3. (Basic) Consider a sequence of integers defined by the following recurrence: f(0) 0,f(1) 1, and f(i) J(i 1) +f(n -2) +J(n -3) (1) (0) for i 2. We would like to compute J(n) using a bottom-up DP method. Describe the DP and analyze its running time . Intermediate) Consider a modification of the rod-ctting problem in which, in addition to a price p for each rod, each cut incurs a fixed cost of c. The revenue associated with a solution is now the sum of the prices of the picces minus the costs of making the cuts. For simplicity, we will be only interested in computing the optimum. (a) Recall that if c-0, then we would have the same recursion we had for the original rod-cutting problem: n maxn(Pr-i). How would you change this recursion? (b) Give a dynamic-programming algorithm to solve this modified