2.2-2 Consider sorting n numbers stored in array A by first finding the smallest element of A and exchanging it with the element in A[1]. Then find the second smallest element of A, and exchange it with A[2]. Continue in this manner for the first n - 1 elements of A. Write pseudocode for this algorithm, which is known as selection sort. What loop invariant does this algorithm maintain? Why does it need to run for only the first n − 1 elements, rather than for all n elements? Give the best-case and worst-case running times of selection sort in O-notation.

2.2-2 Consider sorting n numbers stored in array A by first finding the smallest element of A and exchanging it with the element in A[1]. Then find the second smallest element of A, and exchange it with A[2]. Continue in this manner for the first n - 1 elements of A. Write pseudocode for this algorithm, which is known as selection sort. What loop invariant does this algorithm maintain? Why does it need to run for only the first n − 1 elements, rather than for all n elements? Give the best-case and worst-case running times of selection sort in O-notation.

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

See similar textbooks

Similar questions

Implement MSD string sorting using queues, as follows: Keep onequeue for each bin. On a first pass through the items to be sorted, insert each item intothe appropriate queue, according to its leading character value. Then, sort the sublistsand stitch together all the queues to make a sorted whole. Note that this method doesnot involve keeping the count[] arrays within the recursive method.
The recursive algorithm below takes as input an array A of distinct integers, indexed between s andf, and an integer k. The algorithm returns the index of the integer k in the array A, or ?1 if the integerk is not contained within A. Complete the missing portion of the algorithm in such a way that you makethree recursive calls to subarrays of approximately one third the size of A.• Write and justify a recurrence for the runtime T(n) of the above algorithm.• Use the recursion tree to show that the algorithm runs in time O(n).FindK(A,s,f,k)if s < fif f = s + 1if k = A[s] return sif k = A[f] return felseq1 = b(2s + f)=3cq2 = b(q1 + 1 + f)=2c... to be continued.else... to be continued.
Implement MERGE-SORT() algorithm that reads from a file named “inputHW02.txt” a list of double numbers (max =3,000,000 numbers), sorts those numbers and indicates time consumption. This programming question will address theadvantage of using iteration loops over recursive calls as well as using INSERTION-SORT() as a procedure in MERGESORT().Your program must perform the following actions:1. Opens the given file name and reads all double numbers. For simplicity, we assume this file only containsnumbers and nothing else.2. Implements the function INSERTION-SORT() that only sort an array of maximum 25 numbers. The idea is thatINSERTION-SORT() will be used as a sub-procedure to sort any sub-array when its size is small enough.3. Four versions of MERGE-SORT() namelya. MERGE-SORT-A(): Using recursive calls and NO INSERTION-SORT() as a sub-procedureb. MERGE-SORT-B(): Using ITERATIVE loops (i.e, NO recursion) and NO INSERTION-SORT() as a subprocedure.c. MERGE-SORT-C(): Using recursive calls…
Code in R Write a while loop what prints all numbers up to 20, but it skips a collection of numbers: 3,9,13,19. A next statement is useful when we want to skip the current iteration of a loop without terminatingit. On encountering next, the R parser skips further evaluation and starts next iteration of the loop. x <- 1:5for (val in x) {if (val == 3){next}print(val)}
I need the code from start to end with no errors and the explanation for the code ObjectivesJava refresher (including file I/O)Use recursionDescriptionFor this project, you get to write a maze solver. A maze is a two dimensional array of chars. Walls are represented as '#'s and ' ' are empty squares. The maze entrance is always in the first row, second column (and will always be an empty square). There will be zero or more exits along the outside perimeter. To be considered an exit, it must be reachable from the entrance. The entrance is not an exit.Here are some example mazes:mazeA7 9# # ###### # # ## # # #### # ## ##### ## ########## RequirementsWrite a MazeSolver class in Java. This program needs to prompt the user for a maze filename and then explore the maze. Display how many exits were found and the positions (not indices) of the valid exits. Your program can display the valid exits found in any order. See the examples below for exact output requirements. Also, record…
A majority element is an element that makes up more than half of the items inan array. Given a positive integers array, find the majority element. If there is no majority element,return -1. Do this in O(N) time and 0(1) space.Input: 1 2 5 9 5 9 5 5 5Output: 5
15. Consider the problem of finding the first position in which an array b occurs as a subsequence of an array a. Write two nested loops: let result undefined for (let i = 0; i < a.length - b.length; i++) { for (let j = 0; j < b.length; j++) { if (a[i+j] = b[j]) . . . } } Complete with labeled break and continue statements.
Double Insertion Sort is a variation on Insertion Sort that works from the middle of the array out. At each iteration, some middle portion of the array is sorted. On the next iteration, take the two adjacent elements to the sorted portion of the array. If they are out of order with respect to each other, then swap them. Now, push the left element toward the right in the array so long as it is greater than the element to its right. And push the right element toward the left in the array so long as it is less than the element to its left. The algorithm begins by processing the middle two elements of the array if the array is even. If the array is odd, then skip processing the middle item and begin with processing the elements to its immediate left and right. Implement Double Insertion Sort, being careful to properly handle both when the array is odd and when it is even. By using java, Implement the Double Insertion sort algorithm on a randomly generated list of N integer numbers. Your…
Double Insertion Sort is a variation on Insertion Sort that works from the middle of the array out. At each iteration, some middle portion of the array is sorted. On the next iteration, take the two adjacent elements to the sorted portion of the array. If they are out of order with respect to each other, then swap them. Now, push the left element toward the right in the array so long as it is greater than the element to its right. And push the right element toward the left in the array so long as it is less than the element to its left. The algorithm begins by processing the middle two elements of the array if the array is even. If the array is odd, then skip processing the middle item and begin with processing the elements to its immediate left and right. Implement Double Insertion Sort, being careful to properly handle both when the array is odd and when it is even. Implement the Double Insertion sort algorithm by using JAVA on a randomly generated list of N integer Your program…