2. Suppose the function MergeSort( Vis a recursive implementation of the merge sort algorithm, which takes as input an integer array A. How many times isMergeSort( ) recursively called, if A is of size n? Answer: SelectT SelectOlnlogn3. How many times is the Merge routine called in total,O(1)Oln 2)nswer. ISelect ]

2. Suppose the function MergeSort( O s a recursive implementation of the merge sort algorithm, which takes as input an integer array A. How many tìmes MergeSort() recursively called, if A is of size n? Answer: I Select| Select Ofnlogn) 3. How many times is the Merge routine called in total, O(1) On^2) swer. Select]

2. Suppose the function MergeSort( O s a recursive implementation of the merge sort algorithm, which takes as input an integer array A. How many tìmes MergeSort() recursively called, if A is of size n? Answer: I Select| Select Ofnlogn) 3. How many times is the Merge routine called in total, O(1) On^2) swer. Select]

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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Answer the following regarding Merge Sort: [Select 1. Merge Sort requires an additional space (apart from the input array) of size [Select] 2. Suppose the function MergeSort() is a recursive implementation of the me Oln) as (Select] Ollog n) MergeSort() recursively called, if A is of size n? Answer.
Q: Modify the following algorithm of Merge Sort in such a way that during every recursive call it should divide the array into three partitions instead of two. What will be effect of this modification on the running time of Merge Time? Merge-Sort (A, left, right) if left ≥ right return else middle ← (left+right)/2 Merge-Sort(A, left, middle) Merge-Sort(A, middle+1, right) Merge(A, left, middle, right) Merge(A, left, middle, right) n1 ← middle – left + 1 n2 ← right – middle create array L[n1], R[n2] for i ← 0 to n1-1 do L[i] ← A[left +i] for j ← 0 to n2-1 do R[j] ← A[middle+j] k ← i ← j ← 0 while i< n1 & j< n2 if L[i] < R[j] A[k++] ← L[i++] else A[k++] ← R[j++] while i< n1 A[k++] ← L[i++] while j < n2 A[k++] ← R[j++]
Modify the following algorithm of Merge Sort in such a way that during every recursive call it should divide the array into three partitions instead of two. What will be effect of this modification on the running time of Merge Time? Merge-Sort (A, left, right) if left z right return else middle < (left+right)/2 Merge-Sort(A, left, middle) Merge-Sort(A, middle+1, right) Merge(A, left, middle, right) Merge(A, left, middle, right) n. + middle - left +1 nz+ right – middle create array L[n:], R[n2] fori< 0 to n,-1 do L[j] < A[left +i] forj+ 0 to nz-1 do R[j] < A[middleti] while ik n, &j< n2 if L[] < R[j] A[k++] + L[i++] else A[k++] < R[j++] while ik n. A[k++] < L[i++] while j< n2 A[k++] < R[j++]
Consider the following problems for recursive definition/solution. Answer the following questions. [Remember that a recursive definition/solution requires base case and recursive case] Consider a list of numbers A {55,12,53,56,24,1,7,42}. Sort is by using Merge Sort. Show each step in dividing the list and conquering/combining it.
Perform a non-recursive merge sort on the list L = 78, 78, 78, 1 to ensure the sort's stability.
AssuAssume we want to analyze empirically 4 variants of the Quicksort algorithm by varying the selection of the pivot and the recursive call as follows: ● Try the following values when selecting a pivot: - Pick the last element as pivot - Pick a random element as pivot ● Do not make a recursive call to QuickSort when the list size falls below a given threshold, and use Insertion Sort to complete the sorting process instead. Try the following values for the threshold size: - Log2(N) - Sqrt(N) Therefore, you are asked: a. (12 points) Write the java code for the 4 Quicksort implementations. b. (5 points) Write a driver program that allows you to measure the running time in milliseconds of the 4 implementations for N = 10000, 20000, 40000, 80000 and 160000. For each data size N, generate a random list of N random integers ranging from 1 to 107 and use the same list to measure the running time of the 4 implementations. Present the results in the following table:me we want to analyze…
Your task is sorting the given list by dictionary order, sortingoperation must be realized using the bubble sort algorithm. Additionally,this list implementation should be written using a two-dimensional char ar-ray.Bubble Sort Algorithm1 function swap ( a , b)2 // F i l l own your own !3 end function45 function compare ( a , b)6 // Compare f unc t i on should be implemented7 // to r e a l i z e the s o r t i n g c r i t e r i a .8 // For example , e l ement s in a are s t r i n g s and9 // the y are to be s o r t e d in d i c t i o n a r y order .10 // strcmp f unc t i on can be used in p l a c e11 // of compare f unc t i on .12 end function1314 function bubbl e s o r t ( a , n)15 while n != 016 high = 017 for i=0 to n=2 incremented by 118 i f compare ( a [ i ] , a [ i +1]) > 0 then19 swap ( a [ i ] , a [ i +1])20 high = i+121 end i f22 end for23 n = high24 end while25 end function1
Question 7 Write a program, which returns the index of the minimum repeating element of the array in Jinear time and does just a single traversal of the array. You should use hash table functions like a hash set, hash map, etc. Ardil Subarray arrli+1...n-1] Return index ASAP duplicate is found The implementation can be seen here and requires Qn2) time, where n is the size of the input The idea is to traverse the array from right to left. If the element is seen for the first time insert it into the set; otherwise, update the minimum index to the element's index. Input: {5, 6, 3, 4, 3, 6, 4 } Output: The minimum index of the repeating element is 1 Input: {1 2, 3, 4, 5, 6 } Output: Invalid Input
Suppose the following array were passed in to a mergesort algorithm: 42 39 87 21 56 93 43 35 and Draw what the array looks like after the first recursive call completes, then after the second recursive call (immediately before the final call to merge).
A. Can you draw the animation of Merge sort: given an unsorted array of size 10, show the divide andconquer techniqueb. What is Running time for Merge Sort: O(nlogn) such that n is the size of thearray: Reference code attached
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.
The heart of the mergesort algorithm involves merging two already sorted arrays. The following method merges two presorted arrays (A and B) into an empty array (C). Describe the purpose of the 2nd and 3rd while loops (lines 31-35).