6] An algorithm has a count of basic operations C(n) = 25-n²-log₂(n). For a problem size n implementing the algorithm was timed and found to run in 5 minutes. (a) Your boss is asking to run the program for a problem size n = 100,000 on the same m the time it would take. Is it feasible? • Hint: We do not need Cop because it will simplify in the ratio anyway! Solution:

6] An algorithm has a count of basic operations C(n) = 25-n²-log₂(n). For a problem size n implementing the algorithm was timed and found to run in 5 minutes. (a) Your boss is asking to run the program for a problem size n = 100,000 on the same m the time it would take. Is it feasible? • Hint: We do not need Cop because it will simplify in the ratio anyway! Solution:

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 18SA

See similar textbooks

Similar questions

Consider two programs-A and B that have the following performances: A. O(log n) B. O(n2) If each program requires 7 seconds to solve a problem of size 100, estimate the time required by each program for a problem of size 200. [log 100 = 6.64]
2) 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 T1(n) = 3 n logn and T2(n) = nº/5 . a) Which algorithm is better? Why? b) If we run both algorithms at the same time with an input size of 10°, which algorithm produces results faster than the other one? Why?
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?
2) 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 T1(n) = 3 n log n and T2(n) = nº/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?
2. Algorithm A has a running time described by the recurrence T(n) = 7T(n/2) + n². A competing algorithm B has a running time described by the recurrence T(n) = aT (n/4) + n². What is the largest integer value for a such that B is asymptotically faster than A? Explain your answer.
2. For a problem we have come up with three algorithms: A, B, and C. Running time of Algorithm A is O(n¹000), Algorithm B runs in 0(2¹) and Algorithm C runs in O(n!). How do these algorithms compare in terms of speed, for large input? Explain why.
Problem FIG can be solved in O(RK + R log log n) time usingθ(R) space.Write Algorithm for it
Al and Bob are arguing about their algorithms. Al claims his O(nlogn)-time method is always faster than Bob's O(n²)-time method. To settle the issue, they perform a set of experiments. To Al's dismay, they find that if n 100 is the O(nlogn)-time one better. Explain how this is possible.
You are given a collection of n bolts of different widths and n corresponding nuts. You are allowed to try a nut and bolt together, from which you can determine whether the nut is larger than the bolt, smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to each nut. Design an algorithm for this problem with Θ(n log n) average-case complexity (in terms of nut-bolt comparisons). Explain why your algorithm has Θ(n log n) average case complexity.
Given an n-element array X of integers, Algorithm A executes an O(n) time computation for each even number in X and an O(log-n) time computation for each odd number in X. What are the best case and worst case for running time of algorithm C?
You are given a collection of n bolts of different widths and n corresponding nuts. You are allowed to try a nut and bolt together, from which you can determine whether the nut is larger than the bolt, smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to each nut. Design an algorithm for this problem with Θ(n log n) average-case complexity (in terms of nut-bolt comparisons). Explain why your algorithm has Θ(n log n) average-case complexity. You may use any result without explicitly solving recurrence equations.
Algorithm X has a growth rate that is proportional to n ∗ n ∗ n . What is the function that represents the growth rate of algorithm X? What is the order of algorithm X?