$3.$ Given a hash table with size $7,$ a hash function hash$($x$)=$ x $\%7,$ and keys $5,7,14,1,19,21.$

$($a$)(5$ points$)$ Hash the keys using chaining to resolve collisions. Show your work.

$($b$)(5$ points$)$ Hash the keys using linear probing to resolve collisions. Show your work.

$($c$)(5$ points$)$ Hash the keys using quadratic probing to resolve collisions. Show your work.

$($d$)(5$ points$)$ Hash the keys using double hashing to resolve collisions. Suppose the second hash

function hash$($x$)=3($x $\%3).$ Show your work.

$($e$)(3$ points$)$ What is the load factor after the keys are hashed?