Consider the problem of finding the distance between the two closest and y is computed as x - y.) numbers. (The distance between two numbers x Design a presorting-based algorithm in pseudo code for solving this problem and determine its efficiency class. Answer: // your algorithm goes here Provide the the algorithm efficiency analysis here:

Consider the problem of finding the distance between the two closest and y is computed as x - y.) numbers. (The distance between two numbers x Design a presorting-based algorithm in pseudo code for solving this problem and determine its efficiency class. Answer: // your algorithm goes here Provide the the algorithm efficiency analysis here:

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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You have an array of 10,000 subject scores for a high-school exam and you want to find the scores that are ranked from 4900 to 5100 that is the 201 most middle-ranked scores. Precisely describe two alternative algorithmic ap proaches to doing this - one of which is, in terms of time complexity, more efficient than the other.
You want to design an algorithm, called minMax(A,p,r), that takes an array of integers and indexes of the first and last elements, and returns the minimum and maximum values in that range. Now write the pseudo code of a divide and conquer (and therefore, recursive) algorithm with the same time complexity (Θ(n)). You can assume that p ≤ r. Also, in your code, you can return two numbers by returning a pair, e.g. “return (a, b)”, and can save the output in a similar way, e.g. “(a, b) = minMax(parameters)”. (Short answer please)
Given an unsorted array A of integers of any size, n ≥ 3, and an integer value x, write an algorithm as a pseudo code (not a program!) that would find out if there exist EXACTLY3 occurrences in the array with value x. What is the time complexity of your algorithm, in terms of Big-O? What is the space complexity of your algorithm, in terms of Big-O? What if , the given array A is sorted. Will time complexity change from the case that A was unsorted? • If yes; give a new algorithm that achieves this better complexity (indicate the time complexity as of that algorithm). • If no, explain why such new constraints/conditions cannot lead to a better time complexity.
Given an array A = [10, 7, 4, 2, 1], and target = 7, return the index of the target if found, else return -1. 1. Can this problem be solved in O(logN)? 2. If so, write the implementation. Mention time and space complexity 3. If this problem cannot be solved using O(logN), what is the solution that you suggest - write the code and also mention time and space complexity.
Please help me Josephus Problem is a theoretical problem related to a certain counting-out game. On thiscase, people are standing in a circle waiting to be executed. After a specified number ofpeople are skipped, the next person is executed. The procedure is repeated with theremaining people, starting with the next person, going in the same direction and skippingthe same number of people, until one person remains, and is freed.Arrange the numbers 1 , 2, 3 , ... consecutively (say, clockwise) in a circle. Now removenumber 2 and proceed clockwise by removing every other number, among those thatremain, until one number is left. (a) Let denote the final number which remains. Find formula for .(b) If there are 70 people, what is the safe number (the number that remains)?
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.
1. Consider the algorithm for the sorting problem that sorts an array by counting,for each of its elements, the number of smaller elements and then uses thisinformation to put the element in its appropriate position in the sorted array:ALGORITHMComparisonCountingSort(A[0..n − 1])//Sorts an array by comparison counting//Input: Array A[0..n//Output: Array S[0..n− 1] of orderable values− 1] of A’s elements sorted// in nondecreasing orderfor i ← 0 to nCount− 1 do[i]←0for i ← 0 to n − 2 dofor j ← i +1 to n − 1 doif A[i] < A[j ]Count[j ]← Count[j ] + 1else Count[i]← Count[i] + 1for i ←0 to n−1 doS[Count[i]]←A[i]return Sa. Apply this algorithm to sorting the list 60, 35, 81, 98, 14, 47.b. Is this algorithm stable?c. Is it in-place?
The drawback of this approach, is that with each recursive function call, we only reduce the size of the array by one element, and we use a storage space for one activation record. A faster approach is, with each recursive call, reduce the size of the array by 3 elements. a. Write a reduce-and-conquer recursive function FastRecSum()(C++ or python) that find the sum of all float (real) elements in an array of size n. b. Using addition of float (real) values as a basic operation, set up and solve a recurrence relationship to compute the complexity of your code, as a function of the size n of the array.
The solution must be submitted in the Coral programming language. A program that reads a list of 10 integers, and outputs those integers in reverse. For coding simplicity, follow each output integer by a space, including the last one. Then, output a newline. Ex: If the input is 2 4 6 8 10 12 14 16 18 20, the output is: 20 18 16 14 12 10 8 6 4 2 To achieve the above, first read the integers into an array. Then output the array in reverse.
Write an efficient algorithm (to the best of your knowledge) for the following problem, briefly describe why it is a correct algorithm, provide pseudocode, and analyze the time complexity. Problem: RobotWalk Input: An array A[0...n,0...n] of positive integers. A robot that starts at position A[0,0] and wants to reach A[n,n]. At each step, the robot can only move on step either rightward, along the diagonal, or downward. For example, if the current position is (i,j), then the next possible positions are (i,j+1), (i+1,j+1), or (i+1,j). The cost of a path is the sum of the entries that the robot visits. Output: The most expensive path that the robot can take. Example: Input: A = 50 (robot Starts at A[0,0]) 20 30 10 10 10 10 40 40 (robot ends at A[n,n]) Output: 160 (because of the path 50 -> 20 -> 10 -> 40-> 40.
You are given an arrayof colors (reds, whites, and blues), in no particular order. Sort them into the order of redsfollowed by whites followed by blues.a. Devise an efficient algorithm to solve this problem.b. What is your algorithm's time complexity?For example, if red is represented by 2, white represented by 4 and blue is represented by 6,your input and output array could be of following form:Input: [ 4 6 2 4 2 6 4 2 6 4 4 2 4 ]Output: [ 2 2 2 2 4 4 4 4 4 4 6 6 6]
You have an array of n real numbers and another integer s. Find out whether the array contains two elements whose sum is s. (For example, for the array 5, 9, 1, 3 and s = 6, the answer is yes, but for the same array and s = 7, the answer is no.) Design an algorithm for this problem with a better than quadratic time efficiency.