結果

問題 No.1847 Good Sequence
ユーザー noya2noya2
提出日時 2023-03-30 22:57:50
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 389 ms / 3,000 ms
コード長 8,632 bytes
コンパイル時間 4,726 ms
コンパイル使用メモリ 277,296 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-09-22 07:46:21
合計ジャッジ時間 8,097 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 AC 167 ms
6,944 KB
testcase_03 AC 2 ms
6,940 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,940 KB
testcase_06 AC 3 ms
6,940 KB
testcase_07 AC 3 ms
6,940 KB
testcase_08 AC 4 ms
6,940 KB
testcase_09 AC 7 ms
6,944 KB
testcase_10 AC 2 ms
6,948 KB
testcase_11 AC 2 ms
6,940 KB
testcase_12 AC 2 ms
6,944 KB
testcase_13 AC 3 ms
6,944 KB
testcase_14 AC 3 ms
6,940 KB
testcase_15 AC 6 ms
6,940 KB
testcase_16 AC 11 ms
6,940 KB
testcase_17 AC 25 ms
6,944 KB
testcase_18 AC 44 ms
6,940 KB
testcase_19 AC 75 ms
6,940 KB
testcase_20 AC 2 ms
6,940 KB
testcase_21 AC 341 ms
6,940 KB
testcase_22 AC 49 ms
6,940 KB
testcase_23 AC 2 ms
6,940 KB
testcase_24 AC 2 ms
6,940 KB
testcase_25 AC 93 ms
6,940 KB
testcase_26 AC 2 ms
6,944 KB
testcase_27 AC 9 ms
6,940 KB
testcase_28 AC 97 ms
6,944 KB
testcase_29 AC 2 ms
6,940 KB
testcase_30 AC 8 ms
6,944 KB
testcase_31 AC 201 ms
6,940 KB
testcase_32 AC 45 ms
6,940 KB
testcase_33 AC 182 ms
6,944 KB
testcase_34 AC 2 ms
6,940 KB
testcase_35 AC 2 ms
6,944 KB
testcase_36 AC 348 ms
6,940 KB
testcase_37 AC 92 ms
6,940 KB
testcase_38 AC 2 ms
6,944 KB
testcase_39 AC 2 ms
6,944 KB
testcase_40 AC 389 ms
6,944 KB
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 # 

#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();
}
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