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?

Suppose that you have five different algorithms (A, B, C, D and E) for solving a problem. To solve a problem of size n, the number of operations used by each algorithm is as follows. As n grows, which algorithm uses the most operations? Algorithm number of operations n2+n3 B 2n+1 log n' 26+ log n n(logn)? +1 n100 Algorithm D Algorithm C Algorithm A Algorithm B o Algorithm E

Write an efficient algorithm for the following problem (either pseudocode or java), and describe your reasoning. Determine the Time complexity and if you cannot find any polynomial time algorithm, then give a backtracking algorithm. Problem will be on repeat numbers input will be ARRAY[1,2, ... , n] number of positive numbes. Output will any one number that is repeated more than n/3 times. for example, if you have [1,1,2,2,2,1], since n = 6 and n/3 = 2, both 1 and 2 showed up more than n/3 times. the output will be either 1 or 2 (just one of the values are required)   if you have [1,1,3,4,5,6,7,8,9], since 1 is only repeated twice, and n/3 = 3, output will be "none"

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)

A binary searching algorithm has logarithmic ?(log?) performance. It takes a second to find an item in a list of 10,000 entries. How long do you expect it to take to find an item in a list of 50,000,000 entries? How did you arrive at your answer?

25. Suppose you have a computer that requires 1 minute to solve problem instances of size n = 1,000. Suppose you buy a new computer that runs 1,000 times faster than the old one. What instance sizes can be run in 1 minute, assuming the following time complexities T(n) for our algorithm? (a) T (n) = n (b) T (n) = n³ (c) T (n) = 10"

Given a program designed to calculate rocket trajectories, the algorithm has an O(2n) complexity and takes 1 second for each iteration, and n = 15. How many hours will it take to calculate the trajectories, worst case?

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.

kindly solve this problem using python

Consider the following three sorting algorithms: Insertion Sort, Heapsort, and Quicksort. Here are three statements. A. Iam an incredibly fast sorting algorithm that runs in O(n log n) time on average, though my worst case run time is O(n2). B. I run very quickly for small values of n, but unfortunately am really slow when n is large. My average run time is O(n2). C. I am an in-place sorting algorithm whose average case and worst case running time is O(n log n). For each statement (A, B, C), determine the correct sorting algorithm.