We have a source $x,n=|x|$ such that AAxinx,$p(x)=\frac{1}{n}.$ Let $C$ be a Huffman Code of $x.$

$4+(2+1+1)=8$

$($a$)$ Prove that AAxinx,$|$~$lo{g}_{2}n$~$|-|C(x)|in\{0,1\}.$

$($b$)$ Compute $L(C),(C),$ and $(C)$ as a functions of $n.$