(e) Another recursive algorithm is applied to some data A = (a₁,...,am) wherem = 2* (i.e. 2, 4, 8,16 ...) where x is an integer ≥ 1. The running time T ischaracterised using the following recurrence equations:Determine the running time complexity of this algorithm. You will find it helpfulto recall that:x=∞0x=1T(1) = c when the size of A is 1, and c is a constantT(m) = 2T + m otherwise12kAnd2log2 (x)→ 1= X

Here the recurrence isT(m) = 2T(m/2)+m ............. equation 1also T(m/2) = 2T(m/4)+m/2now…

Answered: (e) Another recursive algorithm is…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question 4: (15 Marks) Find the running times of each of the following functions (in big-O notation), and arrange them in increasing complexity. [Note: your answer should provide a detailed explanation that support your final conclusion] a) T(n) = ET(i) b) T(n) = 6 T( n /2 )+ O( n) c) T(n) = T(n - 2) + log n with T(0) = 1 | Note: You should submit all your answers for the above-mentioned questions in one big word file (one after the other). The file should contain the following items for each question: Criterion Unsatisfactory Average Good O 100% Complete and in a professional format O Explanation of the pseudo-code is provided O looks efficient in terms of running time and of Algorithm Design O Incomplete. O Complete but looks like an essay not a professional algorithm. memory usage O Comments on the efficiency O Organized work, Implementation Using Python Incomplete Completed 100% O Comments on the code Poor use of white with correct use of space, variables, Screen shot of the run…
A problem called S reduces to a problem called T if a T solver can be used as a subroutine to solve S. In pseudocode: Solves(...): ... SolveT(...) ... Assuming that this reduction is correct, answer the following questions regarding what the reduction tells us. If we know that an algorithm exists for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm cannot exist for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm exists for solving Problem T, what does that tell us about Problem S? [ Select ] [ Select ] An algorithm cannot exist for solving Problem S,r solving Problem T, what does that tell us about Nothing An algorithm exists for solving Problem S
Consider the following recursive algorithm Algorithm Q(n)// Input: a positive integer nif n == 1 return 1else return Q(n-1)+2*n-1 1) Set up a recurrence relation for this function’s value and solve it to determine what this algorithm computes. 2) Setup a recurrence relation for the number of multiplication made by this algorithm and solve it to find the total number of multiplications that are executed.
4. Practice with the iteration method. We have already had a recurrence relation ofan algorithm, which is T(n) = 4T(n/2) + n log n. We know T(1) ≤ c.(a) Solve this recurrence relation, i.e., express it as T(n) = O(f(n)), by using the iteration method.Answer:(b) Prove, by using mathematical induction, that the iteration rule you have observed in 4(a) is correct and you have solved the recurrence relation correctly. [Hint: You can write out the general form of T(n) at the iteration step t, and prove that this form is correct for any iteration step t by using mathematical induction.Then by finding out the eventual number of t and substituting it into your generalform of T(n), you get the O(·) notation of T(n).]
The n-th harmonic is the sum of the reciprocals of the first n natural numbers given by: 17 1.1 1 1 H₁ =Σ =1+=+=+ - 2 3 4 k=1 k +. + n (i) Write a recursive algorithm of this function returning, H, with nε N. (ii) Give a recurrence relation for the number of divisions the recursive algorithm calculates for an input n & N. iii) Solve the recurrence relation and give the O(n) of the algorithm.
I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O(n log n) as stated in the question.
Give the solution for T(n) in each of the following recurrences. Assume that T(n) is constant for small n. Provide brief justification for your answers.
Time comp.
5. You are given a set of n positive numbers A = {a₁,..., an} and a positive integer t. Design a dynamic programming algorithm running in O(nt) time that decides whether there exists a subset A' CA such that Σ x = t. Note that each element of A can be xЄA' used at most once. Is the run-time of your algorithm polynomial with respect to the size of the input?
A recursive algorithm is applied to some data A = (a₁,..., am) where m≥ 2. The running time T is characterised using the following recurrence equations: T(2) = c when the size of A is 2 T(m) = T(m-1) + 2c otherwise Determine the running time complexity of this algorithm.
Please help with question: Determine the running time of the following algorithms. Write summations to represent loops and simplify. Show all work. If bounding is used, the upper and lower bounds must only differ by a constant. Note: This is not the line-by-line analysis method. Loops are inclusive.
Explain the complete work !

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