$11\mathrm{.}2\mathrm{.}3$: Efficient trees for prefix codes.

help$\_$outline

Consider the following tree for a prefix code:

$($a$)$

What is the average number of bits per character used in encoding the file?

$($b$)$

Is there a prefix tree for the set $\{$a$,$ b$,$ c$,$ d$,$ e$,$ f$\}$ that would result in fewer bits per character on average for the given frequencies of the characters?