CSCI 2300 Home Work 6

This Home work is on Dynamic Programming Problems Chapter 6 of DG and one problem from CLRS (third edition)Chapter 15 Due on November 15th Do any 5 Problems.
  1. Problem 6.8 (DG)
  2. Problem 6.15 (DG)
  3. Problem 6.17 (DG) Hint similar to knapsack problem.
  4. Problem 6.18 (DG) Hint similar to knapsack problem.
  5. problem 6.19 (DG)
  6. Problem 15.1-3 (page 370) Consider a modification of the rod-cutting prolem in which in addition to a price pi for each rod, each cut incurs a fixed cost c. The revenue associated with a solution is now the sum of prices of th epieces minus the cost of making the cuts. Give a dynamic programming algorithm to solve this modified problem (Please read section 15.1 of CLRS book).
  7. Viterbi Algorithm for speech Recognition (CLRS 15-5 or 16-5 (different edition) Dynamic Programming) You are given a directed graph G=(V,e) in which every edge is labeled by a letter from a finte alphabet Σ that there is a function σ(u,v) gives the label of the edge (u,v) for every pair (u,v) in E. You are also given a distinguished vertex v0 and a string < l1,...,l k > of symbols from Design a Dynamic Algorithm to check whether there is a path starting at v 0 labeled with a given string.