Questions:
   1. When is top-down much faster than bottom-up?
      give me an instance where top-down is 5 times faster than bottom-up.
      (you need to provide the input, output, running times, 
      and number of non-zero cells in opt in each of the two approaches).

   2. When is bottom-up much faster than top-down?
      give me an instance where bottom-up is 5 times faster.

   3. Would your top-down or bottom-up work if the weights are float numbers?
      if not, how would you adapt them to float numbers?
