$($a$)$ Give the definitions of P$,$ NP$,$ NP$-$complete, NP$-$hard.

$($b$)$ For the knapsack problem. Give the differences in its versions $($definition and complexity$).$

$($c$)$ Is the fractional knapsack problem solvable in polynomial time? If yes, give algorithm. If not, why?

$($d$)$ Is the integer knapsack problem solvable in polynomial time? If yes, give algorithm. If not, why?

$($e$)$ What are pseudo$-$polynomial algorithms? Give an example.