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Answer to both a) and b) is no. Knapsack problem is NP-complete.

(a) Yes, this is a special case of the Knapsack problem where the value of each item is the same (described in section 13.10 of the book). If we have n programmes with sizes s1 to sn, where si <= sj if i < j, and we can fit the first k on the disk, there can be no larger subset, since in order to fit the (k+1)th item we must remove at least one other item of smaller or equal size.

(a) No. Let D = 10, and P = { 5, 4, 2, 1, 1, 1 }.

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