Problem 75: Transformations

Failed a quite few times, as usual...

This one requires a variable-sized matrix to be rotated/flipped. I just had to check every operation in the order provided. The analysis wastes more approximately 7 times memory than mine; thus, I consider mine is better.

/*
ID: victor4
PROG: transform
LANG: C++
*/
#include <iostream>
#include <fstream>
#include <string>

using namespace std;

template <class T>
struct matrix{
 int sz;
 T **storage;
 
 matrix(int sz) : sz(sz){
  storage = new T*[sz];
  for(int i = 0; i < sz; ++i)
   storage[i] = new T[sz];
 }
 ~matrix() {
  for(int i = 0; i < sz; ++i)
   delete[] storage[i];
  delete[] storage;
 }
 
 bool operator == (const matrix &t){
  for(int x = 0; x < sz; ++x)
   for(int y = 0; y < sz; ++y)
    if(storage[x][y] != t.storage[x][y])
     return false;
  return true;
 }
 
 void rot90(){ // clockwise
  T old[sz][sz];
  for(int x = 0; x < sz; ++x)
   for(int y = 0; y < sz; ++y)
    old[x][y] = storage[x][y];
  for(int x = 0; x < sz; ++x)
   for(int y = 0; y < sz; ++y)
    storage[x][y] = old[y][sz-1-x];
 }
 
 void reflect_h(){
  T old[sz][sz];
  for(int x = 0; x < sz; ++x)
   for(int y = 0; y < sz; ++y)
    old[x][y] = storage[x][y];
  for(int x = 0; x < sz; ++x)
   for(int y = 0; y < sz; ++y)
    storage[x][y] = old[x][sz-1-y];
 }
};

int main() {
 ofstream fout ("transform.out");
 ifstream fin ("transform.in");
 
 int N;
 fin >> N;
 
 // read matrices
 matrix<char> m1(N), m2(N);
 for(int x = 0; x < N; ++x){
  string in;
  fin >> in;
  for(int y = 0; y < N; ++y){
   m1.storage[x][y] = in[y];
  }
 }
 
 for(int x = 0; x < N; ++x){
  string in;
  fin >> in;
  for(int y = 0; y < N; ++y){
   m2.storage[x][y] = in[y];
  }
 }
 
 m1.rot90();
 if(m1 == m2)
  fout << 1;
 else{
  m1.rot90();
  if(m1 == m2)
   fout << 2;
  else{
   m1.rot90();
   if(m1 == m2)
    fout << 3;
   else{
    m1.rot90(); // back where we started!
    m1.reflect_h();
    if(m1 == m2)
     fout << 4;
    else{
     bool found = false;
     for(int i = 0; i < 3; ++i){
      m1.rot90();
      if(m1 == m2){
       found = true;
       fout << 5;
       break;
      }
     }
     if(!found){
      m1.rot90();
      fout << ((m1 == m2) ? 6 : 7);
     }
    }
   }
  }
 }
 
 fout << endl;
 return 0;
}