Question

Suppose n activities apply for using a common resource. Activity ai (1 ≤ i ≤ n)

has a starting time S[i] and a finish time F[i] such that 0 < S[i] < F[i]. Two activities ai and aj (1

≤ i, j ≤ n) are compatible if intervals [S[i], F[i]) and [S[j], F[j]) do not overlap. We assume the

activities have been sorted such that S [1] ≤ S [2] ≤ …≤ S[n].

(a) Design an O(n2) dynamic programming algorithm to find a set of compatible activities such

that the total amount of time the resource is used by these compatible activities is

maximized. You need to define the sub-problems, establish inductive formula, and show

the initial conditions. Pseudo code is not required.

(b) Apply your algorithm to the following set of activities

i          1    2 3   4 5    6    7   8      9       10        11

S[i]     2    3    5   6   7   9    10   12   13     14       16

F[i]     6    5    7   10 8   13 16 14   14      18       20

Answer 1