Algorithms Answers

Use the following problem to provide an explanation of how you will use this problem to teach learners the steps of problem solving in Information Technology. Your answer must include the complete solution (algorithm) of the problem, but the computer code is not necessary. A company determines its employees’ weekly salaries by using the number of hours the employee worked during the week and rate per hour. If the employee worked more than 45 hours, he/she is paid at double his/her hourly rate for each hour in excess of 45 hours. The employee’s identity number, the number of hours worked per week by the employee and rate per hour are captured. The desired output is a salary slip that will indicate all details of the employee as well as the salary earned by the employee once 25% has been deducted for income tax purposes.

Consider the following Job Completion problem: Given n workers and m jobs, such that each worker has a list of jobs that he can do. Decide if there is an assignment such that every job gets assigned to a worker who can do the job, assuming that each worker is given at most one job. Design an efficient algorithm for the problem. Analyze your algorithm. 

Describe the basic elements of an instruction cycle and the role of interrupts

Write an algorithm that takes the positive integer ‘n’ as input and returns the exponent 2^n as output. Analyze the time complexity of the algorithm using program step table method.

Sort the following elements using merge sort technique 

using the Divide and Conquer strategy. {12,45, 6, 18, 10, 4, 3, 1, 13, 15, 16}

Write the algorithm, draw the flowchart, write and execute the Dart code for the following problem.

A student’s Midterm grade is 60 and the Final Grade is 80. The weight of Midterm and Final exams are % 40 and % 60 respectively.

Find the semester grade for this student.

Using appropriate diagrams, analyses the process flow for recognition evolvement, typically arranged as a hierarchy

Prove the theorem

The elass of regular languages is closed under union operation. In othe words, if Al

and A2 are regular languages, so is (Ai UA2)"for the following languageL-twiw acepts even mumber of 'a' or even number of "b'.

The following flowchart finds if the triangle is isosceles, equilateral, or scalene. Some boxes in the flowchart are filled in for you, fill in the rest of the details.

Hint: In an equilateral triangle three sides are equal.

 In an isosceles triangle two sides are equal.

 In a scalene triangle three sides are not equal. 

EXPLAIN IN DETAIL

A network G = (V, E) has 2²⁰ nodes. Each node v is labeled by a unique number L(v) between 0 to

2²⁰-1. No two nodes have the same label and there is a label for every node.

Two nodes u and v have an undirected edge (u, v) between them if and only if the following is true:

(i)The labels of the nodes L(u) and L(v) differ by a Hamming distance of at most 2 in their

binary representation, and

ii)The magnitude of the difference between the two numbers in the two labels is no

more than 9, i.e. | L(u) – L(v) | < 9. 

Answer all of the following questions:

(a) How many nodes in the graph are unreachable from the node with the label

00000000000000000111?

(b) Is the node 11110000000000000000 reachable from the node 00000000000000001111?

(c) How many edges are present in this graph?

(d) Is this graph bipartite?

(e) How many connected components are present in this graph?