e maximum value of the following function F(x)=2x3 , using the genetic algorithm, performing two iterations
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Find the maximum value of the following function F(x)=2x3 , using the genetic
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- The binomial coefficient C(N,k) can be defined recursively as follows: C(N,0) = 1, C(N,N) = 1, and for 0 < k < N, C(N,k) = C(N-1,k) + C(N - 1,k - 1). Write a function and give an analysis of the running time to compute the binomial coefficients as follows: A. The function is written using dynamic programming.write dynamic programming algorithm that accepts two whole numbers X and N and calculates the exponential XN. (Hint: XN = X times)The binomial coefficient C(N,k) can be defined recursively as follows: C(N,0) = 1, C(N,N) = 1, and for 0 < k < N, C(N,k) = C(N-1,k) + C(N - 1,k - 1). Write a function and give an analysis of the running time to compute the binomial coefficients as follows: A. The function is written recursively.
- Let l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept. If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀). If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁). Instructions Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order: Input x₁ Input y₁ Input x₂The values of x and y should be swapped. Does the following algorithm work?Use summations to determine the exact growth rate of the following algorithm. Assume all variables have been properly declared. y = 1; for (i=1; i<=n; i++) { for (j=1; j<=n; j++) { x = A[i] + A[j]; x = x * y; } y = y + x; }
- A vector is given by x = [9 –1.5 13.4 13.3 –2.1 4.6 1.1 5 –6.1 10 0.2]. Using conditional statements and loops, write a program that rearranges the elements of x in order from the smallest to the largest. solve code in matlabHigher-order functions are the functions that run with higher than O(n) time complexity.Answer: true, falseWrite a fraction calculator program that adds, subtracts, multiplies, and di-vides fractions. Your program should check for the division by 0, have and use the following functions (a) reduce - reduces a given fraction.(b) flip - reduces a given fraction and flips the sign if the denominator is negative.(c) add - finds the reduced sum of a pair of given fractions.
- Write a function that has one input, a square (n x n, for any integer n)matrix. It should return three outputs: D, A, and B. Please use MATLABArrange this functions in increasing order of asymptotic complexity Select one: a. f1, f2, f3 b. f2, f1, f3 c. f2, f3, f1IN PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The vector of constant terms b contains all ones, except that the first and last elements are zero. You can use td to find that x1= −0.10557. The following code format should help: def td(l, m, u, b): '''Solve a linear system Ax = b where A is tridiagonal Inputs: l, lower diagonal of A, n-1 vector m, main diagonal of A, n vector u,…