Give a dynamic programming algorithm for the activity selection problem, based on recurrence (16 2) Have your algorithm compute the sizes c I, j as defined above and also produce the maximum size subset of mutually compatible activities Assume that the inputs have been sorted as in equation (16 1) Compare the running time of your solution to the running time of GREEDY ACTIVITY SELECTOR (16 2) (16 1) if Sij , max c i,k c k, j 1 if Sij c i, j ak ESJ a1 RECURSIVE ACTIVITY SELECTOR(S, f, 0, 11) 2 3 5 RECURSIVE ACTIVvrTY SELECTOR(S, f, 1, 11) a1 3 0 6 a1 a4 4 5 7 m 4 RECURSIVE ACTIVITY SELECTOR(s,f, 4, 11) as 5 a6 6 5 9 7 6 10 a4 ag 8 8 11 a1 nn a4 RECURSIVE ACTIVITY SELECTOR(s, f, 8, 11) 12 ag 10 2 14 ug 11 12 16 m 11 umnum a1 a4 ag RECURSIVE ACTIVITY SELECTOR(Ss, f, 11, 11) ag a11 time 3 4 6 10 11 12 13 14 15 16 9 3

Question: Give a dynamic-programming algorithm for the activity-selection problem, based on recurrence (16.2). Have your algorithm compute the sizes c[I, j] as defined above and also

Give a dynamic-programming algorithm for the activity-selection problem, based on recurrence (16.2). Have your algorithm compute the sizes c[I, j] as defined above and also produce the maximum-size subset of mutually compatible activities. Assume that the inputs have been sorted as in equation (16.1). Compare the running time of your solution to the running time of GREEDY-ACTIVITY-SELECTOR.

(16.2)

$if Sij = Ø , max {c[i,k]+ c[k, j]+ 1} _if Sij + Ø . c[i, j]= ak ES¡J$

(16.1)

ш ши a1 RECURSIVE-ACTIVITY-SELECTOR(S, f, 0, 11) Ш ш 2 3 5 RECURSIVE-ACTIVvrTY-SELECTOR(S, f, 1, 11) a1 3 0 6 a1 a4

if Sij = , max {c[i,k]+ c[k, j]+ 1} _if Sij + . c[i, j]= ak ESJ a1 RECURSIVE-ACTIVITY-SELECTOR(S, f, 0, 11) 2 3 5 RECURSIVE-ACTIVvrTY-SELECTOR(S, f, 1, 11) a1 3 0 6 a1 a4 4 5 7 m = 4 RECURSIVE-ACTIVITY-SELECTOR(s,f, 4, 11) as 5 a6 6 5 9 7 6 10 a4 ag 8 8 11 a1 nn a4 RECURSIVE-ACTIVITY-SELECTOR(s, f, 8, 11) 12 ag 10 2 14 ug 11 12 16 m = 11: umnum a1 a4 ag RECURSIVE-ACTIVITY-SELECTOR(Ss, f, 11, 11) ag a11 time 3 4 6. 10 11 12 13 14 15 16 9. 3.

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