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Part 1 Sorting Algorithms (50) Create sets of 1 Million integers with the following characteristics; • Sets where no numbers repeat • Sets where the range of numbers is 1% of the array size • Sets where no numbers repeat and each integer has 20 digits For each of these arrays compare the performance of the following algorithms; • Quicksort • Quicksort, where you change to Insertion sort when the partition size is small. • Radixsort • Timsort (https://en.wikipedia.org/wiki/Timsort) To compare the performance, these are the steps to do; • Create the array • Run the algorithm • Tabulate the time. Only count the time for sorting, not for creating the array. Repeat this step 10 times. Each time re-create the array, so that you are running the algo- rithm on a possibly new array. 1. Create a table with the rows being the algorithms (4 rows) and the columns representing the runs of each different inputs (10*3=30 columns) (20) Write a short report of your observations about the performance of the algorithm along with graphs to highlight your results (10) Explain with figures how the Timsort algorithm works (20) Part 2 Red Black Tree (50) Create sets of 1 Million integer, where no integer is repeated. Insert these numbers to an (i) AVL tree and (ii) R-B tree. Compute the time taken to insert all the numbers. Repeat the exper- iment 10 times, each time regenerating the set. In a table report (a) the time taken to complete the insertion, (b) the height of the tree, (c) the black height of the R-B Tree (15). Using a random number generator, select 10% of the numbers in the trees and delete them. Repeat the experiment 10 times. Report your answers in a tables (15). Consider the case where in an R-B tree, a red node can have a red child, if its parent is black in color. All other constraints of the R-B tree are maintained. Discuss whether or whether not) the tree will still have (logn) height. Discuss a insertion scheme that will maintain the height and the constraints (20). Show transcribed image text Part 1 Sorting Algorithms (50) Create sets of 1 Million integers with the following characteristics; • Sets where no numbers repeat • Sets where the range of numbers is 1% of the array size • Sets where no numbers repeat and each integer has 20 digits For each of these arrays compare the performance of the following algorithms; • Quicksort • Quicksort, where you change to Insertion sort when the partition size is small. • Radixsort • Timsort (https://en.wikipedia.org/wiki/Timsort) To compare the performance, these are the steps to do; • Create the array • Run the algorithm • Tabulate the time. Only count the time for sorting, not for creating the array. Repeat this step 10 times. Each time re-create the array, so that you are running the algo- rithm on a possibly new array. 1. Create a table with the rows being the algorithms (4 rows) and the columns representing the runs of each different inputs (10*3=30 columns) (20) Write a short report of your observations about the performance of the algorithm along with graphs to highlight your results (10) Explain with figures how the Timsort algorithm works (20) Part 2 Red Black Tree (50) Create sets of 1 Million integer, where no integer is repeated. Insert these numbers to an (i) AVL tree and (ii) R-B tree. Compute the time taken to insert all the numbers. Repeat the exper- iment 10 times, each time regenerating the set. In a table report (a) the time taken to complete the insertion, (b) the height of the tree, (c) the black height of the R-B Tree (15). Using a random number generator, select 10% of the numbers in the trees and delete them. Repeat the experiment 10 times. Report your answers in a tables (15). Consider the case where in an R-B tree, a red node can have a red child, if its parent is black in color. All other constraints of the R-B tree are maintained. Discuss whether or whether not) the tree will still have (logn) height. Discuss a insertion scheme that will maintain the height and the constraints (20).

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Answer to Part 1 Sorting Algorithms (50) Create sets of 1 Million integers with the following characteristics; • Sets where no n…