Suppose that an algorithm has runtime 20 n3 for n <= 100. For n>100, the slowest cases for each n take time 2 n2 log n. The fastest cases for each n take time 10 n2. That is, for n>100, runtime is between 10 n2 and 2 n2 log n. Which of the following are known to be true of the worst-case runtime for the algorithm? (Check all that apply, which may be more than one in a row.)   O( n2 ) O( n2 log n ) O( n3 ) None of these       Ω( n2 ) Ω( n2 log n ) Ω( n3 ) None of these     Θ( n2 ) Θ( n2 log n ) Θ( n3 ) None of these   Which of the following are known to be true of the average-case runtime?      O( n2 ) O( n2 log n ) O( n3 ) None of these       Ω( n2 ) Ω( n2 log n ) Ω( n3 ) None of these     Θ( n2 ) Θ( n2 log n ) Θ( n3 ) None of these   [Each row must have at least one answer checked.]

You solve a non-singular system of 10,000 linear equations with 10,000 unknowns using the Gauss-Jordan algorithm without pivoting with single precision numbers and arithmetics on a computer that natively can do single precision operations very fast, but can operate in double and half precision as well. Your solution has a residual infinity-norm that is unacceptably large. In which order should you apply the following strategies to lower the residual norm? If a strategy is not / no longer helpful, do not list it as an option. a) use half precision numbers and arithmetics instead of single precision; b) use double precision numbers and arithmetics instead of single precision; c) use partial pivoting; d) use pivoting when encountering a zero in the pivot position.

Please provide a correct answer with a full explanation by yourself. Don't copy. Thank you.

The factorial function f(n) = n! is defined by n! = 1 2 3... n whenever n is a positive integer, and O! = 1. Provide big-O estimates for the factorial function and the logarithm of the factorial function. As an illustration, 1! = 1, 2! = 1 2=2, 3! = 1 23 = 6, and 4! = 1 234=24.Take note of how quickly the function n! expands. Consider the following: 20! = 2,432,902,008,176,640,000.

If you have the error formula for the root finding method shown in the image where xn is the approximation of r at step n, en = xn - r is the error and cassi is a value between xn and r, how do you show that the method converges to r. Also what would the convergence rate be?

do it

Write a program to find the solution to Maxone problem (You want to maximize the number of ones) using agenetic algorithm where the population size is 2000 and each chromosome is 20 genes long. Use a mutationprobability of 0.02 and a cross-over probability of 0.5. Make separate functions for different components of thegenetic algorithm.

Which algorithm has the worst time complexity in average?

What do I do for (K + 1)? Please explain as best as possible

John tells you that a certain algorithm runs in time n(n2 +200n), and Bill tells you that the same algorithm runs in time (n). Assume that both statements are correct, which one is more informative, i.e., gives you a better estimation of the running time? Why?