Huffman Coding. The following table lists the character frequencies in a file.

$($a$)$ Apply Huffman's algorithm to the data, and draw the prefix code tree. The

leaves should be annotated with the characters and their frequencies, and internal nodes

should be annotated with the total frequencies of their subtrees. When merging two

subtrees, put the lower$-$frequency subtree on the left. Please make a series of drawings

by hand that show all your work from forest to complete tree. Please do not use a

graphics program.

$($b$)$ Fill out the following table with the Huffman codes for each character. On the

prefix code tree, a left branch is $0,$ and a right branch is $1.$ Assemble the code for each

leaf node character by reading the branch numbers from top to leaf node.

You can draw the Huffman tree by hand, take a picture and include the image in the PDF

file of your submission.