algorithm
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test/yosupo/det.cpp
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- Last update: 2020-07-17 17:36:15+09:00
Code
#define PROBLEM \
https: // judge.yosupo.jp/problem/matrix_det
#include <bits/stdc++.h>
using namespace std;
typedef pair<int, int> pii;
typedef long long ll;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define ALL(c) (c).begin(), (c).end()
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T, class U>
void chmin(T& t, const U& u) {
if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
if (t < u) t = u;
}
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << "(" << p.first << "," << p.second << ")";
return os;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
os << "{";
rep(i, v.size()) {
if (i) os << ",";
os << v[i];
}
os << "}";
return os;
}
#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << " " << H;
debug_out(T...);
}
#define debug(...) \
cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
template <unsigned int MOD>
struct ModInt {
using uint = unsigned int;
using ull = unsigned long long;
using M = ModInt;
uint v;
ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD)
v = (_v < MOD) ? _v : _v - MOD;
return *this;
}
explicit operator bool() const { return v != 0; }
M operator+(const M& a) const { return M().set_norm(v + a.v); }
M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
M operator/(const M& a) const { return *this * a.inv(); }
M& operator+=(const M& a) { return *this = *this + a; }
M& operator-=(const M& a) { return *this = *this - a; }
M& operator*=(const M& a) { return *this = *this * a; }
M& operator/=(const M& a) { return *this = *this / a; }
M operator-() const { return M() - *this; }
M& operator++(int) { return *this = *this + 1; }
M& operator--(int) { return *this = *this - 1; }
M pow(ll n) const {
if (n < 0) return inv().pow(-n);
M x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
M inv() const {
ll a = v, b = MOD, p = 1, q = 0, t;
while (b != 0) {
t = a / b;
swap(a -= t * b, b);
swap(p -= t * q, q);
}
return M(p);
}
bool operator==(const M& a) const { return v == a.v; }
bool operator!=(const M& a) const { return v != a.v; }
friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
static uint get_mod() { return MOD; }
};
using Mint = ModInt<998244353>;
const Mint zero(0);
const Mint one(1);
bool iszero(Mint x) { return x.v == 0; }
bool isone(Mint x) { return x.v == 1; }
// gifted
template <class T>
struct Matrix {
int H, W;
VV<T> a;
Matrix() : H(0), W(0) {}
Matrix(int H, int W) : H(H), W(W), a(VV<T>(H, V<T>(W))) {}
Matrix(const VV<T>& v) : H(v.size()), W(v[0].size()), a(v) {}
static Matrix E(int n) {
Matrix a(n, n);
rep(i, n) a.set(i, i, 1);
return a;
}
T at(int i, int j) const { return a[i][j]; }
void set(int i, int j, T v) { a[i][j] = v; }
Matrix operator+(const Matrix& r) const {
assert(H == r.H && W == r.W);
VV<T> v(H, V<T>(W));
rep(i, H) rep(j, W) v[i][j] = a[i][j] + r.a[i][j];
return Matrix(v);
}
Matrix operator-(const Matrix& r) const {
assert(H == r.H && W == r.W);
VV<T> v(H, V<T>(W));
rep(i, H) rep(j, W) v[i][j] = a[i][j] - r.a[i][j];
return Matrix(v);
}
Matrix operator*(const Matrix& r) const {
assert(W == r.H);
VV<T> v(H, V<T>(r.W));
rep(i, H) rep(k, W) rep(j, r.W) v[i][j] += a[i][k] * r.a[k][j];
return Matrix(v);
}
Matrix& operator+=(const Matrix& r) { return (*this) = (*this) + r; }
Matrix& operator-=(const Matrix& r) { return (*this) = (*this) - r; }
Matrix& operator*=(const Matrix& r) { return (*this) = (*this) * r; }
int sweep(int var) {
int rank = 0;
vector<bool> used(H);
rep(j, var) {
int i = 0;
while (i < H && (used[i] || iszero(a[i][j]))) i++;
if (i == H) continue;
used[i] = true;
rank++;
T t = a[i][j];
rep(k, W) a[i][k] = a[i][k] / t;
rep(k, H) if (k != i) {
T t = a[k][j];
rep(l, W) a[k][l] = a[k][l] - a[i][l] * t;
}
}
return rank;
}
Matrix pow(ll n) const {
assert(H == W);
int h = H;
Matrix x = *this, res(h, h);
res = E(h);
while (n > 0) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
friend ostream& operator<<(ostream& o, const Matrix& A) {
rep(i, A.H) {
rep(j, A.W) o << A.a[i][j] << " ";
o << endl;
}
return o;
}
};
template <class T>
T det(Matrix<T> a) {
const int n = a.H;
Mint ans(1);
rep(i, n) {
for (int j = i + 1; j < n; ++j)
if (a.a[j][i]) {
ans = -ans;
swap(a.a[j], a.a[i]);
break;
}
if (!a.a[i][i]) return 0;
ans *= a.a[i][i];
for (int j = i + 1; j < n; ++j) {
auto w = -a.a[j][i] / a.a[i][i];
for (int k = i; k < n; ++k) a.a[j][k] += a.a[i][k] * w;
}
}
return ans;
}
int main() {
int N;
cin >> N;
Matrix<Mint> a(N, N);
