結果

問題 No.891 隣接3項間の漸化式
ユーザー otamay6otamay6
提出日時 2019-09-20 23:13:21
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
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
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
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 2 ms
5,376 KB
testcase_13 AC 2 ms
5,376 KB
testcase_14 AC 2 ms
5,376 KB
testcase_15 AC 2 ms
5,376 KB
testcase_16 AC 2 ms
5,376 KB
testcase_17 AC 2 ms
5,376 KB
testcase_18 AC 2 ms
5,376 KB
testcase_19 AC 2 ms
5,376 KB
testcase_20 AC 2 ms
5,376 KB
testcase_21 AC 2 ms
5,376 KB
testcase_22 AC 2 ms
5,376 KB
testcase_23 AC 2 ms
5,376 KB
testcase_24 AC 2 ms
5,376 KB
testcase_25 AC 2 ms
5,376 KB
testcase_26 AC 2 ms
5,376 KB
testcase_27 AC 2 ms
5,376 KB
testcase_28 AC 2 ms
5,376 KB
testcase_29 AC 2 ms
5,376 KB
testcase_30 AC 2 ms
5,376 KB
testcase_31 AC 2 ms
5,376 KB
testcase_32 AC 2 ms
5,376 KB
testcase_33 AC 2 ms
5,376 KB
testcase_34 AC 2 ms
5,376 KB
testcase_35 AC 2 ms
5,376 KB
testcase_36 AC 2 ms
5,376 KB
testcase_37 AC 2 ms
5,376 KB
testcase_38 AC 2 ms
5,376 KB
testcase_39 AC 2 ms
5,376 KB
testcase_40 AC 2 ms
5,376 KB
testcase_41 AC 2 ms
5,376 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 # 

#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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