A certain algorithm takes 10-4 x 2n seconds to solve an instance of size n. Show that in a year it could just solve an instance of size 38. What size of instance could be solved in a year on a machine one hundred times as fast? A second algorithm takes 10-2 x n3 seconds to solve an instance of size n. What size instance can it solve in a year? What size instance could be solved in a year on a machine one hundred times as fast? Show that the second algorithm is nevertheless slower than the first for instances of size less than 20

Q: Recall the "better" algorithm to determine whether or not the input positive integer is a prime…

A: Answer : The time complexity of that algorithm is O(N). where N is integer.

Q: Suppose that someone has developed an algorithm to solve a certain problem, which runs in time T(n,…

A: solution given below

Q: Is this algorithm complexity n^3 or is it n^2k? Can you recheck the solution again?

A: The time complexity of the function word_partition given in the root solition is O(n^2). It is not…

Q: performs 10 n2 basic operations, while algorithm B does 300ln(n) basic operations, resulting in a…

A: Given : A performs 10*n^2 basic operations A performs 300*ln(n) basic operations

Q: A O(n log(n)) algorithm is faster than a 0(1.1^n) algorithm when n is sufficiently large. Answer.…

A: According to the information given:- We have to explain the mentioned statement is true or not.

Q: Give an example of an algorithm that is O(1),  an algorithm that is O(n) and an algorithm that is…

A: Consider an example of array of size n and we can provide examples for all time complexities O(1),…

Q: Recall the Babylonian Algorithm for calculating a square root that we discussed in class. What will…

A: The idea is, we are given S for which we want to find S we first make an estimate x of S if x is…

Q: Given an algorithm has quadratic performance and has a runtime of 3 minutes for 1000 inputs, am I…

A: Given: Quadratic performance is O(n^2) runtime of 3 minutes for 1000 inputs   N=1000  => time…

Q: An algorithm A, has a runtime T:(n) defined (in seconds) by the following function:- Ta(n) = n? + n…

A: We need to write a program that performs the algorithm 3 equation and find the value of n (if it…

Q: th The following algorithms were given in Week 6 for computing the n power of a positive integer a.…

A: Use induction to prove the algorithm: Proof by induction is a technique that can demonstrate that an…

Q: Given two algorithms with growth rate functions f(N) = 1000N? and g(N) = N² + N, the algorithm with…

A: Given two algorithms with growth rate functions f(N) = 1000N2  and g(N) = N2 + N, the algorithm with…

Q: ke for input size 500 (assuming that the lower-order terms are negligible) if the running time of…

A: given - An algorithm takes 0.5ms for input size 100. How long will it take for input size 500…

Q: Suppose that you have five different algorithms (A, B, C, D and E) for solving a problem. To solve a…

A: An algorithm (pronounced AL-go-rith-um) is a procedure or formula for solving a problem, based on…

Q: Suppose that you have two different algorithms for solving a problem. To solve a problem of size n,…

A: Suppose that you have two different algorithms for solving a problem. To solve a problem of size n,…