4. Divide and conquer, and the Master Theorem. For each of the following recursive algorithms, give...
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4. Divide and conquer, and the Master Theorem. For each of the following recursive algorithms, give (with brief justification) a recurrence for the algorithm's running time T(n) as a function of the input array size n. State whether the Master Theorem is applicable to the recurrence, and if so, use it to give the closed-form solution; if not, explain why not. (a) (b) 1: function FUNC(A[1,..., n]) if n <3 then 2: 3: return 0 4: FUNC(A[1,..., [n/2]]) 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: i 1 while i (c) 1: function STOOGESORT (A[1,..., n]) if n = 1 then 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: return A if n = 2 and A[1] > A[n] then swap A[1] and A[n] if n > 2 then t [2n/3] STOOGESORT (A[1,, t]) STOOGESORT (A[n t + 1, . . ., n]) STOOGESORT (A[1,..., t]) - return A Solution: (d) Optional extra credit: Prove that STOOGESORT from the previous part is a correct sorting algorithm. Solution: 4. Divide and conquer, and the Master Theorem. For each of the following recursive algorithms, give (with brief justification) a recurrence for the algorithm's running time T(n) as a function of the input array size n. State whether the Master Theorem is applicable to the recurrence, and if so, use it to give the closed-form solution; if not, explain why not. (a) (b) 1: function FUNC(A[1,..., n]) if n <3 then 2: 3: return 0 4: FUNC(A[1,..., [n/2]]) 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: i 1 while i (c) 1: function STOOGESORT (A[1,..., n]) if n = 1 then 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: return A if n = 2 and A[1] > A[n] then swap A[1] and A[n] if n > 2 then t [2n/3] STOOGESORT (A[1,, t]) STOOGESORT (A[n t + 1, . . ., n]) STOOGESORT (A[1,..., t]) - return A Solution: (d) Optional extra credit: Prove that STOOGESORT from the previous part is a correct sorting algorithm. Solution:
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Related Book For
Operations Management
ISBN: 978-0071091428
4th Canadian edition
Authors: William J Stevenson, Mehran Hojati
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