#381796 (C++14) No.891 隣接3項間の漸化式

• 問題: No.891 隣接3項間の漸化式
• ユーザー: otamay6
• 提出日時: 2019-09-20 23:13:21
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 8,041 bytes
• コンパイル時間: 1,989 ms
• コンパイル使用メモリ: 181,756 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-14 19:59:36
• 合計ジャッジ時間: 3,157 ms
• ジャッジサーバーID （参考情報）: judge2 / judge3

ファイルパターン	結果
sample	AC * 3
other	AC * 39

ソースコード

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#include<bits/stdc++.h>
#define REP(i,n) for(int i=0,i##_len=(n);i<i##_len;++i)
#define rep(i,a,b) for(int i=int(a);i<int(b);++i)
#define All(x) (x).begin(),(x).end()
using namespace std;
typedef long long ll;
constexpr ll mod=1e9+7;
constexpr double eps=1e-9;
class mint {
 private:
  ll _num,_mod;
  mint set(ll num){ 
      _num = num ;
      if(_num>=0) _num%=_mod;
      else _num+=(1-(_num+1)/_mod)*_mod; 
      return *this;
  }
  ll _mpow(ll x, ll n){ //x^n(mod) ←普通にpow(x,n)では溢れてしまうため，随時mod計算 2分累乗法だから早い
    ll ans = 1;
    while(n != 0){
        if(n&1) ans = ans*x % _mod;
        x = x*x % _mod;
        n = n >> 1;
    }
    return ans;
  }
  ll imod(ll n){return _mpow(n , _mod-2);}
 public:
  mint(){ _num = 0;_mod=mod; }
  mint(ll num){ _mod = mod; _num = (num+(1LL<<25)*mod) % mod; }
  mint(ll num,ll M){ _mod=M;_num=(num+(1LL<<25)*mod)%_mod; }
  mint(const mint &cp){_num=cp._num;_mod=cp._mod;}
  mint operator= (const ll x){ return set(x); }
  mint operator+ (const ll x){ return mint(_num + (x % _mod) , _mod); }
  mint operator- (const ll x){ return mint(_num - (x % _mod), _mod); }
  mint operator* (const ll x){ return mint(_num * (x % _mod) , _mod); }
  mint operator/ (ll x){ return mint(_num * imod(x) , _mod);}
  mint operator+=(const ll x){ return set(_num + (x % _mod)); }
  mint operator-=(const ll x){ return set(_num - (x % _mod)); }
  mint operator*=(const ll x){ return set(_num * (x % _mod)); }
  mint operator/=(ll x){ return set(_num * imod(x));}
  mint operator+ (const mint &x){ return mint(_num + x._num , _mod); }
  mint operator- (const mint &x){ return mint(_num - x._num , _mod);}
  mint operator* (const mint &x){ return mint(_num * x._num , _mod); }
  mint operator/ (mint x){ return mint(_num * imod(x._num) , _mod);}
  mint operator+=(const mint &x){ return set(_num + x._num); }
  mint operator-=(const mint &x){ return set(_num - x._num); }
  mint operator*=(const mint &x){ return set(_num * x._num); }
  mint operator/=(mint x){ return set(_num * imod(x._num));}
  bool operator<(const mint &x)const{return _num<x._num;}
  bool operator==(const mint &x)const{return _num==x._num;}
  bool operator>(const mint &x)const{return _num>x._num;}
  friend mint operator+(ll x,const mint &m){return mint(m._num + (x % m._mod) , m._mod);}
  friend mint operator-(ll x,const mint &m){return mint( (x % m._mod) - m._num , m._mod);}
  friend mint operator*(ll x,const mint &m){return mint(m._num * (x % m._mod) , m._mod);}
  friend mint operator/(ll x,mint m){return mint(m.imod(m._num) * x , m._mod);}
  explicit operator ll() { return _num; }
  explicit operator int() { return (int)_num; }
  friend ostream& operator<<(ostream &os, const mint &x){ os << x._num; return os; }
  friend istream& operator>>(istream &is, mint &x){ll val; is>>val; x.set(val); return is;}
};
template<typename T> class MAT{
 private:
    int row,col;
    vector<vector<T>> _A;
    MAT set(vector<vector<T>> A){_A = A ; return *this;}
    
