Description

• To explore the impact of the function calls overhead

What you need to do:
1. Implement the greedy recursive algorithm to solve the activity-selection problem
2. Implement the greedy iterative algorithm to solve the activity-selection problem
3. Repeatedly execute both algorithms on the same problem and measure the running time of each algorithm
4. Plot results, compare, analyze and conclude.

Objective:

Programming

1) Implement RecursiveActivitySelector(k,n), the greedy recursive algorithm to solve the activity-selection problem. 2) Implement GreedyActivitySelector(n), the greedy iterative algorithm to solve the activity-selection problem.
3) Implement the following program to collect data to plot and analyze. (submit this program with your assignment)

StudyOverhead(NumberPoints)
Initialize Array_s[n] // start times Initialize Array f[n] // finish times
for i = 1 to NumberPoints
TimeRecursive = 0 TimeIterative = 0 for j = 1 to NumberRuns
Initialize set A //Use an array to represent a set A[i] = 0 if 𝑎𝑖 ∉𝐴
RecursiveActivitySelector(0, i-1)
Collect running time for recursive and add it to TimeRecursive GreedyActivitySelector(i-1)
Collect running time for iterative and add it to TimeIterative
Collect M[i] = TimeRecursive/TimeIterative
Dump M[i] in a file

InitializeArrays(n) // Create about n/2 mutually compatible activities s[0] = 0 f[0] = 0
for i = 1 to n-1
if (i is even) s[i] = f[i-2]
f[i] = s[i] + 2
else s[i] = f[i-1] – 1 // s[1] will be negative, but that is fine.
f[i] = f[i-1]+1

Data collection and analysis
1) (25 points) Plot M[i] versus i Insert here the plot …

Compare the two algorithms, discuss and analyze based on the plot of M[i] versus i. …..

Report
• Write a report that will contain, explain, and discuss the plot. The report should not exceed one page.
• In addition, your report must contain the following information: o whether the program works or not (this must be just ONE sentence) o the directions to compile and execute your program
• Good writing is expected.
• Recall that answers must be well written, documented, justified, and presented to get full credit.

What you need to turn in:
• Electronic copy of your source program (standalone/separately attached to this assignment)
• Electronic copy of the report (including your answers) (standalone). Submit the file as a Microsoft Word or PDF file.

Grading
• Program is worth 30% if it works and provides data to analyze
• Quality of the report is worth 70% distributed as follows: good plot (25%), explanations of plot (10%), discussion and
conclusion (35%).