Devise a parallel algorithm to solve the primality problem for the positive integer n. At the end of the algorithm, every processor should know whether or not n is prime. Further, if n is not prime, every processor should know the smallest prime factor of n. Also, assume no list of primes is initially stored in the memory.

Devise a parallel algorithm to solve the primality problem for the positive integer n. At the end of the algorithm, every processor should know whether or not n is prime. Further, if n is not prime, every processor should know the smallest prime factor of n. Also, assume no list of primes is initially stored in the memory.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter10: Classes And Data Abstraction

Section: Chapter Questions

Problem 19PE

See similar textbooks

Similar questions

Merge sort is an efficient sorting algorithm with a time complexity of O(n log n). This means that as the number of elements (chocolates or students) increases significantly, the efficiency of merge sort remains relatively stable compared to other sorting algorithms. Merge sort achieves this efficiency by recursively dividing the input array into smaller sub-arrays, sorting them individually, and then merging them back together. The efficiency of merge sort is primarily determined by its time complexity, which is , where n is the number of elements in the array. This time complexity indicates that the time taken by merge sort grows logarithmically with the size of the input array. Therefore, even as the number of chocolates or students increases significantly, merge sort maintains its relatively efficient performance. Regarding the distribution of a given set of x to y using iterative and recursive functions, the complexity analysis depends on the specific implementation of each…
Suppose that two matrices A and B with dimension n x n are stored on a 2D mesh of n2 processors such that P_(i,j) holds A[I,j] and B[j,i] . Write C-style pseudocode for an asynchronous algorithm that computes the product of A and B in O(n) time. (10 points) (WRITE THE PSEUDOCODE! IF YOU DON'T WRITE PSEUDOCODE, YOU WILL BE WRONG!! C-STYLE ONLY!!!)
Group scheduling Scheduling tasks to actors (people, CPUs, machines etc) is a problem that one encounters very often in practice. In this small exercise, we practice how to solve such a problem by using recursive problem solving. More specifically, we solve the following problem: We are organizing a course and have n� tutorial groups. To run the groups, we are hiring m� teaching assistants. Due to other responsibilities, an assistant is not necessarily able to teach all possible tutorial groups but has a set of groups that s/he can teach. We call this set of possible groups the preferences of the assistant.Is it possible to assign each tutorial group one assistant in a way that (i) all the assistants' preferences are respected, and (ii) each assistant teaches at most one tutorial group?Needless to say, this a very simplified version of the problem; in real life, some groups need more assistants, some assistants can teach more groups, consecutive group times for an assistant should be…
Sudoku is a popular logic puzzle that uses a 9 by 9 array of squares that are organized into 3 by 3 subarrays. The puzzle solver must fill in the squares with the digits 1 to 9 such that no digit is repeated in any row, any column, or any of the nine 3 by 3 subgroups of squares. Initially, some squares are filled in already and cannot be changed. For example, the following might be a starting configuration for a Sudoku puzzle: Create a class SudokuPuzzle.java Download SudokuPuzzle.java that has the attributes • board—a 9 by 9 array of integers that represents the current state of the puzzle, where 0 indicates a blank square • start—a 9 by 9 array of boolean values that indicates which squares in board are given values that cannot be changed and the following methods: • SudokuPuzzle—a constructor that creates an empty puzzle • toString—returns a string representation of the puzzle that can be printed • addInitial(row, col, value)—sets the given square to the given value as an…
Design and implement an algorithm using recursion and backtracking to sort an array of integers into ascending order. Consider the given array as input and produce a sorted array as output. Each time you take an integer from the input array, place it at the end of the output array. If the result is unsorted, backtrack.
1- Suppose a genetic algorithm uses chromosomes of the form X = abcdefgh with a fixed length of eight genes. Each gene can be any digit between 0 and 9. Let the fitness of individual X be calculated as: f(X) = (a + b)−(c+d) + (e+f) - (g+h) Let the initial population consist of 6 following chromosomes: I. II. III. X1=65413532 X2=87126601 X3 239 21285 X4=41852094 X5 83 931775 X6=52769863 Evaluate the fitness of each individual (show all stages). Then select 4 of them for next generation and write chromosomes which are selected. (Consider maximization.) Perform the following crossover operation on the initial population: Do crossover on X2 and X6 (parents) and name offspring as X7 and X8. Consider one-point crossover and the crossover point between "c" and "d". Write chromosomes X7 and X8. Evaluate offspring generated by crossover operation above (Chromosomes X7 and X8). Do their fitness are better than their parents?
Complete the following analysis of an algorithm such that the time complexity, T(n), of the given algorithm is determined. The analysis uses instruction count (i.e. number of times the statement is executed) as the measure for the analysis. The instruction count of each instruction in the algorithm is indicated at the right of the statement after the //. You should replace each of the question marks(?) by the corresponding instruction count in order to complete the analysis. The total instruction count is obtained by adding all the instruction counts. Note that in this exercise, the linear search algorithm is analyzed in a case where the item to be searched is assumed not found in the array (i.e.Worst Case Analysis) int linearSearch(item, array) { // worst case instruction countint index = 0; // ?while (index < array.length) { // ?if (array[index] == item) { // ?return index; // ?}index++; // ?}return -1; // ?} // ------// T(n) = ? where n is the array size
Complete the following analysis of an algorithm such that the time complexity, T(n), of the given algorithm is determined. The analysis uses instruction count (i.e. number of times the statement is executed) as the measure for the analysis. The instruction count of each instruction in the algorithm is indicated at the right of the statement after the //. You should replace each of the question marks(?) by the corresponding instruction count in order to complete the analysis. The total instruction count is obtained by adding all the instruction counts. Note that in this exercise, the binary search algorithm is analyzed in a case where the item to be searched is assumed to be NOT found in the sorted array (i.e. Worst Case Analysis). // Worst Case Analysis (e.g., item not in array)int binarySearch(item, sortedArray) { // Instruction Countint low = 0; // 1int high = sortedArray.length - 1; // 1int mid = 0; // 1while (low <= high) { // ≈ log(n) + 1mid = (low + high) / 2; // ≈ log(n)if…
Please do not give solution in image formate thanku. Write a Python code for the following scenario : 1: Use Breadth First Search and Recursive Best First Search and implement the algorithms in Python. The program should be able to dynamically take in start and goal nodes from the user at run time. Compare to interpret the results in terms of the algorithm working, performance & shortest path if obtained relevant to the given problem 2: Print the minimum connections that keep the whole network up and running. For each incremental depth limit, the corresponding node generating sequence should be legibly printed in the result Consider Heuristic Value as : The edge cost is an approximation towards the transmission cost between any pair of nodes. For heuristic design, consider all the possible paths between any arbitrary node n to the goal node. The average of the total transmission cost across all these paths is the heuristic value h(n) Consider the following undirected graph…
7. Suppose that you have two different algorithms for solving a problem. To solve a problem of size n, the first algorithm uses exactly n(log2 n) operations and the second algorithm uses exactly n3/2 operations. As n grows, which algorithm uses fewer operations?
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.
Please help