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4. (a) State clearly the lower bound proved for the worst-case number of key- comparisons for any comparison-based sorting algorithm. 4 (b) For n = 4, use the above result to determine the lower bound (exact number) for the worst-case number of key-comparisons. 4 (c) Show how Mergesort is used to sort n = 4 elements. Show the merge-tree and compute the worst-case number of key-comparisons. How does your result compare with the above lower bound?

4. (a) State clearly the lower bound proved for the worst-case number of key- comparisons for any comparison-based sorting algorithm. 4 (b) For n = 4, use the above result to determine the lower bound (exact number) for the worst-case number of key-comparisons. 4 (c) Show how Mergesort is used to sort n = 4 elements. Show the merge-tree and compute the worst-case number of key-comparisons. How does your result compare with the above lower bound?

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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can you solve 2020 image one I also provided refrences how MY prof solved so based on that pleease solve this image 2020 one step by step formet please use from refrnecs 

4. Consider sorting n = 6 real-valued keys. Compute the worst-case number of key comparisons (exact number, not order) for each of the following cases. Show the work. (a) Insertion sort Comp: Total = 1+2+3+4+5 = 0 0 0 0 0 0 12345 (b) Mergesort (Assume recursive implementation of mergesort.) Show the merge tree. Show the number of comparisons for each merge, and compute the total. 00 X 2 = 15 5 COMP Total = 1+1+2+2+5 (c) What is the theoretical lower bound on the worst-case number of comparisons? (Give the exact worst-case number.) How does this lower bound compare with the above upper bounds? [lag (6!)] = [loy (6.5.4.3-2)] [lay 720] = 10 So, hower Round "D he Cause 2²=512 < 720 < 2 =1024 10 Mergesort is very
Transcribed Image Text:4. Consider sorting n = 6 real-valued keys. Compute the worst-case number of key comparisons (exact number, not order) for each of the following cases. Show the work. (a) Insertion sort Comp: Total = 1+2+3+4+5 = 0 0 0 0 0 0 12345 (b) Mergesort (Assume recursive implementation of mergesort.) Show the merge tree. Show the number of comparisons for each merge, and compute the total. 00 X 2 = 15 5 COMP Total = 1+1+2+2+5 (c) What is the theoretical lower bound on the worst-case number of comparisons? (Give the exact worst-case number.) How does this lower bound compare with the above upper bounds? [lag (6!)] = [loy (6.5.4.3-2)] [lay 720] = 10 So, hower Round "D he Cause 2²=512 < 720 < 2 =1024 10 Mergesort is very
4. (a) State clearly the lower bound proved for the worst-case number of key- comparisons for any comparison-based sorting algorithm. 4 (b) For n = 4, use the above result to determine the lower bound (exact number) for the worst-case number of key-comparisons. 4 (c) Show how Mergesort is used to sort n = 4 elements. Show the merge-tree and compute the worst-case number of key-comparisons. How does your result compare with the above lower bound?
Transcribed Image Text:4. (a) State clearly the lower bound proved for the worst-case number of key- comparisons for any comparison-based sorting algorithm. 4 (b) For n = 4, use the above result to determine the lower bound (exact number) for the worst-case number of key-comparisons. 4 (c) Show how Mergesort is used to sort n = 4 elements. Show the merge-tree and compute the worst-case number of key-comparisons. How does your result compare with the above lower bound?
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