結果

問題 No.1750 ラムドスウイルスの感染拡大-hard
ユーザー Sooh317
提出日時 2021-11-19 21:58:06
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 355 ms / 2,000 ms
コード長 22,572 bytes
コンパイル時間 2,119 ms
コンパイル使用メモリ 206,020 KB
最終ジャッジ日時 2025-01-25 20:20:19
ジャッジサーバーID
(参考情報)
judge4 / judge1
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ファイルパターン 結果
sample AC * 4
other AC * 30
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ソースコード

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プレゼンテーションモードにする

/**
* author: Sooh
* created: 19.11.2021 21:18:29
**/
#include<bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <utility>
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
for (long long a : {2, 7, 61}) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
using namespace atcoder;
using mint = modint998244353;
//using mint = modint1000000007;
#endif
#pragma region template
using ll = long long;
template <class T> using V = vector<T>;
#define rep(i,n) for(int i=0;i<n;++i)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#ifdef LOCAL
#define debug(var) do{std::cerr << "\033[1;36m" << #var << ": \033[0m";view(var);std::cerr << std::endl;}while(0)
template<typename T> void view(T e){std::cerr << e;}
template<typename T, typename K> void view(pair<T, K> e){std::cerr << "("; view(e.fi); std::cerr << ", "; view(e.se); std::cerr << ")";}
template<typename T> void view(const set<T> &st){ std::cerr << "\n";for(const auto& e : st){view(e); std::cerr << " ";}}
template<typename T, typename K> void view(const map<T, K> &mp){ std::cerr << "\n";for(const auto& [k, v]: mp){std::cerr << "("; view(k); std::cerr
    << ", "; view(v); std::cerr << ") ";}}
template<typename T> void view(const unordered_map<int, T> &mp){ std::cerr << "\n";for(const auto& [k, v]: mp){std::cerr << "("; view(k); std::cerr
    << ", "; view(v); std::cerr << ") ";}}
template<typename T> void view(const std::vector<T>& v){std::cerr << "\n";for(const auto& e : v){ view(e); std::cerr << " "; }}
template<typename T> void view(const std::vector<std::vector<T> >& vv){std::cerr << "\n";int cnt = 0;for(const auto& v : vv){cerr << cnt << "th : ";
    view(v); cnt++; std::cerr << std::endl;}}
#else
#define debug(var) 0
#endif
ll power(ll a, ll p){ll ret = 1; while(p){if(p & 1){ret = ret * a;} a = a * a; p >>= 1;} return ret;}
ll modpow(ll a, ll p, ll mod){ll ret = 1; while(p){if(p & 1){ret = ret * a % mod;} a = a * a % mod; p >>= 1;} return ret;}
ll modinv(ll a, ll m) {ll b = m, u = 1, v = 0; while (b) {ll t = a / b ;a -= t * b; swap(a, b);u -= t * v; swap(u, v);}u %= m;if (u < 0) u += m
    ;return u;}
template<class T, class K>bool chmax(T &a, const K b) { if (a<b) { a=b; return 1; } return 0; }
template<class T, class K>bool chmin(T &a, const K b) { if (b<a) { a=b; return 1; } return 0; }
#pragma endregion
int dx[]={1,0,-1,0};
int dy[]={0,1,0,-1};
const int inf = 1001001001;
const ll INF = 1001001001001001001ll;
//const double pi = acos(-1);
//const ll mod = 998244353;
const ll mod = 1000000007;
// reference : https://ei1333.github.io/luzhiled/snippets/math/matrix.html
// gauss_jordan_F2 : https://atcoder.jp/contests/typical90/submissions/25903321
// gauss_jordan : unverified
// matrix exponentiation : verified in https://atcoder.jp/contests/abc129/tasks/abc129_f
// matrix exponentiation (mod) : verified in https://atcoder.jp/contests/arc020/submissions/27320350
template<class T>
struct Matrix{
std::vector<std::vector<T>> A;
// ll modulo;
Matrix(){}
Matrix(int _n):A(_n, std::vector<T>(_n, 0)){}
Matrix(int _n, int _m):A(_n, std::vector<T>(_m, 0)){}
//Matrix(int _n, int _m, ll md):A(_n, std::vector<T>(_m, 0)){modulo = md;}
Matrix(std::vector<std::vector<T>> &_A){ A = _A;}
int height()const{return A.size();}
int width()const{return A[0].size();}
void multiply_vector(std::vector<T> &v){
assert(width() == v.size());
std::vector<T> res(height());
for(int i = 0; i < height(); i++){
