$5$ You are a space explorer preparing for a mission to a distant planet. Your spacecraft has limited cargo space, and

you need to choose equipment and supplies to bring with you while maximizing the total "Utility" of the items

within this space.

$\backslash$table$[[$SN$,$Item name,Size $($Cubic meters$),$Utility $($Galactic credits$)],[1,$Dried Meat,$3,150],[2,$Bionic Suit,$5,200],[3,$Lightsaber,$2,100],[4,$Space Gun,$7,300],[5,$MRE $($Meal$-$Ready$-$to$-$Eat$),4,180]]$

$5$

Your spacecraft's cargo hold can accommodate a maximum volume of $10$ cubic meters. Using Dynamic Programming, determine the optimal combination of items to pack that maximizes the total utility without exceeding the volume limit of your cargo hold, providing the names of the items taken and the maximum utility.

What is the time complexity of the $\frac{0}{1}$ knapsack problem if we try to solve it using $($I$)$ Brute force, and $($II$)$ Dynamic

$1$

programming?