Question
This Project involves an analysis of the results that you obtained in first project. You are to submit a paper, written with Microsoft Word, that discusses the results of your analysis.
• A brief introduction of the sorting algorithm that you have selected and how the two versions of the algorithm compare
• A discussion of the critical operation that you chose to count with an explanation of why you selected it
• A Big-Θ analysis of the two versions of the algorithm
• A discussion of the results of your study, which should include
o graphs of your results
o a comparison of the performance of the two versions of the algorithm (Comparing
the recursive and iterative algorithm in Project 1)
o a comparison of the critical operation results and the actual execution time measurements
o a discussion of the significance of the standard deviation results and how it reflects the data sensitivity of your algorithm
o how your results compare to your Big-Θ analysis
• A conclusion that summarizes the important observations of your study
If for any reason, it was necessary to revise the program you submitted in project 1, the revised source code should also be included along with the paper.
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In this project, we are analyzing the merge sort algorithm. Merge sort is a general purpose algorithm which sorts a set of values in an array through the use of comparisons. It was invented by John von Neumann in 1945 and belongs to a broader class of algorithms called “divide and conquer” algorithms. As a divide and conquer algorithm, merge sort recursively breaks the sorting problem down into sub-problems, which once executed achieve sorting of the original array.
The merge sort algorithm works through the following strategy:
Initially, the unsorted list must be divided into sublists. This is usually done with halfway splits of the original list, which occur until the unsorted list is
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        Backtrace
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        Backtrace
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        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        2.05mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        3.05mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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        Bindings
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        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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        • 18. app/Repositories/HomeworkLibraryRepository.php:39
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      • select * from `subjects` where `subjects`.`id` in (142)
        1.11mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
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      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 51325 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.36mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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