Recall the rod cutting problem we discussed in class and in the book. While it might be possible for a theoretical person to cut the rod of length n, up to n times to achieve the maximum possible sale value, enterprising children do not possess the stamina to cut the rod so many times. They instead get tired or bored after only k cuts. Design a dynamic programming algorithm to maximize the value of selling cut rods if at most we can cut the rod k times. Please use elements in the table P to calculate the value of a continuous rod, e.g. an uncut rod of length i has value pi. Further you should analyze: 1. The time complexity of a baseline solution that does not use dynamic programming or memoization that exhaustively explores all potential solutions 2. The time complexity of your dynamic programming solution 3. Describe how you could change your algorithm to so to reconstruct the actual cuts in order achieve the highest value for the rod pieces.

Recall the rod cutting problem we discussed in class and in the book. While it might be possible for a theoretical person to cut the rod of length n, up to n times to achieve the maximum possible sale value, enterprising children do not possess the stamina to cut the rod so many times. They instead get tired or bored after only k cuts. Design a dynamic programming algorithm to maximize the value of selling cut rods if at most we can cut the rod k times. Please use elements in the table P to calculate the value of a continuous rod, e.g. an uncut rod of length i has value pi. Further you should analyze: 1. The time complexity of a baseline solution that does not use dynamic programming or memoization that exhaustively explores all potential solutions 2. The time complexity of your dynamic programming solution 3. Describe how you could change your algorithm to so to reconstruct the actual cuts in order achieve the highest value for the rod pieces.