Description
Note. The Weighted Interval Scheduling problem is described in the posted file
Weighted Interval Scheduling.ppt
Memoization is described in the above file and more completely in the posted file
Chap04 Memoization.pdf
Both of these files are posted in the folder “Lecture Notes”.
This project must be done alone.
The Weighted Interval Scheduling problem is this: Given a set of weighted
intervals, choose a set of nonoverlapping intervals such that the total weight
is maximal. You may think of the “weight” as the profit for doing the work in
the given interval
A weighted interval x can be represented by a triple
x = (s, f, v),
where
s = start time of x, f = finish time of x, v = weight or profit of this job
For example, consider the test case for Weighted Interval Scheduling problem
depicted below:
These weighted intervals can be represented by the triples
(0,3,3) (1,4,2) (0,5,4) (3,6,1) (4,7,2) (3,9,5) (5,10,2) (8,10,1)
Write a program to compute a solution to the Weighted Interval Scheduling
problem.
Your program must read in a set of weighted intervals. Each interval should
be entered as 3 integers. The intervals must be given in a textfile and also be
entered in increasing order of finish time. In the above case we would have
0 3 3 1 4 2 0 5 4 3 6 1 …
The program must print out the value of the total weight or profit of the
optimum solution and the indices of the jobs. The output must be in the
following format (the output below does NOT have the correct result).
Optimum profit: 7
Usng Jobs: 2 5
The program MUST use recursion. An iterative solution will not receive full
credit. Use of memoization will receive 20 points extra credit.
You must submit a run using the example above. You must also submit a run
using the following sample data set:
Number of Jobs n = 4
Job Details {Start Time, Finish Time, Profit}
Job 1: {1, 2, 50}
Job 2: {3, 5, 20}
Job 3: {6, 19, 100}
Job 4: {2, 100, 200}
In both cases you must submit a printout of the input file used.