Algorithms Answers

A. The Fibonacci numbers are the numbers in the following integer sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation. 

         Fn = F n-1 + F n-2

B. Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. For example, factorial of 6 is 6*5*4*3*2*1 which is 720.

         n! = n * (n - 1) * …….. 1 

 Write the algorithms to display the Fibonacci series and the factorial value for a given number using Pseudo code.

Define what an algorithm is and outline the characteristics of a good algorithm. Write the algorithms to display the Fibonacci series and the factorial value for a given number using Pseudo code. Determine the steps involved in the process of writing and executing a program.

Take a sample number and dry run the above two algorithms. Show the outputs at the end of each iteration and the final output. Examine what Big-O notation is and explain its role in evaluating efficiencies of algorithms. Write the Python program code for the above two algorithms and critically evaluate their efficiencies using Big-O notation.

A.   The Fibonacci numbers are the numbers in the following integer sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation. 

                 F_n = F _n-1 + F _n-2

B.   Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. For example, factorial of 6 is 6*5*4*3*2*1 which is 720.

                 n! = n * (n - 1) * …….. 1 

Create a pseudocode that will input values for A and B. Compare two values inputted and print which of the values is higher including the remark “Higher”.  

Construct an algorithm that will count from 1 to 10 and print each number counted using repetition structure. 

Construct an algorithm that will input a grade of student and determine whether the grade is passed or failed(Passing grade is 60). Print the, grade and remark of student.

Create an algorithm that will input values for A and B. Compare two values inputted and print which of the values is higher including the remark “Higher”. 

.Create a pseudocode and flowchart that will input values for A and B. Compare two values inputted and print which of the values is higher including the remark “Higher”. 

Suppose you are a manager of an event management company. Your team is responsible for running various events. Each event, depending on its nature, runs for varied lengths. Your company policy is such that you charge a flat amount for each event your team is managing (irrespective of the duration a particular event). The size of the team that you are running is such that your team can manage to run one event at a particular time i.e. your company is unable to run multiple events at a particular time. More formally, if there are two events i and j, the events are mutually compatible (i.e. you can select both i andj) if s>f, ors,>fwhere s; and fi are the start and finish time of the event i. You are required to select events that your team is going to manage so that you can maximize the profit for your company. The following table shows some candidate events for your company to manage for a particular day. Find out which events would you select such that you can maximize the profit for your company.