Analyze the time complexity of the following variant of merge sort: given a constant k, divide...

Analyze the time complexity of the following variant of merge sort: given a constant k, divide the array into k parts, sort each part recursively, and merge the results.

Expert Solution

venereology answered 1 year ago

Consider a sorting algorithm that combines merge sort and insertion sort algorithm. We still use divide...

Consider a sorting algorithm that combines merge sort and insertion sort algorithm. We still use divide and conquer like merge sort, however when the number of elements in an array is at most k elements (k is a parameter), we stop dividing the elements as the regular merge sort, instead, we call the insertion sort. Assuming we have defined the following two procedures: insertion-sort(A[p..q]) which sort the subarray A[p..q] merge(A[p,q,r]) which merges the sorted subarray A[p..r] and A[r+1..q] Try to...

a. Develop a divide-and-conquer algorithm to perform a parallel merge sort of an array. Hint: After...

a. Develop a divide-and-conquer algorithm to perform a parallel merge sort of an array. Hint: After division, each process sorts its part of the array using an efficient algorithm. Then, the subarrays are merged into larger sorted subarrays. b. Analyze the communication and computation times if the number of processes is equal to the number of array elements, n. c. Repeat Part b if the number of processes is less than the number of array elements. Assume that the computation...

Derive the recurrence for the average time complexity of Quick Sort.

2 real-time examples on the Insertion sort, Bubble sort, Selection sort, Quick sort, Shell sort, Merge...

2 real-time examples on the Insertion sort, Bubble sort, Selection sort, Quick sort, Shell sort, Merge sort, Radix sort, Bucket sort, and Counting sort.

Write a program in Java to sort the given array using merge sort, quick sort, insertion...

Write a program in Java to sort the given array using merge sort, quick sort, insertion sort, selection sort and bubble sort based on the input from the user which sorting technique they wanted to use. Get the array size, array elements from the user, and also display the sorted array along with the name of the sorting technique used.

1. Mathematically analyze the given Recurrence Relation and find out the time complexity of the algorithm....

1. Mathematically analyze the given Recurrence Relation and find out the time complexity of the algorithm. T(n) = T(n-1)+1 , if n> 0 1 if n = 0

Which of the following sorting algorithms are stable: insertion sort, selection sort, merge sort and quick...

Which of the following sorting algorithms are stable: insertion sort, selection sort, merge sort and quick sort? Give a simple scheme that makes any sorting algorithm stable. How much additional time and space does your scheme entail?

Consider the following variation of merge sort: split the list into thirds, sort each third, and...

Consider the following variation of merge sort: split the list into thirds, sort each third, and then merge all three sorted lists. (a) Write pseudo-code for this sorting algorithm in python. (b) Write a recurrence relation for the run-time of this algorithm, and use the master theorem to find the “big O” run time of the algorithm. (c) How does the run time compare to the usual merge sort? Is this an improvement?

Design and analysis of Algorithms: How do I write a k way merge sort algorithm from...

Design and analysis of Algorithms: How do I write a k way merge sort algorithm from a merge sort algorithm that splits 2 arrays while sorting?

4. Write out the pseudocode for when Merge-Sort is stable based on the information given below:...

4. Write out the pseudocode for when Merge-Sort is stable based on the information given below: Comparision Based Stable Sorts such as Merge Sort maintain stability by ensuring that Element A[ j ] comes before A[ i ] if and only if A[ j ] < A[ i ], here i, j are indices and i < j. The relative order is preserved if A[ i ] comes before A[ j ]. Mergesort is stable, provided its implementation employs the...

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