Question

Instead of always selecting the first activity to finish, select the last activity to start that is compatible with all previously selected activities. Accomplish this by implementing a greedy algorithm in either Python or C++. This is similar to a first-to-start algorithm, but in reverse; the goal is to select the start-times that appear later. See the example below and ensure that your output matches the example below.

Include a verbal description of your algorithm, pseudocode and analysis of the theoretical running time. The program should read input from a file named “act.txt”. The file contains lists of activity sets with number of activities in the set in the first line followed by lines containing the activity number, start time & finish time.

Example act.txt:

11

1 1 4

2 3 5

3 0 6

4 5 7

5 3 9

6 5 9

7 6 10

8 8 11

9 8 12

10 2 14

11 12 16

3

3 6 8

1 7 9

2 1 2

In the above example the first activity set contains 11 activities with activity 1 starting at time 1 and finishing at time 4, activity 2 starting at time 3 and finishing at time 5, etc.. The second activity set contains 3 activities with activity 3 starting at time 6 and finishing at time 8 etc. The activities in the file are not in any sorted order.

Your results including the number of activities selected and their order should be outputted to the terminal. For the above example the results are:

Set 1

Number of activities selected = 4

Activities: 2 4 9 11

Set 2

Number of activities selected = 2

Activities: 2 1

Note: There is an alternative optimal solution for Set 1. Since activities 8 and 9 have the same start time of 8, 2 4 8 11 would be an alternative solution. Your program only needs to find one of the optimal solutions. For either solution the activities differ from the solution presented in the text which uses the earliest-finish time criteria.

Answer 1

answering using greedy algorithm, here it goes

we can only get optimal solution if we select last activity to start first