rank time bounds: (randomized) Rank various time bounds (functions of input size n, e.g., n², 2n) in order of their asymptotic growth rates. The functions will be given as LATEX-like code, e.g., (0) log n (1) 2 log n (2) 1 (3) 2^n You will rank them by uploading a text file with the proper nondecreasing order of asymptotic growth rates. Assume all logarithms are base 2. Some time bounds may have the same asymptotic growth rate, in which case listing them in either relative order would be considered correct. More precisely, a correct ordering f₁, f2,... satisfies fi = O(fi+1) for all i. In the above example, since 1 = o(log n), log n = 0(2 log n), and log n = o(2"), there are two correct solutions:

Question in image Please explain the algorithm with the answer. Python programming

Java-.Selection and insertion sort  3.a    Show steps of selection sort for the given array. You may need to add more rows to the table.   Selection Sort Initial value 3 2 7 5 4 8 9 10 1 Search 0 . . . end 3 2 7 5 4 8 9 10 1 Swap index 0                   Search 1 . . . end                   . . .                                                                                                                                                               3.b    Show steps of insertion sort for the given array. You may need to add more rows to the table.   Insertion Sort Initial value 3 2 7 5 4 8 9 10 1 , first item is sorted 3 2 7 5 4 8 9 10 1 , first 2 items are…

import numpy as np import torch import matplotlib.pyplot as plt Quiz Preparation Question 1. Write a function that generates a random tensor of n x n (n is the input). The output is the mean of the tensor. = 2, 4, 8, 16, ... 1024 and generate a vector 2. Write a code (for loop) that call that calls the function above with n = M(n). Plot the vector as a function of the log of n. 3. Given an n x m array write a code that replaces every element that is larger than 0.5 with 0.5. 4. The second derivative of a function can be approximated by the finite difference 1 ƒ"(x₂) = 73 (ƒ(£;+1) — 2ƒ(x;) + f(x;-1)) Given a vector f with values f = [f(xo),..., f(n) write a code that computes the approximation to f"(x) 5. The power method is a method to compute the largest eigenvalue of a matrix. Your google search is using this method every time you perform a google search. The method consists of the iteration Vj+1 = Av; || Avi|| where v; is a vector with chosen as a random vector, and A is the matrix…