結果
| 問題 |
No.1810 RGB Biscuits
|
| コンテスト | |
| ユーザー |
 Nachia
|
| 提出日時 | 2022-01-14 21:47:50 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 14 ms / 2,000 ms |
| コード長 | 6,038 bytes |
| コンパイル時間 | 934 ms |
| コンパイル使用メモリ | 83,476 KB |
| 最終ジャッジ日時 | 2025-01-27 11:16:01 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 20 |
ソースコード
#include <vector>
#include <cassert>
#include <utility>
#include <vector>
#include <utility>
namespace nachia{
template<unsigned int MOD>
struct StaticModint{
private:
using u64 = unsigned long long;
unsigned int x;
public:
using my_type = StaticModint;
StaticModint() : x(0){}
StaticModint(unsigned int v) : x(v){}
unsigned int operator*() const { return x; }
my_type& operator+=(const my_type& r){ auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
my_type operator+(const my_type& r) const { my_type res = *this; return res += r; }
my_type& operator-=(const my_type& r){ auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
my_type operator-(const my_type& r) const { my_type res = *this; return res -= r; }
my_type operator-() const { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }
my_type& operator*=(const my_type& r){ x = (u64)x * r.x % MOD; return *this; }
my_type operator*(const my_type& r) const { my_type res = *this; return res *= r; }
my_type pow(unsigned long long i) const {
my_type a = *this, res = 1;
while(i){ if(i & 1) res *= a; a *= a; i >>= 1; }
return res;
}
my_type inv() const { return pow(MOD-2); }
unsigned int val() const { return x; }
static unsigned int get_mod() { return MOD; }
my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }
my_type operator/(const my_type& r) const { return operator/(r.inv()); }
};
}
namespace nachia{
template<class Elem>
struct MatrixModulo{
private:
int h;
int w;
std::vector<Elem> elems;
public:
MatrixModulo(int new_h, int new_w){ h = new_h; w = new_w; elems.assign(h * w, 0); }
MatrixModulo(const MatrixModulo&) = default;
int height() const { return h; }
int width() const { return w; }
typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y * w); }
typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y * w); }
static MatrixModulo identity(int idx){ auto res = MatrixModulo(idx, idx); for(int i = 0; i < idx; i++) res[i][i] = 1; return res; }
MatrixModulo operator*(const MatrixModulo& r) const {
assert(w == r.h);
auto res = MatrixModulo(h, r.w);
for (int i=0; i<h; i++) for (int j=0; j<w; j++) for (int k=0; k<r.w; k++) res[i][k] += (*this)[i][j] * r[j][k];
return res;
}
Elem det() const {
assert(h == w);
MatrixModulo g = *this;
Elem ans = 1;
for (int i=0; i<h; i++) {
int tg = -1;
for (int j=i; j<h; j++) { if (g[j][i] != 0) tg = j; }
if (tg == -1) return 0;
if (tg != i) ans = -ans;
for (int j=0; j<h; j++) std::swap(g[i][j], g[tg][j]); tg = i;
ans *= g[i][i];
Elem const_coeff = g[i][i].inv();
for (int j=0; j<h; j++) g[i][j] *= const_coeff;
for (int j=i+1; j<h; j++) for(int k=h-1; k>=i; k--) g[j][k] -= g[j][i] * g[i][k];
}
return ans;
}
int rank() const {
MatrixModulo g = *this;
int y = 0;
for (int d=0; d<w; d++) {
if(y == h) break;
int tg = -1;
for (int i=y; i<h; i++) { if (g[i][d] != 0){ tg = i; break; } }
if (tg == -1) continue;
for (int j=d; j<w; j++) std::swap(g[y][j], g[tg][j]); tg = y;
Elem const_coeff = g[y][d].inv();
for (int j=d; j<w; j++) g[y][j] *= const_coeff;
for (int i=y+1; i<h; i++) for(int j=w-1; j>=d; j--) g[i][j] -= g[i][d] * g[y][j];
y++;
}
return y;
}
MatrixModulo linear_equation() const {
MatrixModulo g = *this;
int y = 0;
std::vector<std::pair<int,int>> det_var;
std::vector<int> rank_var;
for (int d=0; d<w-1; d++) {
int tg = -1;
for (int i=y; i<h; i++) { if (g[i][d] != 0){ tg = i; break; } }
if (tg == -1){ rank_var.push_back(d); continue; }
for (int j=d; j<w; j++) std::swap(g[y][j], g[tg][j]); tg = y;
Elem const_coeff = g[y][d].inv();
for (int j=d; j<w; j++) g[y][j] *= const_coeff;
for (int i=0; i<h; i++) if (i != y) for(int j=w-1; j>=d; j--) g[i][j] -= g[i][d] * g[y][j];
det_var.push_back(std::make_pair(d,y));
y++;
}
for (int i=y; i<h; i++) if (g[i][w-1].val() != 0) return MatrixModulo(0,0);
MatrixModulo solution(1 + rank_var.size(), w);
for (auto [x,i] : det_var) { solution[0][x] = g[i][w-1]; }
solution[0][w-1] = 1;
for (int d=0; d<rank_var.size(); d++) {
int varid = rank_var[d];
solution[d+1][varid] = -1;
for (auto [x,i] : det_var) { solution[d+1][x] = g[i][varid]; }
}
return solution;
}
};
}
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
using i32 = int;
using u32 = unsigned int;
#define rep(i,n) for(int i=0; i<(n); i++)
using m32 = nachia::StaticModint<1000000007>;
using Mat = nachia::MatrixModulo<m32>;
Mat pow_mat(Mat A, unsigned long long i) {
Mat a = A, res = Mat::identity(A.height());
while(i){ if(i & 1) res = res * a; a = a * a; i >>= 1; }
return res;
}
int main() {
int A,B; cin >> A >> B;
int N; cin >> N;
Mat G0 = Mat::identity(3);
G0[0][2] = B;
G0[1][2] = A;
Mat G1(3,3);
G1[1][0] = 1;
G1[2][1] = 1;
Mat G01 = G0 * G1;
rep(i,N){
u64 T; cin >> T;
Mat res_mat = pow_mat(G01, T/2);
if(T & 1) res_mat = res_mat * G0;
m32 ans = 0;
rep(a,2) rep(b,3) ans += res_mat[a][b];
cout << *ans << endl;
}
return 0;
}
struct ios_do_not_sync{
ios_do_not_sync(){
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
}
} ios_do_not_sync_instance;