#include <iostream>
using namespace std;

class Mat22//the class for 2 by 2 matrices
{

public:

    Mat22(){// default constructor
      input(0,0,0,0);
    };

    Mat22(int ma,int mb, int mc, int md):// set the matrix as  the input
      ma(ma),
      mb(mb),
      mc(mc),
      md(md)
    {};

    Mat22(const Mat22 &b):// copy constructor
      ma(b.ma),
      mb(b.mb),
      mc(b.mc),
      md(b.md)
    {};

    Mat22 operator=(const Mat22 &b){// assignment operator
      ma = b.ma;
      mb = b.mb;
      mc = b.mc;
      md = b.md;
      return *this;
    };

    Mat22 operator+(const Mat22 &b){// add two matrices
      Mat22 temp;
      temp.ma = ma + b.ma;
      temp.mb = mb + b.mb;
      temp.mc = mc + b.mc;
      temp.md = md + b.md;
      return temp;
    };

    Mat22 operator-(const Mat22 &b){//subtract two matrices
      Mat22 temp;
      temp.ma = ma - b.ma;
      temp.mb = mb - b.mb;
      temp.mc = mc - b.mc;
      temp.md = md - b.md;
      return temp;
    };

    Mat22 operator*(const Mat22 &b){//multiply two matrices
      Mat22 temp = *this; //creating temporary Mat22 obj and assigning value of LHS to it
      Mat22 temp2;        //creating second temporary Mat22 obj to avoid lvalue and rvalue issues
      temp2.ma = (temp.ma * b.ma) + (temp.mb * b.mc);
      temp2.mb = (temp.ma * b.mb) + (temp.mb * b.md);
      temp2.mc = (temp.mc * b.ma) + (temp.md * b.mc);
      temp2.md = (temp.mc * b.mb) + (temp.md * b.md);
      return temp2;
    };

    Mat22 FastExp(Mat22 &b, int n){// compute matrix to the power of n
      Mat22 temp(1,0,0,1);         //creating temp matrix with value of one (in matrix form)

      if(n==0){  //base case, returns "one" (in matrix)
        return temp;
      }

      else if(n%2==0){ //even n conditional, recursive call
        temp = FastExp(b, n/2);
        temp = temp*temp; //squaring temp prior to return
        return temp;
      }

      else if(n%2==1){ //odd n conditional, also recursive
        temp = FastExp(b, (n-1)/2);
        temp = temp*temp;
        return temp*b;  //multiplying by b to compensate for the (n-1)/2 recursive call
      }
    };

    void display(ostream &out) const{// print the matrix, whatever way you like as long as it makes sense
      out << "Values: " << endl;
      out << "a: " << ma << endl;
      out << "b: " << mb << endl;
      out << "c: " << mc << endl;
      out << "d: " << md << endl;
    };

    int display(int n){ //overload display to return specified private int from matrix obj
      if(n==0){ //conditionals for each int
        return ma;
      }
      else if(n==1){
        return mb;
      }
      else if(n==2){
        return mc;
      }
      else if(n==3){
        return md;
      }
    };

    void input(istream &in){//function to ask for input for 2x2 matrices variables
      cout << "Please enter values one a time for your matrix, starting with a:" << endl;
      in >> ma >> mb >> mc >> md;
    };

    Mat22 input(int a, int b, int c, int d){//overloaded input function for individual variable explicit input
      ma = a, mb = b, mc = c, md = d;
      return *this;
    };

private:

    int ma,mb,mc,md;// store matrix  [ma,mb]
                    //               [mc,md]
};


ostream& operator<<(ostream &out, const Mat22 &b){ //chainable << operator
  b.display(out); //uses display fx, passing first param of << op to display
  return out;
};

istream& operator>>(istream &in, Mat22 &b){ //chainable >> operator
  b.input(in); //input fx is passed first param of >> op
  return in;
};

int FastFib(int n){ //retrieve the nth term of the fibonacci sequence
  Mat22 FibMat(1,1,1,0); //using one of default constructors to build an appropriate matrix for sequence
  FibMat = FibMat.FastExp(FibMat, n);
  return FibMat.display(1); //using overloaded display function to access private int
};


int main()
{
  //some test matrices
  Mat22 T1(1,2,3,4);
  Mat22 T2(4,3,2,1);
  Mat22 T3(5,5,5,5);
  Mat22 T4(1234,5678,9101,1121);

  //retrieving n value from user for testing
  int n;
  cout << "Please enter your value for n (used in both FastExp and FastFib): ";
  cin >> n;

  //testing FastExp
  cout << "***FASTEXP TEST***" << endl << "Starting Matrix " << T1;
  T1 = T1.FastExp(T1, n);
  cout << "To the power of " << n << ":" << endl << "Final " << T1 << endl;

  //testing FastFib
  cout << endl << "***FASTFIB TEST***" << endl;
  int g;
  g = FastFib(n);
  cout << "Term " << n << " of the Fibonacci sequence is : " << g << endl;

  //testing overloads
  cout << endl << "***OVERLOAD TEST***" << endl;
  //testing assignment
  T4 = T3;
  cout << T4;
  //testing subtraction and modification of only LHS
  T3 = T2-T3;

  cout << T2;
  //testing chained >> and <<
  cin >> T2 >> T3;
  cout << T2 << T3;

  return 0;
};