$2.$ Huffman Codes $(3$ points$)$

Based on the textbook explanation, do what is asked for the following file content. Note that the exercise is case sensitive$.$ Use the $""$ symbol to represent blank spaces and the ASCII table as a frequency tiebreaker. In case $\backslash ($ z $\backslash ).$freq is equal to a value already contained in the queue, it will be placed at the end of the values that equal it$.$ Example: Assume that $\backslash ($ z $.$ f r e q$=2\backslash )$ and the current content of the queue is $\backslash ($ Q$[$a: $2$ b: $2$ c: $2$ f: $3]\backslash ),$ the node is inserted as: $\backslash ($ Q$[$a: $2$ b: $2$ c: $2\backslash )(2)\backslash ($ f: $3]\backslash )$

File $1$: $\backslash (\backslash$quad $\backslash )$ This is an exercise

$($a$)$ Tree

$($b$)$ Prefix$-$free code for each character

$($c$)$ What is the cost of the tree?

$(0\mathrm{.}7$ points$)$

$($d$)$ Encode the file

$(0\mathrm{.}3$ points$)$

$(0\mathrm{.}2$ points$)$

$(0\mathrm{.}3$ points$)$

File $2$:

David A$.$ Huffman

$($a$)$ Tree

$(0\mathrm{.}7$ points$)$

$($b$)$ Prefix$-$free code for each character

$(0\mathrm{.}3$ points$)$

$($c$)$ What is the cost of the tree?

$(0\mathrm{.}2$ points$)$

$($d$)$ Encode the file

$(0\mathrm{.}3$ points$)$