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Question 2: Recurrences (a) Below is the pseudo-code for two algorithms: Practicel(A,s,f) and Practice2(A,s,f), which take as input a sorted array A, indexed from s to f. The algorithms make a call to Bsearch(A,s,f,k) which we saw in class. Determine the worst-case runtime recurrence for each algorithm: T1(n) and T2(n). Show that T1(n) is O((log n)²) and T2(n) is 0(n log n). Practicel (A,s,f) if s < f ql = [(s+ f)/2] if BSearch(A,s,q1,1) = true Practice2(A,s,f) if s< f if BSearch(A,s+1,f,1) = true return true return true else else return Practice2(A, s, f-1) return Practicel(A, ql+1, f) else else return false return false

Question 2: Recurrences (a) Below is the pseudo-code for two algorithms: Practicel(A,s,f) and Practice2(A,s,f), which take as input a sorted array A, indexed from s to f. The algorithms make a call to Bsearch(A,s,f,k) which we saw in class. Determine the worst-case runtime recurrence for each algorithm: T1(n) and T2(n). Show that T1(n) is O((log n)²) and T2(n) is 0(n log n). Practicel (A,s,f) if s < f ql = [(s+ f)/2] if BSearch(A,s,q1,1) = true Practice2(A,s,f) if s< f if BSearch(A,s+1,f,1) = true return true return true else else return Practice2(A, s, f-1) return Practicel(A, ql+1, f) else else return false return false

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question 2: Recurrences (a) Below is the pseudo-code for two algorithms: Practicel (A,s,f) and Practice2(A,s,f), which take as input a sorted array A, indexed from s to f. The algorithms make a call to Bsearch(A,s,f,k) which we saw in class. Determine the worst-case runtime recurrece for each algorithm: T1(n) and T2(n). Show that T(n) is O((log n)²) and T2(n) is O(n log n). Practicel (A,s,f) if s< f ql = L(s+ f)/2] if BSearch(A,s,ql,1) = true Practice2(A,s,f) if s < f if BSearch(A,s+1,f,1) = true return true return true else else return Practice2(A, s, f-1) return Practicel(A, ql+1, f) else else return false return false
Transcribed Image Text:Question 2: Recurrences (a) Below is the pseudo-code for two algorithms: Practicel (A,s,f) and Practice2(A,s,f), which take as input a sorted array A, indexed from s to f. The algorithms make a call to Bsearch(A,s,f,k) which we saw in class. Determine the worst-case runtime recurrece for each algorithm: T1(n) and T2(n). Show that T(n) is O((log n)²) and T2(n) is O(n log n). Practicel (A,s,f) if s< f ql = L(s+ f)/2] if BSearch(A,s,ql,1) = true Practice2(A,s,f) if s < f if BSearch(A,s+1,f,1) = true return true return true else else return Practice2(A, s, f-1) return Practicel(A, ql+1, f) else else return false return false
Expert Solution
Step 1

For algorithm 1

From the above pseudo code we have

The worst case time complexity will be

( T(0)+T(n))/2

By getting the big O notation of it. It will be

O (n)/2.
Therefore the worst case time complexity for the 1st algorithm is O(n)/2

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