CSC 464 - 01 Assignment 5
Given: March 14, 2003 Due: March 21, 2003
Value: 45 points
Objectives:
understand use of the dynamic programming strategy in the traveling salesperson
problem
compare and contrast greedy and dynamic programming in solving the 0-1 knapsack
problem
Please do the work neatly in pencil on one side of a page.
1. For the traveling salesperson problem #26 on page 133, show all steps
(consideration of all subsets, one by one, as in class) in the solution to the
problem. Work carefully (and not microscopically) and double check your work
because errors will propagate.
[25 points]
Write width-wise instead of length-wise if necessary for the clarity of the dynamic
programming array.
2. Given the following items:
item 1 2 3
weight 10 20 30
profit 60 100 120
a. Calculate the greedy solution to this 0-1 knapsack problem for W = 40
considering the items in order with largest profit per unit weight first. Show all
steps (consideration of each item and inclusion or rejection).
[2]
b. Calculate the dynamic programming solution to the problem for W = 40;
i.e., develop the 2-dimensional array. You can show the array entries for weights
in multiples of 10 from 0 through 40.
[8]
3. Given the following items:
item 1 2 3
weight 3 4 7
profit 4 5 10
and assuming the capacity W of the knapsack is 11.
a. Calculate the greedy solution to this 0-1 knapsack problem, considering the
items in order with largest profit per unit weight first. Show all steps.
[2]
b. Calculate the dynamic programming solution to this problem, show all
array entries for weights from 0 through 11.
[8]
Assignment 5 1