Java Question 19: The complexity of an algorithm may be specified using the Big-Ohnotation or simply O notation. The Big-Oh of an algorithm gives anapproximate measure of the computing time of the algorithm for a largenumber of inputs.Suppose you are to choose between two different algorithms for acertain problem where one of the algorithms has O(n) and the other isO(n^2). Which algorithm should you prefer? For the purpose of this item,n^2 should be read as n raised to 2. *O The algorithm that is O(n*2)O The algorithm that is O(n)

here we have some time complexity discussions.

Answered: The complexity of an algorithm may be…

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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For a given problem with inputs of size n, algorithms running time,one of the algorithm is o(n), one o(nlogn) and one o(n2). Some measured running times of these algorithm are given below: Identify which algorithm is which and explain the observed running Times which algorithm would you select for different value of n?
Second order Spada numbers are well established in the insurance industry. Formally they are defined by the recurrence: Si={Si−1 %( Si−2+1) :i≥ 2 , 1:i=0 ,7 :i=1} Give an O(n) time algorithm to compute the n-th Second order Spada number
A computer science student designed two candidate algorithms for a problem while working on his part-time job The time complexity of these two algorithms are T,(n) = 3 n logn and T2(n) = n6/5 a) Which algorithm is better? Why? b) If we run both algorithms at the same time with an input size of 105, which algorithm produces results faster than the other one? Why?
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Another recursive algorithm is applied to some data A = (a₁, ..., am) where m = 2* (i.e. 2, 4, 8,16 ...) where x is an integer ≥ 1. The running time T is characterised using the following recurrence equations: T(1) = c when the size of A is 1 T(m) = 2T (2) + c otherwise Determine the running time complexity of this algorithm.
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Consider array A of n numbers. We want to design a dynamic programming algorithm to find the maximum sum of consecutive numbers with at least one number. Clearly, if all numbers are positive, the maximum will be the sum of all the numbers. On the other hand, if all of them are negative, the maximum will be the largest negative number. The complexity of your dynamic programming algorithm must be O(n2). However, the running time of the most efficient algorithm is O(n). Design the most efficient algorithm you can and answer the following questions based on it. To get the full points you should design the O(n) algorithm. However, if you cannot do that, still answer the following questions based on your algorithm and you will get partial credit. Write the recursion that computes the optimal solution recursively based on the solu- (a) tion(s) to subproblem(s). Briefly explain how it computes the solution. Do not forget the base case(s) of your recursion.
Question 10 There are two algorithms A and B for solving the same problem. Algorithm A has a worst-case time complexity T (n) that satisfies the recurrence relation TA(n) 7× TA (n/2) + 100 × n², where n is the input size. Algorithm B has a worst-case time complexity TÂ(n) that satisfies the recurrence relation TÂ(n) = a × TÂ(n/3) + 200 × n², where n is the input size and a is a positive integer. = Assume that a = 9. What is the asymptotic notation of TB (n)? O(nloga log n) (n¹0g3 a log n) O(nlog, a) ○(nlog, a)
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Given a matrix of size N x M where N is the number of rows and M is the number of columns, write an algorithm to find the shortest path from the top-left cell to the bottom-right cell that passes through all the cells with a prime value and avoids cells with composite values. The algorithm should have a time complexity of O(NM log(max(N,M))).

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