$2.(5$ points$)$ Suppose we have a hash table of size $29$ and we want to implement a system for looking

up a friend$$s information given his$/$her name. Which of the following hash functions is the best?

Justify your choice. $($Assuming none of the names is empty.$)$ Short Answer and Letter choice

$($a$)$ h$($x$)=$ x

$($b$)$ h$($x$)=$ n $\%13,$where n is the number of characters in x

$($c$)$ h$($x$)=($ord$($x$[0])+$ ord$($x$[1]))\%29,$ where x$[0]$ is the first character in the name and x$[1]$

is the last.

$($d$)$ h$($x$)=29$

n

$($e$)$ h$($x$)=$

$$

i$=0$

ord$($x$[$i$]),$ where n is the number of characters in x$,$ x$[$i$]$ the ith character in x$,$

and ord$($c$)$ returns the ordinal value of a character. $($Instruction on the $\backslash$Sigma summation symbol