結果
| 問題 |
No.1847 Good Sequence
|
| コンテスト | |
| ユーザー |
 noya2
|
| 提出日時 | 2023-03-30 22:57:50 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 379 ms / 3,000 ms |
| コード長 | 8,632 bytes |
| コンパイル時間 | 4,765 ms |
| コンパイル使用メモリ | 265,000 KB |
| 最終ジャッジ日時 | 2025-02-11 19:22:33 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 41 |
ソースコード
#line 1 "c.cpp"
#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,n) for (int i = 0; i < int(n); ++i)
#define repp(i,n,m) for (int i = m; i < int(n); ++i)
#define reb(i,n) for (int i = int(n)-1; i >= 0; --i)
#define all(v) v.begin(),v.end()
using namespace std;
using namespace atcoder;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<int, int>;
using PL = pair<long long, long long>;
using pdd = pair<long double, long double>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
template<class T>istream &operator>>(istream &is,vector<T> &v){for(auto &e:v)is>>e;return is;}
template<typename T>bool range(T a,T b,T x){return (a<=x&&x<b);}
template<typename T>bool rrange(T a,T b,T c,T d,T x,T y){return (range(a,c,x)&&range(b,d,y));}
template<typename T> T rev(const T& str_or_vec){T res = str_or_vec; reverse(res.begin(),res.end()); return res; }
template<typename T>bool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;}
template<typename T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<typename T>void uniq(vector<T> &v){sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());}
template<typename T1, typename T2>void print(pair<T1,T2> a);
template<typename T>void print(vector<T> v);
template<typename T>void print(vector<vector<T>> v);
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
void print(unsigned int a){ printf("%u", a); }
void print(unsigned long long a) { printf("%llu", a); }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
template<typename T1,typename T2>void print(pair<T1,T2> a){print(a.first);print(),print(a.second);}
template<typename T>void print(vector<T> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())print();}}
template<typename T>void print(vector<vector<T>> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())out();}}
void yes(){out("Yes");}
void no (){out("No");}
void yn (bool t){if(t)yes();else no();}
void fast_io(){cin.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(20);}
void o(){out("!?");}
namespace noya2{
const int INF = 1001001007;
const long long mod1 = 998244353;
const long long mod2 = 1000000007;
const long long inf = 2e18;
const long double pi = 3.14159265358979323;
const long double eps = 1e-7;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
} // namespace noya2
using namespace noya2;
//using mint = modint998244353;
using mint = modint1000000007;
//using mint = modint;
void out(mint a){out(a.val());}
void out(vector<mint> a){vector<ll> b(a.size()); rep(i,a.size()) b[i] = a[i].val(); out(b);}
void out(vector<vector<mint>> a){for (auto v : a) out(v);}
istream &operator>>(istream &is,vector<mint> &v){for(auto &e:v){ll _x;is>>_x;e=_x;}return is;}
#line 2 "Matrix.hpp"
#line 4 "Matrix.hpp"
namespace noya2{
using namespace std;
template<typename T> struct Matrix{
int rows;
int cols;
vector<vector<T>> m;
Matrix (int h = 0, int w = 0, T init = T(0)) : m(h,vector<T>(w,init)), rows(h), cols(w){}
Matrix (vector<vector<T>> _init) : m(_init), rows(_init.size()), cols(_init.at(0).size()){}
