(i) The time complexity of an'algorithm gives an indication of the amount of time the algorithm will take to run completely. (a) Is the time complexity of an algorithm based on the best-case or the worst-case scenario of the Algorithm? (b) Give the tight upper bound for the algorithms with the following time functions. Use the big O notation for your answers. 1. n²+3n+1 2. 2n + logn 3. n+n'+2" (c) Which of the algorithms in (i)(b) is most efficient?

(i) The time complexity of an'algorithm gives an indication of the amount of time the algorithm will take to run completely. (a) Is the time complexity of an algorithm based on the best-case or the worst-case scenario of the Algorithm? (b) Give the tight upper bound for the algorithms with the following time functions. Use the big O notation for your answers. 1. n²+3n+1 2. 2n + logn 3. n+n'+2" (c) Which of the algorithms in (i)(b) is most efficient?

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

Precisely specify the conditions under which the following algorithm returns true, and then discuss, in detail, the running time of the algorithm. If you think it has different best- and worst-case running times then these should be considered separately, and you should explain the conditions under which best and worst cases arise. explain your answer and use O, Ω and ø Algorithm Ex1 ((?1, ... ??), (?1, ... , ??)) ?←0 for ? ← 1 to ? do ?←1 while ? ≤ ? do If ?? ==?? ?←?+1 ?←?+1 return ? > 0
Subject: Theory of Computation Design a brute-force algorithm for solving this problem (below) and demonstrate that this algorithm's time complexity grows exponentially with input length. Adding 2 binary numbers, w is the length of the input which is the number of digits in the numbers. Suppose the input has the same number of digits
Suppose we have a problem that currently takes 100,000 hours of computer time usingcurrent technology to solve. Which of the following would give us the solution first: (1)Replace the algorithm used in the current solution by one that runs twice as fast and runit on the current technology, or (2) Wait 3 years, assuming Moore’s law doubles theperformance of a computer every 18 months, and find the solution using the currentalgorithm with the new technology?
For function f(n)=log n and time t=1 second, determine the largest size n of a problem that can be solved in time t, assume that the algorithm to solve the problem takes f(n) microseconds.
Part(a): Explain Race Condition with example. Part(b): What are the conditions that need to hold to solve critical section problem? Explain. Part(c): What is the problem with the following algorithm?
Under what circumstances might the A* algorithm fail even when using admissible heuristics? Give a clear example.
Question 15 pap Suppose we have a Monte Carlo algorithm, A, and a deterministic algorithm, B, for testing if the output of A is correct. How can we use A and B to construct a Las Vegas algorithm? Also, if A succeeds with probability ½ and both A and B run O(n) time, what is the expected running time of the Las Vegas algorithm that is produced? Full explain this question and text typing work only We should answer our question within 2 hours takes more time then we will reduce Rating Dont ignore this line
2 Although A* algorithm works better with a more informed heuristic function, theoverall computing time can be smaller with a less informed heuristic. How can thatbe possible?
Design a reasonably efficient algorithm for solving each of the following problems and determine its efficiency class. c. For a given positive integer n, find the pair of integers whose sum is n and whose product is as large as possible.
This question concerns computational complexity.In this question, the perfect square problem is the problem of determining if a positive integer, n, is a perfect square i.e. if n = x^2 where x is a positive integer. (c) Given that Heron's algorithm always overestimates the square root, explain how Heron's algorithm can be adapted into a decision algorithm for the perfect square problem. (d) Based on the Heron-adapted algorithm, what is the complexity class of the perfect square problem? Show your reasoning.
30. What is the worst-case runtime complexity of your algorithm?
Use previous solution to Derive Big Oh for the algorithms from Problem 1. This is the pervious solution starting with Step 1 and Step 2: Step 1 - We need to provide the asymptotic equation that will describe the complexity of the provided code snippets. Step 2 :: 1. First code :: -> In this we have 3 operations and all the operation take constant time. We are considering (input = n). Lets take time taken for :: x = 2 , y = 2 -> a (Constant time) x = ((y + z) * 80) /4 -> b (Constant time) print x ,y, z -> c (Constant time) Here all are constant operations. So, T(n) = a + b + c , which can also be written as :: T(n) = k (Constant) 2. Second code :: -> In this code we have a loop and so the operation will take linear time. We are considering (input = n). Lets take time taken for :: x = 1 , y = 5 -> a (Constant time) loop, (y = y + 5) , (print x, y) -> 4*n (Linear time) T(n) = a + 4*n or, T(n) = a + b*n ( a, b =…