rep(i, N) rep(j, N) cin >> a.a[i][j].v;
cout << det(a) << endl;
return 0;
}#line 1 "test/yosupo/det.cpp"
#define PROBLEM \
https: // judge.yosupo.jp/problem/matrix_det
#include <bits/stdc++.h>
using namespace std;
typedef pair<int, int> pii;
typedef long long ll;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define ALL(c) (c).begin(), (c).end()
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T, class U>
void chmin(T& t, const U& u) {
if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
if (t < u) t = u;
}
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << "(" << p.first << "," << p.second << ")";
return os;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
os << "{";
rep(i, v.size()) {
if (i) os << ",";
os << v[i];
}
os << "}";
return os;
}
#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << " " << H;
debug_out(T...);
}
#define debug(...) \
cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
template <unsigned int MOD>
struct ModInt {
using uint = unsigned int;
using ull = unsigned long long;
using M = ModInt;
uint v;
ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD)
v = (_v < MOD) ? _v : _v - MOD;
return *this;
}
explicit operator bool() const { return v != 0; }
M operator+(const M& a) const { return M().set_norm(v + a.v); }
M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
M operator/(const M& a) const { return *this * a.inv(); }
M& operator+=(const M& a) { return *this = *this + a; }
M& operator-=(const M& a) { return *this = *this - a; }
M& operator*=(const M& a) { return *this = *this * a; }
M& operator/=(const M& a) { return *this = *this / a; }
M operator-() const { return M() - *this; }
M& operator++(int) { return *this = *this + 1; }
M& operator--(int) { return *this = *this - 1; }
M pow(ll n) const {
if (n < 0) return inv().pow(-n);
M x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
M inv() const {
ll a = v, b = MOD, p = 1, q = 0, t;
while (b != 0) {
t = a / b;
swap(a -= t * b, b);
swap(p -= t * q, q);
}
return M(p);
}
bool operator==(const M& a) const { return v == a.v; }
bool operator!=(const M& a) const { return v != a.v; }
friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
static uint get_mod() { return MOD; }
};
using Mint = ModInt<998244353>;
const Mint zero(0);
const Mint one(1);
bool iszero(Mint x) { return x.v == 0; }
bool isone(Mint x) { return x.v == 1; }
// gifted
template <class T>
struct Matrix {
int H, W;
VV<T> a;
Matrix() : H(0), W(0) {}
Matrix(int H, int W) : H(H), W(W), a(VV<T>(H, V<T>(W))) {}
Matrix(const VV<T>& v) : H(v.size()), W(v[0].size()), a(v) {}
static Matrix E(int n) {
Matrix a(n, n);
rep(i, n) a.set(i, i, 1);
return a;
}
T at(int i, int j) const { return a[i][j]; }
void set(int i, int j, T v) { a[i][j] = v; }
Matrix operator+(const Matrix& r) const {
assert(H == r.H && W == r.W);
VV<T> v(H, V<T>(W));
rep(i, H) rep(j, W) v[i][j] = a[i][j] + r.a[i][j];
return Matrix(v);
}
Matrix operator-(const Matrix& r) const {
assert(H == r.H && W == r.W);
VV<T> v(H, V<T>(W));
rep(i, H) rep(j, W) v[i][j] = a[i][j] - r.a[i][j];
return Matrix(v);
}
Matrix operator*(const Matrix& r) const {
assert(W == r.H);
VV<T> v(H, V<T>(r.W));
rep(i, H) rep(k, W) rep(j, r.W) v[i][j] += a[i][k] * r.a[k][j];
return Matrix(v);
}
Matrix& operator+=(const Matrix& r) { return (*this) = (*this) + r; }
Matrix& operator-=(const Matrix& r) { return (*this) = (*this) - r; }
Matrix& operator*=(const Matrix& r) { return (*this) = (*this) * r; }
int sweep(int var) {
int rank = 0;
vector<bool> used(H);
rep(j, var) {
int i = 0;
while (i < H && (used[i] || iszero(a[i][j]))) i++;
if (i == H) continue;
used[i] = true;
rank++;
T t = a[i][j];
rep(k, W) a[i][k] = a[i][k] / t;
rep(k, H) if (k != i) {
T t = a[k][j];
rep(l, W) a[k][l] = a[k][l] - a[i][l] * t;
}
}
return rank;
}
Matrix pow(ll n) const {
assert(H == W);
int h = H;
Matrix x = *this, res(h, h);
res = E(h);
while (n > 0) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
friend ostream& operator<<(ostream& o, const Matrix& A) {
rep(i, A.H) {
rep(j, A.W) o << A.a[i][j] << " ";
o << endl;
}
return o;
}
};
template <class T>
T det(Matrix<T> a) {
const int n = a.H;
Mint ans(1);
rep(i, n) {
for (int j = i + 1; j < n; ++j)
if (a.a[j][i]) {
ans = -ans;
swap(a.a[j], a.a[i]);
break;
}
if (!a.a[i][i]) return 0;
ans *= a.a[i][i];
for (int j = i + 1; j < n; ++j) {
auto w = -a.a[j][i] / a.a[i][i];
for (int k = i; k < n; ++k) a.a[j][k] += a.a[i][k] * w;
}
}
return ans;
}
int main() {
int N;
cin >> N;
Matrix<Mint> a(N, N);
rep(i, N) rep(j, N) cin >> a.a[i][j].v;
cout << det(a) << endl;
return 0;
}