Jesse wants to know the minimum number of bags needed to fill an

order of $n8$ kilos assuming unlimited supply of bags of sizes $3,5$

and $8$ kilos. Let $f(n)$ be the minimum number of bags needed.

$($a$)$ Write a recurrence relation for $f(n).$ Hint: Use the minimum

function in your recurrence relation; it may also be useful to use

the value $$ for some of your base cases.

$($b$)$ Use your recurrence relation to fill in an array of $f(n)$ values for

nin$[0,16].$

$($c$)$ Describe an algorithm to compute $f(n)$ for any given $n$ using

your recurrence relation. What is the runtime of your algorithm?

How might you augment your algorithm to return the actual set

of bags used to achieve the minimum value $f(n)?$ Hint: you can

put back$-$arrows in your array.