vector<T>& operator[](const int i) const {return m[i];}
vector<T>& operator[](const int i) {return m[i];}
Matrix &operator+= (const Matrix &r){
assert(this->rows == r.rows && this->cols == r.cols);
for (int i = 0; i < r.rows; ++i){
for (int j = 0; j < r.cols; ++j){
m[i][j] += r.m[i][j];
}
}
return *this;
}
Matrix &operator-= (const Matrix &r){
assert(this->rows == r.rows && this->cols == r.cols);
for (int i = 0; i < r.rows; ++i){
for (int j = 0; j < r.cols; ++j){
m[i][j] -= r.m[i][j];
}
}
return *this;
}
Matrix &operator*= (const Matrix &r){
assert(this->cols == r.rows);
Matrix res(rows, r.cols);
for (int i = 0; i < rows; ++i){
for (int j = 0; j < r.cols; ++j){
for (int k = 0; k < r.rows; ++k){
res[i][j] += m[i][k] * r.m[k][j];
}
}
}
return *this = res;
}
Matrix operator+ (const Matrix &r) const {return Matrix(*this) += r;}
Matrix operator- (const Matrix &r) const {return Matrix(*this) -= r;}
Matrix operator* (const Matrix &r) const {return Matrix(*this) *= r;}
bool operator== (const Matrix &r){
if (rows != r.rows || cols != r.cols) return false;
for (int i = 0; i < r.rows; ++i){
for (int j = 0; j < r.cols; ++j){
if (m[i][j] != r.m[i][j]) return false;
}
}
return true;
}
Matrix& operator+=(const T &r){
for (int i = 0; i < rows; ++i){
for (int j = 0; j < cols; ++j){
m[i][j] += r;
}
}
return *this;
}
Matrix& operator-=(const T &r){
for (int i = 0; i < rows; ++i){
for (int j = 0; j < cols; ++j){
m[i][j] -= r;
}
}
return *this;
}
Matrix& operator*=(const T &r){
for (int i = 0; i < rows; ++i){
for (int j = 0; j < cols; ++j){
m[i][j] *= r;
}
}
return *this;
}
Matrix& operator/=(const T &r){
for (int i = 0; i < rows; ++i){
for (int j = 0; j < cols; ++j){
m[i][j] /= r;
}
}
return *this;
}
Matrix operator+ (const T &r) const {return Matrix(*this) += r;}
Matrix operator- (const T &r) const {return Matrix(*this) -= r;}
Matrix operator* (const T &r) const {return Matrix(*this) *= r;}
Matrix operator/ (const T &r) const {return Matrix(*this) /= r;}
Matrix e(){
assert(this->rows == this->cols);
Matrix res(this->rows, this->rows);
for (int i = 0; i < rows; ++i) res[i][i] = 1;
return res;
}
Matrix pow(long long n){
assert(this->rows == this->cols);
if (n == 0) return e();
Matrix f = pow(n / 2);
Matrix ans = f * f;
if (n % 2 == 1) ans *= *this;
return ans;
}
// for T = int, long long, double, long double
void show(){
for (int i = 0; i < rows; ++i){
for (int j = 0; j < cols; ++j){
cout << m[i][j] << (j+1 == this->cols ? "\n" : " ");
}
}
}
};
} // namespace noya2
#line 78 "c.cpp"
void solve(){
ll l; cin >> l;
int n, m; cin >> n >> m;
vector<int> a(n);
rep(i,m){
int k; cin >> k; k--;
a[k]++;
}
int np = n+1;
auto id = [&](int i, int j){
return i * np + j;
};
Matrix<mint> mat(n*np,n*np);
for (int i = 0; i < n; i++) for (int j = 0; j <= i+1; j++) {
for (int k = 0; k < n; k++){
if (i == k){
if (j == i+1){
mat[id(i,i+1)][id(i,j)]++;
}
else {
mat[id(i,j+1)][id(i,j)]++;
}
}
else if (a[i] == 1){
if (j != i){
mat[id(k,0)][id(i,j)]++;
}
}
else {
mat[id(k,0)][id(i,j)]++;
}
}
}
Matrix<mint> ini(n*np,1);
for (int i = 0; i < n; i++){
ini[id(i,0)][0] = 1;
}
auto f = mat.pow(l-1) * ini;
mint ans = mint(n).pow(l);
for (int i = 0; i < n; i++) for (int j = 0; j <= i+1; j++) {
if (a[i] == 1){
if (j != i){
ans -= f[id(i,j)][0];
}
}
else {
ans -= f[id(i,j)][0];
}
}
out(ans);
}
int main(){
fast_io();
int t = 1; //cin >> t;
while(t--) solve();
}