3. The following problems deal with the concept of Huffman Coding. (a) Suppose your friend tells you that they have written a program to generate Huffman codes. You test it out by entering the text of Wuthering Heights, and it generates the following codes for the first several letters of the alphabet: Letter Code a b d 01 00101 101 00111 1 000 0011 e f Even without knowing the exact distribution of letters in Wuthering Heights, you are immediately suspicious of your friend's program. Explain why this is not a possible valid set of Huffman codes. (b) Generate Huffman codes for the following set of letters with their given frequencies. Show your work by writing out the list of nodes and their respective frequencies available at each step. You can refer to nodes containing multiple letters in their subtree using a capitalized list of letters in alphabetical order, for example, if after some step you had a node representing a subtree containing a and e with frequency 0.6, you could refer to it in your list as (AE,0.6). Don't forget to list the final codes at the end! Letter Frequency a b d 0.25 0.15 0.2 0.05 0.35 e