rectangles

#include <vector>
#include <algorithm>
#include <iostream>

using namespace std;
const int N = 5;

int mask2bits[1 << N];
int mask2bitsAllSet = 0; // 1023 = 1111111111 binary

// count the number of bits set in x
int popcnt( int x )
{
   return x ? popcnt(x&(x-1))+1 : 0;
}

//
void initMask2bits()
{
   int ct = 0;
   for ( int i = 0; i < (1<<N); i++ )
   {
      int pop = popcnt( i );
      mask2bits[i] = pop == 2 ? 1 << ct++ : 0;
   }
   mask2bitsAllSet = (1<<ct)-1;
}

bool check( int a[], int b[] )
{
   int m = 0;
   int masky = 0;
   // scan top-to-bottom left-to-right
   for ( int y = 0; y < N*2; y++ )
   {
      masky ^= 1 << b[y]; // masky keeps track of which rectangles are currently on, considering only y-coordinate
                          // 00001 (binary) means just rectangle 0
                          // 00010 (binary) means just rectangle 1
                          // 00011 (binary) means just rectangle 0 and 1
      int maskx = 0;
      for ( int x = 0; x < N*2; x++ )
      {
         maskx ^= 1 << a[x]; // masky keeps track of which rectangles are currently on, considering only y-coordinate
         m |= mask2bits[maskx&masky]; // maskx&masky determines which rectangles are active at x,y
                                      // if that value has exactly 2 bits set, we keep track of that in 'm'
                                      // 'm' is another bitmask with 10 positions that must be set for a winner
      }
   }
   return m == mask2bitsAllSet;
}
int main(int n,char**p)
{
   initMask2bits();
   int a[] = {0,1,2,3,4,0,1,2,3,4}; // relative order of rectangle start or stop on x-axis
   int b[] = {0,1,2,3,4,0,1,2,3,4}; // relative order of rectangle start or stop on y-axis
   int x = 0;
   do {
      do {
         do { // for every permutation of first/last 5 elements of y and last 5 elements of x
            if ( check( a, b ) ) // check if we have a winner
            {
               for ( int i = 0; i < N*2; i++ ) cout << a[i] << " "; cout << endl;
               for ( int i = 0; i < N*2; i++ ) cout << b[i] << " "; cout << endl;
               return 0;
            }
         } while( next_permutation( b+N, b+N*2 ) );
      } while( next_permutation( b+0, b+N ) );
   } while( next_permutation( a+N, a+N*2 ) );
   cout << "found no match" << endl;
   return 0;
}