Given a text T in alphabet $\{$a$,$b$,$c$,$d$\},$ which contains $8$ of a symbols, $2$ of b symbols, $6$ of

c symbols and $4$ of d symbols. Consider the following code A :

CODE A $=$

a $00$

b $01$

c $10$

d $11$

Prove that the prefix code A is not optimal.

Build two prefix codes B and C which are both optimal for a text T $.$

Construct binary trees associated with codes A$,$ B and C$.$