for(int j = 0; j < width(); j++){
res[i] += (A[i][j] * v[j]);
//res[i] += (A[i][j] * v[j]) % modulo;
//if(res[i] >= modulo) res[i] -= modulo;
}
}
v.swap(res);
return;
}
// the result will be in B
std::pair<int, T> gauss_jordan(Matrix &B){
int rank = 0;
T ret = 1;
B = Matrix(*this);
int n = height(), m = width();
for(int col = 0; col < m; col++){
for(int i = rank; i < n; i++){
if(B[i][col] != 0){
if(i != rank) ret *= -1;
swap(B[i], B[rank]);
break;
}
}
if(B[rank][col] == 0) continue;
ret *= B[rank][col];
for(int j = m - 1; j >= col; j--) B[rank][j] /= B[rank][col];
for(int r = 0; r < n; r++){
if(r == rank || B[r][col] == 0) continue;
for(int c = m - 1; c > col; c--) B[r][c] -= B[r][col] * B[rank][c];
B[r][col] = 0;
}
if(++rank == n) break;
}
return std::pair<int, T>(rank, ret);
}
Matrix inv(){ //
int n = height(), m = width();
assert(n = m);
int rank = 0;
Matrix B = Matrix(*this), C = identity(n);
for(int col = 0; col < m; col++){
for(int i = rank; i < n; i++){
if(B[i][col] != 0){
std::swap(B[i], B[rank]);
std::swap(C[i], C[rank]);
break;
}
}
if(B[rank][col] == 0) return identity(n);
for(int j = 0; j < m; j++) C[rank][j] /= B[rank][col];
for(int j = m - 1; j >= col; j--) B[rank][j] /= B[rank][col];
for(int r = 0; r < n; r++){
if(r == rank || B[r][col] == 0) continue;
for(int c = 0; c < m; c++) C[r][c] -= B[r][col]*C[rank][c];
for(int c = m - 1; c > col; c--) B[r][c] -= B[r][col]*B[rank][c];
B[r][col] = 0;
}
if(++rank == n) break;
}
return C;
}
Matrix LU_decomposition(){ // L1LUL
assert(height() == width());
Matrix LU = Matrix(*this);
int n = height();
for(int k = 0; k < n; k++){
for(int i = k + 1; i < n; i++){
LU[i][k] /= LU[k][k];
}
for(int i = k + 1; i < n; i++){
for(int j = k + 1; j < n; j++){
LU[i][j] -= LU[j][k] * LU[k][i];
}
}
}
return LU;
}
T det(){
assert(height() == width());
Matrix B;
auto[rank, ret] = gauss_jordan(B);
if(rank < height()) return T(0);
return ret;
}
Matrix identity(int n){
Matrix I(n);
for(int i = 0; i < height(); i++) I[i][i] = 1;
return I;
}
Matrix &operator+=(const Matrix &B){
int n = height(), m = width();
assert(n == B.height() && m == B.width());
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){
int n = height(), m = width();
assert(n == B.height() && m == B.width());
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){
int n = height(), m = width(), l = B.width();
assert(m == B.height());
std::vector<std::vector<T>> C(n, std::vector<T>(m, 0));
for(int i = 0; i < n; i++) for(int j = 0; j < l; j++){
for(int k = 0; k < m; k++){
C[i][j] += ((*this)[i][k] * B[k][j]);
//C[i][j] += ((*this)[i][k] * B[k][j]) % modulo;
//if(C[i][j] >= modulo) C[i][j] -= modulo;
}
}
A.swap(C);
return (*this);
}
Matrix &operator^=(long long k){
Matrix B = Matrix::identity(height());
// B.modulo = this->modulo;
while(k){
if(k & 1) B *= *this;
*this *= *this;
k >>= 1;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B)const{return (Matrix(*this) += B);}
Matrix operator-(const Matrix &B)const{return (Matrix(*this) -= B);}
Matrix operator*(const Matrix &B)const{return (Matrix(*this) *= B);}
Matrix operator^(const long long k)const{return (Matrix(*this) ^= k);}
inline std::vector<T> &operator[](int k){ return A.at(k);}
inline const std::vector<T> &operator[](int k)const{ return A.at(k);}
friend ostream &operator<<(ostream &os, Matrix &p){
size_t n = p.height(), m = p.width();
for(int i = 0; i < n; i++) {
os << "[";
for(int j = 0; j < m; j++) {
os << p[i][j] << (j + 1 == m ? "]\n" : ",");
}
}
return (os);
}
};
int main(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
//cout << fixed << setprecision(20);
ll n, m, t; cin >> n >> m >> t;
V<V<int>> G(n);
Matrix<mint> A(n, n);
rep(i,m){
int a, b; cin >> a >> b;
A[a][b] = A[b][a] = 1;
}
A ^= t;
V<mint> dp(n);
dp[0] = 1;
A.multiply_vector(dp);
cout << dp[0].val() << endl;
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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0