Algorithm A 1. Set sum = 0. // 1 assignment2. Set i = 0. // 1 assignment 3. While (i <= n): // n comparisonsa.Set sum = sum + i. // n arithmetic operations, n assignmentsb.Increment i by 1. // n increments 4.Display (sum). // 1 write Algorithm B 1.Set sum = (n × (n + 1))/2. // 3 arithmetic operations, 1 assignment2.Display (sum). // 1 write Both, Algorithm A and Algorithm B, perform the same task. This means that both determine the sum of the first nnatural numbers. Algorithm A adds each number iteratively to a variable, sum. However, Algorithm B uses a formula to calculate the sum of the first n natural numbers. The execution time required for Algorithm A is given by:T = (n + 2) × a + n × b + 1 × c + n × d + n × eT = an + 2n + bn + c + dn + enT = c + n (a + b + d + e + 2)As T is a linear function of n, the algorithm is of the order, O (n).Now, determine the time required to execute Algorithm B:T = 1 × a +1 × c + 3 × eT = a + c + 3eUnlike Algorithm A, the time taken by Algorithm B is constant and does not depend on the value of n.  Therefore, the algorithm is of the order __________ ?

For each of the following algorithms, indicate (i) a natural size metric for itsinputs, (ii) its basic operation, and (iii) whether the basic operation count canbe different for inputs of the same size:a. computing the average of n numbersb. computing n/n!c. finding the smallest element in a list of n numbersd. reverse display a list of n numberse. reverse a list of n numbersf. pen-and-pencil algorithm for adding two n-digit decimal integers

Compare and contrast an algorithm and a program (4 marks

John, Ram, and Joseph are comparing their finances after receiving their monthly salaries and incurring some expenditures.Your task is to create a program that, with the input of their salaries and expenditures, utilizes assignment operators (+= and -=) to compute and identify which friend has the highest remaining amount.Input format :The first line of input consists of two space-separated integers, representing John's salary and expenditure.The second line of input consists of two space-separated integers, representing Ram's salary and expenditure.The third line of input consists of two space-separated integers, representing Joseph's salary and expenditure.Output format :The output displays the name of the friend who has the highest remaining amount in the format "{Name} has more money".Refer to the sample output for the formatting specifications.Code constraints :In the given scenario, the test cases will fall under the following constraints:100 ≤ salary ≤ 1050 ≤ expenditure ≤ 105Sample test cases :Input 1 :2000 501500 307500 10Output 1 :Joseph has more moneyInput 2 :50000 1000057000 20000100000 100000Output 2 :John has more moneyInput 3 :2500 103500 251000 10Output 3 :Ram has more money

Algorithm Analysis

Consider the following recursive algorithm.ALGORITHM Q(n)//Input: A positive integer nif n = 1 return 1else return Q(n − 1) + 2 ∗ n − 1a. Set up a recurrence relation for this function’s values and solve it to deter-mine what this algorithm computes.b. Set up a recurrence relation for the number of multiplications made by thisalgorithm and solve it.c. Set up a recurrence relation for the number of additions/subtractions madeby this algorithm and solve it.