Given a hash table with size $9,$ a hash function hash $(x)=x\%9,$ and keys $1,3,5,7,14,11,19,21.$

$($a$)(9$ points$)$ Hash the keys using chaining to resolve collisions. Show your work.

$($b$)(9$ points$)$ Hash the keys using linear probing to resolve collisions. Show your work.

$($c$)(9$ points$)$ Hash the keys using quadratic probing to resolve collisions. Show your work.

$($d$)(9$ points$)$ Hash the keys using double hashing to resolve collisions. Suppose the second hash

function $has{h}^{\text{'}}(x)=5-(x\%5).$ Show your work.

$($e$)(4$ points, one each$)$ What is the load factor after the keys are hashed? $($For each collision

strategy, state whether or not it would be too full. $)$