結果

問題 No.1706 Many Bus Stops (hard)
ユーザー milanis48663220milanis48663220
提出日時 2021-10-08 23:13:28
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 5,248 bytes
コンパイル時間 2,470 ms
コンパイル使用メモリ 123,916 KB
最終ジャッジ日時 2025-01-24 23:19:38
ジャッジサーバーID
(参考情報)
judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 41
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>
#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
using namespace std;
typedef long long ll;
const ll MOD = 1000000007;
class ModInt{
public:
ll v;
ModInt(ll _v = 0){
if(_v < 0) _v = (_v%MOD)+MOD;
if(_v >= MOD) _v %= MOD;
v = _v;
}
ModInt operator+(ll n){
return ModInt((v+n)%MOD);
}
ModInt operator-(ll n){
return ModInt((v-n+MOD)%MOD);
}
ModInt operator*(ll n){
if(n >= MOD) n %= MOD;
return ModInt((v*n)%MOD);
}
ModInt operator/(ll n){
return ModInt((ModInt(n).inv()*v).v%MOD);
}
void operator+=(ll n){
v = (v+n)%MOD;
}
void operator-=(ll n){
v = (v-n+MOD)%MOD;
}
void operator*=(ll n){
v = (v*n+MOD)%MOD;
}
ModInt operator+(ModInt n){
return ModInt((v+n.v)%MOD);
}
ModInt operator-(ModInt n){
return ModInt((v-n.v+MOD)%MOD);
}
ModInt operator*(ModInt n){
return ModInt((v*n.v)%MOD);
}
ModInt operator/(ModInt n){
return ModInt((n.inv()*v).v%MOD);
}
void operator+=(ModInt n){
v = (v+n.v)%MOD;
}
void operator-=(ModInt n){
v = (v-n.v+MOD)%MOD;
}
void operator*=(ModInt n){
v = (v*n.v)%MOD;
}
void operator=(ModInt n){
v = n.v;
}
bool operator==(ModInt n){
return v == n.v;
}
bool operator!=(ModInt n){
return v != n.v;
}
void operator=(ll n){
v = n%MOD;
}
ModInt inv(){
if(v == 1) return ModInt(1);
else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
}
};
ostream& operator<<(ostream& os, const ModInt& m){
os << m.v;
return os;
}
istream & operator >> (istream &in, ModInt &m){
in >> m.v;
return in;
}
ModInt pow(ModInt a, ll n) {
assert(n >= 0);
ModInt ans = 1;
ModInt tmp = a;
for (int i = 0; i <= 60; i++) {
ll m = (ll)1 << i;
if (m & n) {
ans *= tmp;
}
tmp *= tmp;
}
return ans;
}
template <typename T>
struct matrix{
int n, m;
vector<vector<T>> dat;
matrix(int n_, int m_){
n = n_; m = m_;
for(int i = 0; i < n; i++){
dat.push_back(vector<T>(m));
}
}
matrix(int n, int m, T val): n(n), m(m){
for(int i = 0; i < n; i++){
dat.push_back(vector<T>(m, val));
}
}
matrix(int n, int m, vector<vector<T>> dat): n(n), m(m), dat(dat){
assert((int)dat.size() == n);
for(int i = 0; i < n; i++) assert(dat[i].size() == m);
}
vector<T>& operator[](int x) {
return dat[x];
}
};
template <typename T>
bool prod(matrix<T> a, matrix<T> b, matrix<T> &ans){
assert(a.m == b.n);
for(int i = 0; i < a.n; i++){
for(int j = 0; j < b.m; j++){
ans.dat[i][j] = 0;
for(int k = 0; k < b.n; k++){
ans.dat[i][j] += (a.dat[i][k]*b.dat[k][j]);
}
}
}
return true;
}
template <typename T>
void copy_mat(matrix<T> a, matrix<T> &b){
assert(a.n == b.n);
assert(a.m == b.m);
for(int i = 0; i < a.n; i++){
for(int j = 0; j < a.m; j++){
b.dat[i][j] = a.dat[i][j];
}
}
}
template <typename T>
void pow_mat(matrix<T> a, ll n, matrix<T> &ans){
assert(n < ((ll)1<<61));
matrix<T> buf(a.n, a.n);
matrix<T> tmp(a.n, a.n);
copy_mat(a, tmp);
for(int i = 0; i < a.n; i++) {
for(int j = 0; j < a.n; j++){
ans.dat[i][j] = 0;
}
ans.dat[i][i] = 1;
}
for(int i = 0; i <= 60; i++){
ll m = (ll)1 << i;
if(m&n){
prod(tmp, ans, buf);
copy_mat(buf, ans);
}
prod(tmp, tmp, buf);
copy_mat(buf, tmp);
}
}
template <typename T>
void print_mat(matrix<T> a){
for(int i = 0; i < a.n; i++){
for(int j = 0; j < a.m; j++){
cout << a.dat[i][j] << ' ';
}
cout << endl;
}
}
template <typename T>
ostream& operator<<(ostream& os, const matrix<T>& m){
print_mat<T>(m);
return os;
}
using mint = ModInt;
using M = matrix<mint>;
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
cout << setprecision(10) << fixed;
int c, n, m; cin >> c >> n >> m;
M mat(4, 4);
mat[0][0] = mint(c).inv();
mat[2][0] = mint(c).inv()*(c-1);
mat[1][1] = mint(c).inv();
mat[2][1] = mint(c).inv()*(c-2);
mat[3][1] = mint(c).inv();
mat[1][2] = 1;
mat[0][3] = 1;
M v(4, 1);
v[0][0] = 1;
M p(4, 4), ans(4, 1);
pow_mat(mat, n, p);
prod(p, v, ans);
mint prob = ans[0][0];
mint aa = mint(1)-pow(mint(1)-prob, m);
cout << aa << endl;
}
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