#include<iostream>
#include<fstream>
using namespace std;
typedef pair<int,int> Point;
template<class T>
class Matrix{
private:
	T* start;
	int row;//行数 
	int col;//列数 
public:
	Matrix(){
		start=NULL;row=0;col=0;
	}

	Matrix(Matrix<T>& m){//拷贝操作 
		row=m.getRow();col=m.getCol();
		start=new T[row*col];
		for(int i=0;i<row;i++){
			for(int j=0;j<col;j++){
				set(i,j,m.get(i,j));
			}
		}
	}
	Matrix(int i,int j){//构造i*j的matrix 
		start = new T[i*j];
		row=i;col=j;
	}
	int getRow(){return row;}//获取行数 
	int getCol(){return col;}//获取列数 
	void init(T t){//用t初始化 
		T* p=start;
		for(int i=0;i<row*col;i++){
			*p++=t;
		}
	}
	T get(int i,int j){return start[i*col+j];}//获取i行j列的数 
	void set(int i,int j,Matrix<T>& m){//设置 i行j列 处 的该块 矩阵为m 
		if(m.getCol()+j>this->col){
			cout<<"size error\n";
			return;
		}
		if(m.getRow()+i>this->row){
			cout<<"size error\n";
			return ;
		}
		for(int k=i;k<i+m.getRow();k++){
			for(int l=j;l<j+m.getCol();l++){
				set(k,l,m.get(k-i,l-j));
			}
		}
	}
	void set(T t){//设置4个顶角的值
		set(0,0,t);set(0,col-1,t);set(row-1,0,t);set(row-1,col-1,t);
	}
	void set(int i,int j,T t){//设置i,j处为t 
		start[i*col+j]=t;
	}
	friend ostream& operator<<(ostream& o,Matrix<T>& m){//输出m 
		m.print(o);
		return o;
	}
	void print(ostream& o){
		for(int i=0;i<row;i++){
			for(int j=0;j<col;j++){
				o<<get(i,j)<<" ";
			}
			o<<endl;
		}
	}
	~Matrix(){
		delete []start;
	}
	Matrix<T> operator*(Matrix<T>& m){//矩阵乘法 
	    if(col!=m.row){cout<<"error ! matrix's col isn't equal the second matrix's row\n";exit(0);}
	    Matrix<T> result(row,m.col);
	    for(int i=0;i<row;i++){
	        for(int j=0;j<m.col;j++){
	            T acc=T();
	            for(int k=0;k<col;k++){
	                acc+=get(i,k)*m.get(k,j);
	            }    
	            result.set(i,j,acc);
	        }    
	    }    
	    return result;
	}    
	Point find(T t){//查找t的位置 
		Point* p=new Point;
		for(int i=0;i<row;i++){
			for(int j=0;j<col;j++){
				if(get(i,j)==t){
					p->first=i;p->second=j;
				}
			}
		}
		return *p;
	}
	Matrix& operator=(Matrix<T>& m){//赋值操作 
		delete []start;
		row=m.getRow();
		col=m.getCol();
		start=new T[row*col];
		for(int i=0;i<row;i++){
			for(int j=0;j<col;j++){
				set(i,j,m.get(i,j));
			}
		}
		return *this;
	}
	friend istream& operator>>(istream& i,Matrix<T>& m){
	    m.input(i);
	    return i;
	    
	}    
	void input(istream& i){
	    for(int j=0;j<row*col;j++){
                i>>start[j];
	    }    
	    
	}    

};
template<typename T, int N>
Matrix<T> power(Matrix<T>& m,int n){//matrix m的n次方
	ifstream f;f.open("E:\\matrix_identity.txt");//matrix_identity中存N*M的单位矩阵
	Matrix<T> result(N,N);f>>result;

    Matrix<T> tmp(N,N);tmp=m;

	for(;n;n>>=1){
		if(n&1){
			result=result*tmp;
		}
		tmp=tmp*tmp;
	}

	return result;

}
int main(){
	ifstream f2;f2.open("E:\\matrix_A.txt");
    Matrix<int> a2(2,2);f2>>a2;
    
	cout<<"fibonaci--a0=1;a1=1\ninput fibonaci's N\n";
	int N;cin>>N;

    Matrix<int> result=power<int,2>(a2,N-1);

	cout<<"result is "<<result.get(0,0)+result.get(1,0)<<endl;// (A[n],A[n-1]) = (A[1],A[0]) * a2^(N-1)

	f2.close();
    
    system("pause");
}    

E:\\matrix_A.txt中存放 1 1

                                        1  0

E:\\matrix_identity中存放 1 0

                                              0 1