b[0], m * b[1]};
}
template<class Mint>
vc<Mint> characteristic_polynomial(vvc<Mint> M) {
if (M.empty()) return {1};
assert(size(M) == size(M[0]));
const int N = size(M);
vc P(N, vc<array<Mint, 2>>(N));
for(int i = 0; i < N; i++)
for(int j = 0; j < N; j++)
P[i][j] = {-M[i][j], i == j};
//reduce to lower Hessenberg Matrix
for(int r = 0; r < N - 2; r++) {
const int c = r + 1;
int i = c;
while(i < N and P[r][i][0] == 0) i++;
if (i == N) continue;
if (i > c) {
P[i].swap(P[c]);
for(int j = 0; j < N; j++)
swap(P[j][i], P[j][c]);
}
Mint inv = P[r][c][0].inverse();
for(int j = c + 1; j < N; j++) {
Mint R = -inv * P[r][j][0];
for(int k = 0; k < N; k++)
P[k][j] = P[k][j] + R * P[k][c];
}
for(int j = r + 2; j < N; j++) {
Mint R = -P[r + 1][j][1];
for(int k = 0; k < N; k++)
P[r + 1][k] = P[r + 1][k] + R * P[j][k];
}
}
auto add = [&](vector<Mint> a, vector<Mint> b) {
if (ssize(a) < ssize(b)) a.resize(size(b));
for(int i = 0; i < ssize(b); i++)
a[i] += b[i];
return a;
};
auto mul = [&](vector<Mint> &a, array<Mint, 2> b) {
vector<Mint> c(ssize(a) + 1);
for(int i = 0; i < ssize(a); i++) {
c[i] += a[i] * b[0];
c[i + 1] += a[i] * b[1];
}
return c;
};
auto neg = [&](array<Mint, 2> a) { return array<Mint, 2>{-a[0], -a[1]}; };
for(int i = 0; i < N; i++)
for(int j = 0; j < N; j++)
assert((i == j) xor (P[i][j][1] == 0));
for(int i = 0; i < N; i++)
for(int j = i + 2; j < N; j++)
assert(P[i][j][0] == 0);
//DP
vc dp(1, vc<Mint>{1});
for(int i = 0; i < N - 1; i++) {
vc<vc<Mint>> nxt(i + 2);
for(int j = 0; j < ssize(dp); j++) {
nxt[j] = add(nxt[j], mul(dp[j], P[i][i + 1]));
nxt[i + 1] = add(nxt[i + 1], mul(dp[j], (i - j) % 2 ? neg(P[i][j]) : P[i][j]));
}
dp.swap(nxt);
}
vc<Mint> C = {0};
for(int j = 0; j < N; j++)
C = add(C, mul(dp[j], (N - 1 - j) % 2 ? neg(P[N - 1][j]) : P[N - 1][j]));
return C;
}
//compute det(M0 + M1x) with N/MOD probability to fail
template<class Mint>
auto det_poly(matrix<Mint> M0, matrix<Mint> M1) {
const int N = ssize(M0);
assert(N > 0 and ssize(M1) == N and ssize(M0[0]) == N and ssize(M1[0]) == N);
mt19937_64 rng(clock);
mint a = rng() % Mint::get_mod();
for(int i = 0; i < N; i++)
for(int j = 0; j < N; j++)
M0[i][j] += a * M1[i][j];
swap(M0, M1);
auto [ok, M1I] = M1.inv();
if (!ok) return pair(false, vc<Mint>(N + 1, 0));
auto p = characteristic_polynomial(-M1I * M0);
mint inv_det = M1I.det().inverse();
for(mint &x : p) x *= inv_det;
vc<Mint> q(N + 1);
for(int i = 0; i < ssize(p); i++)
q[N - i] = p[i];
binomial<Mint> bn(N + 1);
vc<Mint> r(N + 1);
for(int i = 0; i < ssize(q); i++) {
mint mul = 1;
for(int j = 0; j <= i; j++, mul *= -a)
r[i - j] += q[i] * mul * bn.binom(i, j);
}
return pair(true, r);
}
signed main() {
ios::sync_with_stdio(false), cin.tie(NULL);
int n; cin >> n;
matrix<mint> M0(n, n), M1(n, n);
cin >> M0 >> M1;
for(mint x : det_poly(M0, M1).second)
cout << x << '\n';
return 0;
}