Consider the following divide and conquer algorithm for searching for a value K in a sorted listL[1.n]:11. If the list is empty, then the element is not found. If the list contains only one element,then simply compare it to the value K and act accordingly.2. Otherwise, search recursively by comparing K with the element located at [n/4]. If it isequal, then youre done. If its smaller then continue with the sublist to the left of [n/4].3. If, on the other hand, its bigger than [n/4], then compare it with the element located at[3n/4] and do exactly as you did in (2) i.e. you either found it at [3n/4] or you continuewith one of the sublists that are on the left or right of [3n/4].(b) Set up a recurrence desginating a lower bound on the number of key comparisons.(c) Set up a recurrence designating an upper bound on the number of key comparisions.

(b)Key comparisons on the lower bound:2K times Base condition is checked for K iterations: K times.…

Answered: (b) Set up a recurrence desginating a…

(b) Set up a recurrence desginating a lower bound on the number of key comparisons. (c) Set up a recurrence designating an upper bound on the number of key comparisions.

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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Consider the Sort-and-Count algorithm explained in section 5.3 of our text: "Counting Inversions"Suppose that the initial list is: 92 71 36 91 27 48 14 34 81 26 24 65 78 51 37 22 Sort-and-Count makes two recursive calls. The first recursive call inputs the first half of the initial list: 92 71 36 91 27 48 14 34 and returns the sorted version of the first half, as well as the number of inversions found in the first half (22). The second recursive call inputs the second half of the initial list: 81 26 24 65 78 51 37 22 and returns the sorted version of the second half, as well as the number of inversions found in the second half (19). Sort-and-Count then calls Merge-and-Count. To Merge-and-Count, Sort-and-Count passes the sorted versions of the two halves of the original list: 14 27 34 36 48 71 91 92, and 22 24 26 37 51 65 78 81 Merge-and-Count begins merging the two half-lists together, while counting…
design an algorithm to find all the common elements in two sorted lists of numbers. For example, for the lists 2, 5, 5, 5 and 2, 2, 3, 5, 5, 7, the output should be 2, 5, 5.What is the maximum number of comparisons your algorithm makes if the lengths of the two given lists are m and n, respectively?
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Consider the QuickSelect. This algorithm solves the problem of finding k-th smallest value in a given list A with length n. Below is a summary of the pseudocode for QuickSelect:(1) Pick a pivot element p at random from A and Split A into subarrays left and right by comparing each element to p as in Quicksort. While we are at it, count the number L of elements going in to left.
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