Answer to Question #254266 in Algorithms for Shanu

Question

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, ……..

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 

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.

Answer 1

A)

START

   Step 1  Declare variables A, B, C,n

   Step 2  Set A = 0, B = 0

   Step 3  DISPLAY A, B

   Step 4  C = A + B

   Step 5  DISPLAY C

   Step 6  Set A = B, B = C

   Step 7  REPEAT from 4 - 6, for n times

STOP

B)

Start

   Step 1: Declare variables n, fact, i

   Step 2: Read number from User

   Step 3: Initialize variables fact=1 and i=1

   Step 4: Repeat Until i<=number

            4.1 fact=fact*i

            4.2 i=i+1

   Step 5: Print fact

Stop