Activity-Selection (scheduling) problem

• S = {1, 2, .., n} proposed activities
• All want the same resource (classroom), used by one at a time
• Each activity i has start time s_i and finish time f_i, , [s_i, f_i)
• Two activities i and j are compatible if they do not overlap ( or )

Problem: Select maximum-size set of compatible activities. Assume the input is sorted by (O(nlgn)).

Greedy algorithm:

Greedy-AS(s, f)
1 $\;\;\;\;\;$n = length(s)
2 $\;\;\;\;\;$A = {1} $\;\;\;\;\;$ $\;\;\;\;\;$ $\;\;\;\;\;$; Initialize A
3 $\;\;\;\;\;$j = 1
4 $\;\;\;\;\;$for i = 2 to n
5 $\;\;\;\;\;$ $\;\;\;\;\;$if $s_i \geq f_j$ $\;\;\;\;\;$ $\;\;\;\;\;$; Compatible
6 $\;\;\;\;\;$ $\;\;\;\;\;$then A = A $\cup$ {i}
7 $\;\;\;\;\;$ $\;\;\;\;\;$ $\;\;\;\;\;$j = i
8 $\;\;\;\;\;$return A