a) Give a polynomial-time algorithm for minimizing the number of visible boxes in

your apartment.

b) State the asymptotic running time of your algorithm, and give a brief proof of this

running time.

c) Give a proof that your algorithm produces a minimal number of visible boxes.

"The cycle never ends" After the shopping spree of Homework 3, you now have dozens of empty Amazon boxes piled up in your tiny apartment. However, you anticipate that another shopping spree will come as soon as you get paid at the end of the month, and that means more boxes, and you will need to somehow make space for them You realize that you can fit some of the empty boxes inside of other boxes, thus your room space wil only be used by the largest box in each set of nested boxes. Suppose you have n empty boxes, and each box bi has dimensions {4, u, hi}, and a box bi can be nested inside of box bj lf there is a permutation of bi's dimensions {a,b,c} such that a