Question

1. (25 points) Quicksort and Analysis Consider the quick sort algorithm in our textbook as shown below QUICKSORT(A, p,r) 1 if p < r 2 q = PARTITION(A, p,r) 3 QUICKSORT(A, p, q - 1) 4 QUICKSORT(A, q + 1, r) (1) (10 points) Explain when we can expect a best-case partitioning. (2) (15 points) Assume that the algorithm always produces a best-case partitioning discussed above, provide a tight bound on the running time of quicksort in this case. Show your answer (a) in recurrence and (b) solve the recurrence (show your rational how to solve). You do not need to prove the answer with the substitution method.

          1. (25 points) Quicksort and Analysis
Consider the quick sort algorithm in our textbook as shown below
QUICKSORT(A, p,r)
1 if p < r
2  q = PARTITION(A, p,r)
3  QUICKSORT(A, p, q - 1)
4  QUICKSORT(A, q + 1, r)
(1) (10 points) Explain when we can expect a best-case partitioning.
(2) (15 points) Assume that the algorithm always produces a best-case partitioning discussed
above, provide a tight bound on the running time of quicksort in this case. Show your answer
(a) in recurrence and (b) solve the recurrence (show your rational how to solve). You do not
need to prove the answer with the substitution method.

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1. (25 points) Quicksort and Analysis
Consider the quick sort algorithm in our textbook as shown below
QUICKSORT(A, p,r)
1 if p < r
2 q = PARTITION(A, p,r)
3 QUICKSORT(A, p, q - 1)
4 QUICKSORT(A, q + 1, r)
(1) (10 points) Explain when we can expect a best-case partitioning.
(2) (15 points) Assume that the algorithm always produces a best-case partitioning discussed
above, provide a tight bound on the running time of quicksort in this case. Show your answer
(a) in recurrence and (b) solve the recurrence (show your rational how to solve). You do not
need to prove the answer with the substitution method.

Added by Scott M.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Nick Johnson

Step 1

In other words, the pivot element is the median of the array. This ensures that the two recursive calls in the QUICKSORT function will have roughly equal-sized subarrays to sort. (2) Assuming the algorithm always produces a best-case partitioning, we can analyze Show more…

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Quicksort and Analysis Consider the quicksort algorithm in our textbook as shown below: QUICKSORT(A, p, r) 1. if p < r 2. q = PARTITION(A, p, r) 3. QUICKSORT(A, p, q-1) 4. QUICKSORT(A, q+1, r) (1) Explain when we can expect a best-case partitioning. (2) Assume that the algorithm always produces a best-case partitioning discussed above, provide a tight bound on the running time of quicksort in this case. Show your answer (a) in recurrence and (b) solve the recurrence (show your rationale on how to solve). You do not need to prove the answer with the substitution method.

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