 public:
    MAT(){ }
    MAT(int n,int m){
        if(n<1 || m<0){cout << "err Matrix::Matrix" <<endl;exit(1);}
        row = n;
        col = m?m:n;//m=0のとき単位行列を作る
        REP(i,row){
            vector<T> a(col,0.0);
            _A.push_back(a);
        }
        //  値の初期化
        if(m==0) REP(i,n) _A[i][i]=1.0;
    }
    MAT(const MAT &cp){_A=cp._A;row=cp.row;col=cp.col;}
    T* operator[] (int i){return _A[i].data();}
    MAT operator= (vector<vector<T>> x) {return set(x);}
    MAT operator+ (MAT x) {
        if(row!=x.row || col!=x.col){
            cout << "err Matrix::operator+" <<endl;
            cout << "  not equal matrix size" <<endl;
            exit(0);
        }
        MAT r(row, col);
        REP(i,row) REP(j,col) r[i][j]=_A[i][j]+x[i][j];
        return r;
    }
    MAT operator- (MAT x) {
        if(row!=x.row || col!=x.col){
            cout << "err Matrix::operator-" <<endl;
            cout << "  not equal matrix size" <<endl;
            exit(0);
        }
        MAT r(row, col);
        REP(i,row) REP(j,col) r[i][j]=_A[i][j]-x[i][j];
        return r;
    }
    MAT operator* (MAT x) {
        if(col!=x.row){
            cout << "err Matrix::operator*" <<endl;
            cout << "  not equal matrix size" <<endl;
            exit(0);
        }
        MAT r(row, x.col);
        REP(i,row) REP(j,x.col) REP(k,col) r[i][j]+=_A[i][k]*x[k][j];
        return r;
    }
    MAT operator/ (T a){
        MAT r(row,col);
        REP(i,row) REP(j,col) r[i][j]=_A[i][j]/a;
        return r;
    }
    MAT operator^ (ll n){
        if(row!=col){
            cout << "err Matrix::operator^" <<endl;
            cout << "  not equal matrix size" <<endl;
            exit(0);
        }
        MAT r(row,0),A=*this;
        while(n){
            if(n&1) r *= A;
            A*=A;
            n>>=1;
        }
        return r;
    }
    MAT operator+= (MAT x) {
        if(row!=x.row || col!=x.col){
            cout << "err Matrix::operator+=" <<endl;
            cout << "  not equal matrix size" <<endl;
            exit(0);
        }
        MAT r(row, col);
        REP(i,row) REP(j,col) r[i][j]=_A[i][j]+x[i][j];
        return set(r._A);
    }
    MAT operator-= (MAT x) {
        if(row!=x.row || col!=x.col){
            cout << "err Matrix::operator-=" <<endl;
            cout << "  not equal matrix size" <<endl;
            exit(0);
        }
        MAT r(row, col);
        REP(i,row) REP(j,col) r[i][j]=_A[i][j]-x[i][j];
        return set(r._A);
    }
    MAT operator*= (MAT x) {
        if(col!=x.row){
            cout << "err Matrix::operator*" <<endl;
            cout << "  not equal matrix size" <<endl;
            exit(0);
        }
        MAT r(row, x.col);
        REP(i,row) REP(j,x.col) REP(k,col) r[i][j]+=_A[i][k]*x[k][j];
        return set(r._A);
    }
    MAT operator/=(T a){
        MAT r(row,col);
        REP(i,row) REP(j,col) r[i][j]=_A[i][j]/a;
        return r;
    }
    friend MAT operator* (T n,MAT x){
        MAT r(x.row,x.col);
        REP(i,x.row) REP(j,x.col) r[i][j]=n*x[i][j];
        return r;
    }
    friend MAT operator* (MAT x,T n){
        MAT r(x.row,x.col);
        REP(i,x.row) REP(j,x.col) r[i][j]=n*x[i][j];
        return r;
    }
    explicit operator vector<vector<T>>(){return _A;}
    friend ostream &operator<<(ostream &os,const MAT &x){ REP(i,x.row) REP(j,x.col) os<<x._A[i][j]<<" \n"[j==x.col-1]; return os;}
    friend istream &operator>>(istream &is,MAT &x){REP(i,x.row) REP(j,x.col) is>>x._A[i][j];return is;}
    int size_row(){return row;}
    int size_col(){return col;}
    MAT transpose(){
        MAT r(col,row);
        REP(i,col) REP(j,row) r[i][j]=_A[j][i];
        return r;
    }
    MAT inverse(){
        T buf;
        MAT<T> inv_a(row,0);
        vector<vector<T>> a=_A;
        //掃き出し法
        REP(i,row){
            buf=1/a[i][i];
            REP(j,row){
                a[i][j]*=buf;
                inv_a[i][j]*=buf;
            }
            REP(j,row){
                if(i!=j){
                    buf=a[j][i];
                    REP(k,row){
                        a[j][k]-=a[i][k]*buf;
                       inv_a[j][k]-=inv_a[i][k]*buf;
                    }
                }
            }
        }
        return inv_a;
    }
    // O( n^3 ).
    int rank() {
        vector<vector<T>> A=_A;
        const int n = row, m = col;
        int r = 0;
        for(int i = 0; r < n && i < m; ++i) {
            int pivot = r;
            for(int j = r+1; j < n; ++j) if(fabs(A[j][i]) > fabs(A[pivot][i])) pivot = j;
            swap(A[pivot], A[r]);
            if(fabs(A[r][i]) < eps) continue;
            for (int k = m-1; k >= i; --k) A[r][k] /= A[r][i];
            rep(j,r+1,n) rep(k,i,m) A[j][k] -= A[r][k] * A[j][i];
            ++r;
        }
        return r;
    }
};
int main(){
    MAT<mint> x(2,1),A(2,2);
    ll a,b,n;cin>>a>>b>>n;
    A[0][0]=a;A[0][1]=b;A[1][0]=1;
    x[0][0]=1;x[1][0]=0;
    x=(A^n)*x;
    cout<<x[1][0]<<endl;
}
 
 
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