You have n boxes with square bases, the i-th box has height hi, each side of the base has length si, and the weight of the box is wi. You can stack box j on top of box k if sj sk and wj wk. So you can only stack a box on top of another if its both no heavier and has a base no bigger.

Let H(i) be the tallest stack of boxes you can build. The tallest stack of boxes that you can build with box j on the top is

The overall maximum height stack will be

A. Using pesudocode, implement a dynamic programming solution to this problem.

B. Analyze the running time of the dynamic programming algorithm.

H(j) = max(H (i)) + h KJ wi2WJ sizsj