/*
Chad Brewbaker

This program enumerates the co-efficents for pairs of hypercube cycle about the all zero configurations.


Example:    10|00|01 =1 pair, 100|000|010,100|000|001,001|000|010 =3 pairs

We need to fill in the other information between the basis vectors. This is the co-efficent we want to find.



*/



#include <iostream.h>


int VEC[10][100];
int DIM;//The alphabet length of our cycle: 101=3, 11001=5
int COUNT;
int PLACE_SUM[10];


void printStuff(int depth)
{
  int i,j;

  for(i=0;i<DIM;i++)
    if(VEC[i][depth-1]%2)
      PLACE_SUM[i]++;
  for(i=0;i<=depth;i++)
    {
      cout<<"\n";
      for(j=0;j<DIM;j++)
	cout<<VEC[j][i]%2<<" ";
    }
  return;
}

void traverse(int depth)
{
  int i,j,k;
  int done,sameCount;
  
  cout <<"\nDepth "<<depth<<": ";
  for(i=0;i<DIM;i++)
    cout<<VEC[i][depth]<<"  ";

  sameCount=0;
  for(j=0;j<DIM;j++)
    sameCount+=VEC[j][depth];
  if(sameCount==2*DIM)
    {COUNT++; printStuff(depth+1);cout<<"\n COUNT_RETURN";return;}


  //copy me to the next depth
  for(i=0;i<DIM;i++)
    VEC[i][depth+1]=VEC[i][depth];
  
  for(i=0;i<DIM;i++)
    {      
      //Don't write to a position more than twice
      if(VEC[i][depth]==2)
	continue;
      VEC[i][depth+1]++;
      //Either add a new letter...
      if(VEC[i][depth]==0)
	{cout<<"\nADD_RETURN:"<<depth<<"."<<i; traverse(depth+1);return;}
      //OR: Delete an added letter,not getting an earlier vector
   
      
      //In case we are done...
      sameCount=0;
      for(j=0;j<DIM;j++)
	sameCount+=VEC[j][depth+1];
      if(sameCount==2*DIM)
	{COUNT++; printStuff(depth+1);cout<<"\n COUNT_RETURN";return;}
      
      //OR: Delete an added letter,not getting an earlier vector
      done=1;
      for(j=0;j<=depth;j++)
	{
	  sameCount=0;
	  for(k=0;k<DIM;k++)
	    {
	      if((VEC[k][j]%2)==(VEC[k][depth+1]%2))
		sameCount++;
	    }
	  if(sameCount==DIM)
	    {done=0;break;}
	}
      if(done)
	{cout<<"\nDelete:"<< depth<<"."<<i;traverse(depth+1);}
      //Clean up
      VEC[i][depth+1]--;
    }
  cout <<"\n NAUGHTY_RETURN"<<depth;
  //printStuff(depth+1);
  return;
}




int main()
{
  int i,j,k; 
  cout<<"\nInput a dimension:";
  cin >>DIM;
  COUNT=0;
  for(i=0;i<DIM;i++)
    PLACE_SUM[i]=0;

  for(i=0;i<DIM;i++)
    VEC[i][0]=VEC[i][1]=0;
  VEC[0][1]=1;
  traverse(1);

  cout<<"\n\n Count:"<<COUNT<<"\n";
  for(i=0;i<DIM;i++)
    cout <<PLACE_SUM[i]<<"\t";
  cout <<"\n";

  return 0;
}