AIM: Write a program to do Binary Search using a given Search Key in a Sorted Linear Array 'A' which has N values in it. Description: The binary search algorithm can only be used with sorted array and eliminates one half of the elements in the array being searched after each comparison. The binary search algorithm applied to our array A works as follows: Algorithm: (Binary Search) Here A is a sorted Linear Array with N elements stored in it in sorted order and SKEY is a given item of information to search. This algorithm finds the location of SKEY in A and if successful, it returns its location otherwise it returns -1 for unsuccessful. BinarySearch (A, N, SKEY) [Initialize segment variables.] 1. Set START=0, END=N-1 and MID=int((START+END)/2). 2. Repeat Steps 3 and 4 while START ≤ END and A[MID]+SKEY. 3. If SKEY< A[MID] Then Set END=MID-1. Else Set START=MID+1. [End of If Structure.] Set MID=int((START +END)/2). [End of Step 2 loop.] 5. If A[MID] = SKEY then Else 4. Set LOC = -1 [End of IF structure.] 6. return LOC and End Set LOC= MID

Prompt: In Python language, write a function that applies the logistic sigmoid function to all elements of a NumPy array. Code:   import numpy as np import math import matplotlib.pyplot as plt import pandas as pd   def sigmoid(inputArray):               modifiedArray = np.zeros(len(inputArray))               #YOUR CODE HERE:               return(modifiedArray) def test(): inputs = np.arange(-100, 100, 0.5) outputs = sigmoid(inputs) plt.figure(1) plt.plot(inputs) plt.title('Input') plt.xlabel('Index') plt.ylabel('Value') plt.show() plt.figure(2) plt.plot(outputs,'Black') plt.title('Output') plt.xlabel('Index') plt.ylabel('Value') plt.show() test()

DESIGN YOUR OWN SETTING Task: Devise your own setting for storing and searching the data in an array of non-negative integers redundantly. You may just describe the setting without having to give an explicit algorithm to explain the process by which data is stored. You should explain how hardware failures can be detected in your method. Once you have described the setting, include the following to your answer: Write a pseudocode function to describe an algorithm where the stored data can be searched for a value key: if the data is found, its location in the original array should be returned; -1 should be returned if the data is not found; -2 should be returned if there is a data storage error Include a short commentary explaining why your pseudocode works Describe the worst-case and best-case inputs to your search algorithm Derive the worst-case and best-case running times for the search algorithm Derive the Theta notation for the worst-case and best-case running times

1. (100 points) Write a Java program that ● ● ● Define an integer array with length of 10. Populate the array with random integer numbers. Sort this array into non-decreasing/decreasing order based on three sorting algorithms. bubble sort selection sort O insertion sort Test these 3 sorting methods Give a big-Oh characterization, in terms of n, of the running time of these three algorithms. Improve the bubble sort so that the time complexity of them are O(N) for the best case (extra