In lectures we saw how use the Merge sort algorithm to sort a sequenceof length n = 2" into ascending order. In fact the algorithm can be applied to sequencesof any length n e N. At each iteration the current sorted sub-sequences are merged inpairs as for the 2" case but if there are an odd number of sub-sequences then the 'left over'one just joins, unchanged, the newly formed sub-sequences at the next iteration. Thiswill mean that the merge algorithm will sometimes need to merge sequences of unequallengths, but this causes no problems.For example, if Merge sort is used to sort the letters of the word PROVISIONAL intoalphabetical order then the subsequences at each stage will be:after Oth iteration (P),(R),(0), (V),(I),(S),(I),(0),(N),(A), (L);after 1st iteration (P,R),(0,V),(I,S),(I,0),(A,N),(L);after 2nd iteration (0,P,R,V),(I,I,0,S),(A,L,N);after 3rd iteration (I,I,0,0,P,R,S,V),(A,L,N);after 4th iteration (A,I,I,L,N,0,0,P,R,S,V).(a) Apply the Merge sort algorithm to sort the letters of the word STEREOPHOTOGRAPHICinto alphabetical order, showing the results of each iteration as in the example above.(b) How many comparison operations are used to merge sort STEREOPHOTOGRAPHIC? Asin Worksheet Q5, remember that when the merge algorithm reaches the stage whereone of its input lists is empty, it does not need any more comparisons to completeits task. For example, for PROVISIONAL there are only 5 comparisons during the firstiteration, 8 in the 2nd, 7 in the 3rd and 5 in the last.(c) How many comparison operations would be used if STEREOPHOTOGRAPHIC were sortedusing the Selection sort algorithm?

Merger sort :- Here i am using python language st=input() l=list(st)b=[-1 for i in range(len(l))]…

For example, if Merge sort is used to sort the letters of the word PROVISIONAL into alphabetical order then the subsequences at each stage will be: after Oth iteration (P),(R),(0), (V),(I),(S),(I),(0), (N), (A), (L); after 1st iteration (P,R),(0,V),(1,S),(I,0),(A,N),(L); after 2nd iteration (0,P,R,V),(I,1,0,S),(A,L,N); after 3rd iteration (I,I,0,0,P,R,S,V),(A,L,N); after 4th iteration (A,I,I,L,N,0,0,P,R,S,V). (a) Apply the Merge sort algorithm to sort the letters of the word STEREOPHOTOGRAPHIC into alphabetical order, showing the results of each iteration as in the example above.

For example, if Merge sort is used to sort the letters of the word PROVISIONAL into alphabetical order then the subsequences at each stage will be: after Oth iteration (P),(R),(0), (V),(I),(S),(I),(0), (N), (A), (L); after 1st iteration (P,R),(0,V),(1,S),(I,0),(A,N),(L); after 2nd iteration (0,P,R,V),(I,1,0,S),(A,L,N); after 3rd iteration (I,I,0,0,P,R,S,V),(A,L,N); after 4th iteration (A,I,I,L,N,0,0,P,R,S,V). (a) Apply the Merge sort algorithm to sort the letters of the word STEREOPHOTOGRAPHIC into alphabetical order, showing the results of each iteration as in the example above.

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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Given an array A and two indices p and r consider the following modified merge sort algorithm write a recurrence relation describing the running time of algorithm modified merge sort(A, p,r) include base case. mofified merge sort (A, p, r) if p<r n = r - p + 1 q = n/3 foo(A,p,p + q) foo (A,p, + q + 1, p + 2q) foo(A, P + 2q + 1, r) merge (A, p, p + q, p + 2q) merge(A, p,p + 2q,r)
Given an array A and two indices p and r consider the following modified merge sort algorithm solve the recurrence relation to give a tight bound on the running time. mofified merge sort (A, p, r) if p<r n = r - p + 1 q = n/3 foo(A,p,p + q) foo (A,p, + q + 1, p + 2q) foo(A, P + 2q + 1, r) merge (A, p, p + q, p + 2q) merge(A, p,p + 2q,r)
Given an arrayAofndistinct numbers, we apply Merge-Sort, Hoare-Quicksort, andLomuto-Quicksort separately to sortAinto ascending order. Consider the case whenA is given in descending order. Select the correct answer for each question.a.Which sorting algorithmwill make the greatestnumber of key comparisons? Hoare-Quicksort, Lomuto-Quicksort, or Merge-Sortb.Which sorting algorithmwill make the fewest number of keycomparisons? Hoare-Quicksort, Lomuto-Quicksort ,or Merge-Sort
What is the average-case running time for Merge Sort and Quick Sort, respectively? Why do we prefer Quick Sort algorithm in practice? Please provide at least two benefits of Quick Sort and also provide explanations for each benefit (plain language explanation is fine).
That's enough for you! def first_preceded_by_smaller(items, k=1): Find and return the 0irst element of the given list of items that is preceded by at least k smaller elements in the list. These required k smaller elements can be positioned anywhere before the current element, not necessarily consecutively immediately before that element. If no element satisfying this requirement exists in the list, this function should return None. Since the only operation performed for the individual items is their order comparison, and especially no arithmetic occurs at any point during execution, this function should work for lists of any types of elements, as long as those elements are pairwise comparable with each other. items k Expected result [4, 4, 5, 6] 2 5 [42, 99, 16, 55, 7, 32, 17, 18, 73] 3 18 [42, 99, 16, 55, 7, 32, 17, 18, 73] 8 None ['bob', 'carol', 'tina', 'alex', 'jack', 'emmy', 'tammy', 'sam', 'ted']…
does increasing the number of partitions of the merge sort function worsen its time complexity? Example: Original recurrence relation: T(n)=2T(n/2) New recurrence relation: T(n)=4T(n/2) provide a simple explanation aside from master's theorem.
Modify the FindBestPlan(S) function to create a function FindBestPlan(S, O),where O is a desired sort order for S, and which considers interesting sortorders. A null order indicates that the order is not relevant. Hints: An algorithmA may give the desired order O; if not a sort operation may need to be added to get the desired order. If A is a merge-join, FindBestPlan must be invoked on the two inputs with the desired orders for the inputs.
Professor JAson uses the following algorithm for merging k sorted lists, each having n/k elements. He takes the first list and merges it with the second list using a linear-time algorithm for merging two sorted lists, such as the merging algorithm used in mergesort. Then, he merges the resulting list of 2n/k elements with the third list, merges the list of 3n/k elements that results with the fourth list, and so forth, until he ends up with a single sorted list of all n elements. Analyze the worst-case running time of the professor’s algorithm in terms of n and k.
t. Suppose instead of dividing in half at each step, you divideinto thirds, sort each third, and combine using a 3-way merge. What is the order ofgrowth of the overall running time of this algorithm?
solution should have O(l1.length + l2.length) time complexity, since this is what you will be asked to accomplish in an interview. Given two singly linked lists sorted in non-decreasing order, your task is to merge them. In other words, return a singly linked list, also sorted in non-decreasing order, that contains the elements from both original lists.
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.
Multiple Choice: Suppose we want to apply Radix Sort to sort 100,000 4-letter words, with each letter taken from the English alphabet (26 letters, all lower cases). Assuming that the running time for sorting n elements within range 1..k using Counting Sort is 2n+2k, whichof the following strategies will lead to the lowest running time? Show the justification.(1) treat letters at each of the four positions as a digit or(2) treat 2-letter subwords at positions 1-2 as a digit and 2-letter subwords at positions 3-4 as another digit or(3) treat all 4 letters as a digit.