EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
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Create an implementation of mergesort that uses k-way merges rather than 2-way merges. Analyse your algorithm, formulate a theory about the ideal value of k, and conduct tests to support your theory.
What is the asymptotic time (big Oh) of the merge operation in mergesort?
Develop a mergesort implementation based on the idea ofdoing k-way merges (rather than 2-way merges). Analyze your algorithm, develop a hypothesis regarding the best value of k, and run experiments to validate your hypothesis
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EBK DATA STRUCTURES AND ALGORITHMS IN C
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- ve the sequence of subarray sizes in the merges performed by both the topdown and the bottom-up mergesort algorithms, for N = 39arrow_forwardDesign and implement a hash table which uses chaining (linked lists) to handle collisions.arrow_forwardRun mergesort for huge random arrays and determine empirically, as a function of N (the total of the two subarray sizes for a given merge), the average length of the other subarray when the first subarray exhausts.arrow_forward
- Consider the following variation of mergesort:(a) If n ≤ 1, we are done.(b) Divide the n elements into b subarrays of n/b elements each.(c) Recursively call mergesort to sort each of the b subarrays.(d) Merge the b sorted subarrays.For example, the standard mergesort has b = 2, and merging takes Θ(n) comparisons.If b = 3, then we have a 3-way mergesort, and one can show that it takes Θ(n) comparisons to merge 3 sorted lists. In fact, one may show that merging b sorted lists (for any fixed b) can be done in Θ(n) comparisons.Now consider the following argument: if we set b = n, we recursively sort n subarrays of size 1, and then merge them into one list with Θ(n) comparisons. Thus, the complexitycan be expressed by:T(1) = 0T(n) = nT(1) + Θ(n) = Θ(n)Therefore, this variation of mergesort sorts an array in Θ(n) comparisons.What is wrong with this argument? Hint: think about how to implement this variation.arrow_forwardWhat is a recurrence relation for the following Mergesort algorithm? MergeSort(A, p, r): if p > r return q = (p+r)/2 mergeSort(A, p, q) mergeSort(A, q+1, r) // swap array elements if A[r] > A[q] mergeSort(A, p, q, r)arrow_forwardWhat is a recurrence relation for the following Mergesort algorithm? MergeSort(A, p, r): if p > r return q = (p+r)/2 mergeSort(A, p, q) mergeSort(A, q+1, r) // reorder array elements mergeSort(A, p, r-1)arrow_forward
- Does a hash table of size m always have the same number of linked lists? No matter how long I try, I just can't put my finger on the function of a hash function. Give a case study to demonstrate your point.arrow_forwardDoes a hash table of size m consistently contain the same number of linked lists? I am unable to identify the purpose of a hash function, no matter how hard I attempt. To demonstrate your thesis, provide an example.arrow_forwardRun mergesort for large random arrays, and make an empirical determination of the average length of the other subarray when the first subarray exhausts, as a function of N (the sum of the two subarray sizes for a given merge).arrow_forward
- What is the worse case complexity of this recurrence relation: T(n) = T(n-1) + n represents ? A)Quicksort B)Mergesort C)Quicksort and Mergesort D)None of the abovearrow_forwardShow the result when we insert the keys 5; 28; 19; 15; 20; 33; 12; 17; 10 into a hash table with collisions resolved by linked list at each slot. Let the hash table have 9 slots, and let the hash function be h(x) = (2x+1) mod 9. (You are expected to draw the final hash table)arrow_forwardFor a list L[1:9] = 0.56, 0.87, 0.21, 0.43, 0.77, 0.62, 0.33, 0.28, 0.99 of floating point integers in the [0-1] range, trace bucket sort for k = 10 buckets.arrow_forward
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