$[5$ points.$]$ Consider a hashtable implementation using separate chaining of unsorted linked lists with $N$ buckets $($table size$)$ and $k$ items currently in the table.

$($a$)$ Which of the following is true?

i$.kNk>NkN2NkNk$ must hold

$ii.kN$ must hold

iii. Neither

$(b)$ What $is$ the average number $of$ items $in$ a bucket?

$(c)In$ the worst$-$case, how many items could $bein$ a single bucket?

$(d)$ Given that $k>N,$ which $of$ the following are true?

$i.$ Some buckets may $be$ empty

$ii.$ Some buckets may $be$ full $so$ that they cannot receive more items

iii. Neither

$(e)$ What $is$ the worst case running time $in$ terms $ofk$ and $N$ for finding the minimum value $in$ the table?

$(f)$ What $is$ the worst case run time for inserting a new item $in$ the table $?$

$(g)Ifwe$ resize the table $to$ a table $of$ size $2N,$ what $is$ the worst case running time $in$ terms $ofk$ and $Nto$ put all the items $in$ the new table?