(b) Prove that your algorithm from part (a) is optimal up to constant factors. In other words, if f (n) is the number of times your algorithm calls SQRTSORT, prove that no algorithm can sort using o(f (n)) calls to SQRTSORT.
(b) Prove that your algorithm from part (a) is optimal up to constant factors. In other words, if f (n) is the number of times your algorithm calls SQRTSORT, prove that no algorithm can sort using o(f (n)) calls to SQRTSORT.
Computer Networking: A Top-Down Approach (7th Edition)
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Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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plz solve question (b) with complete explanation asap
![24. (a) Describe an algorithm that sorts an input array A[1..n] by calling a subroutine SQRTSORT(k),
which sorts the subarray A[k +1..k + vn] in place, given an arbitrary integer k between 0
and n- n as input. (To simplify the problem, assume that n is an integer.) Your algorithm
is only allowed to inspect or modify the input array by calling SQRTSORT; in particular, your
algorithm must not directly compare, move, or copy array elements. How many times does
your algorithm call SQRTSORT in the worst case?
(b) Prove that your algorithm from part (a) is optimal up to constant factors. In other words, if
f (n) is the number of times your algorithm calls SQRTSORT, prove that no algorithm can sort
using o(f (n)) calls to SQRTSORT.
(c) Now suppose SQRTSORT is implemented recursively, by calling your sorting algorithm from
part (a). For example, at the second level of recursion, the algorithm is sorting arrays roughly
of size n'/4. What is the worst-case running time of the resulting sorting algorithm? (To
simplify the analysis, assume that the array size n has the form 22", so that repeated square
roots are always integers.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f6cb6e1-fe6d-499d-9709-0907f031e50b%2F264db308-31fe-457d-9f4b-7bf835317858%2Fe5nfbl_processed.png&w=3840&q=75)
Transcribed Image Text:24. (a) Describe an algorithm that sorts an input array A[1..n] by calling a subroutine SQRTSORT(k),
which sorts the subarray A[k +1..k + vn] in place, given an arbitrary integer k between 0
and n- n as input. (To simplify the problem, assume that n is an integer.) Your algorithm
is only allowed to inspect or modify the input array by calling SQRTSORT; in particular, your
algorithm must not directly compare, move, or copy array elements. How many times does
your algorithm call SQRTSORT in the worst case?
(b) Prove that your algorithm from part (a) is optimal up to constant factors. In other words, if
f (n) is the number of times your algorithm calls SQRTSORT, prove that no algorithm can sort
using o(f (n)) calls to SQRTSORT.
(c) Now suppose SQRTSORT is implemented recursively, by calling your sorting algorithm from
part (a). For example, at the second level of recursion, the algorithm is sorting arrays roughly
of size n'/4. What is the worst-case running time of the resulting sorting algorithm? (To
simplify the analysis, assume that the array size n has the form 22", so that repeated square
roots are always integers.)
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