Suppose we have an optimal prefix code on a set c={0,-1} of characters and we wish to transmit this code using as few bits as possible. show how to represent any optimal prefix code on c using only 2n -1 + n[lgn]. (hint: use 2n -1 bits to specify the structure of the tree, as discovered by a walk of the tree.)

Scientists have changed the model of the atom as they have gathered new evidence. one of the atomic models is shown below. what experimental evidence led to the development of this atomic model from the one before it? a few of the positive particles aimed at a gold foil seemed to bounce back. the colors of light emitted from heated atoms had very specific energies. experiments with water vapor showed that elements combine in specific proportions. cathode rays were bent in the same way whenever a magnet was brought near them.