Question

Objectives: - Practice designing/implementing algorithms - Practice use of functions

Code and document the following functions using NON-RECURSIVE ITERATION only.

Test the functions by calling them from a simple interactive main() function using a menu, with different values used to select the choice of function. Overall, you should have one C program (call it Lab1.c) containing one main() function and 5 other functions, where the functions are called based on an interactive user menu. The program should contain a loop that permits users to enter a new choice of function for each loop, until exit from the loop explicitly.

Write a explanation for each line
1
Factorial(0) = 1;

Factorial(n) = n * (n-1) * . . . * 2 * 1

Requirement: n >= 0; reject with error message otherwise

2
Fibonacci(0) = 0;

Fibonacci(1) = 1; Fibonacci(n) = Fibonacci(n-1) + Fibonacci(n-2);

Requirement: n >= 0; reject with error message otherwise

3
gcd (x, y) = x, if y=0

gcd (x, y) = gcd (y, x MOD y), if y > 0

Requirement: x and y both > 0; reject with error message otherwise

4
Power(a,b) = ??

Requirement: a > 0, b > 0, b is an integer; reject with error message otherwise

5
digProduct (x) = x if x <9

digProduct (x) = rightDigit * digProduct ( x/10)

Requirement: x is an unsigned integer (> 0); reject with error message otherwise

Sample Interaction

Lab 1

-----

1 - int Factorial(int n);

2 - int Fibonacci(int n);

3 - int Gcd(int x, int y);

4 - double Power(int a, int b);

5 – int digProduct (int x);

0 - QUIT

Please enter a selection: 6

Invalid Input.

Lab 1

-----

1 - int Factorial(int n);

2 - int Fibonacci(int n);

3 - int Gcd(int x, int y);

4 - double Power(int a, int b);

5 – int digProduct (int x);

0 - QUIT

Please enter a selection: 1

Enter a positive Integer: 5

Answer: 15

Lab 1

-----

1 - int Factorial(int n);

2 - int Fibonacci(int n);

3 - int Gcd(int x, int y);

4 - double Power(int a, int b);

5 – int digProduct (int x);

0 - QUIT

Please enter a selection: 4

Enter the first positive Integer: 2

Enter the second positive Integer: 3

Answer: 8

Lab 1

-----

1 - int Factorial(int n);

2 - int Fibonacci(int n);

3 - int Gcd(int x, int y);

4 - double Power(int a, int b);

5 – int digProduct (int x);

0 - QUIT

Please enter a selection: 0

Goodbye!

Answer 1

C Code :

#include<stdio.h>           // for using printf() and scanf()

int Factorial(int n)           // this function will return the factorial of n
{
   int result = 1;           // initially the result will 1
  
   for(int i=n;i>=1;i--)               // now calculating the factorial of n
   {
       result = result * i;               // multiplying all the numbers till n
   }
  
   return result;           // returning the value of factorial of n
}

int Fibonacci(int n)           // this function will return the nth fibonacci number
{
   int fib[n+1];                   // this array will store all the fibonacci numbers
   fib[0] = fib[1] = 0;           // first and second fibonacci numbers are always 0
   for(int i=2;i<=n;i++)          
   fib[i] = fib[i-1]+fib[i-2];               // calculating rest of the fibonacci numbers by adding previous two values
  
   return fib[n];           // returning the nth fibonacci number
}

int Gcd(int x, int y)           // this function will return the gcd of both x and y
{
   while(x!=y)            // iterating till x not equals to y
   {
        if(x>y)            // if x is greater than y
        x=x-y;                // we'll simply subtract y from x
        else           // otherwise
        y=y-x;                // we'll simply subtract x from y
    }
    return x;                // and at last, x will be the gcd of both x and y
}

double Power(int a, int b)               // this function will return the pow(a,b)
{
   double result = 1.0;               // initially this double variable will store 1.0
  
   for(int i=1;i<=b;i++)           // iterating b times
   result = result * a;           // multiplying the value of a, b times to get the pow(a,b)
  
   return result;               // returning the value of pow(a,b)
}

int digProduct (int x)               // this function will return the product of digits in the x
{
   int result = 1;               // initially the result will be 1
  
   while(x>0)           // iterating till x>0
   {
       int rem = x%10;               // finding each digits of the x
       result = result * rem;               // multiplying all the digits of x
       x = x/10;               // and each time, we'll remove the digits of the x
   }
  
   return result;               // returning the value of result
}

int main()
{      
   while(true)           // unitl user exits the program
   {
       printf("\n\nLab 1\n\n-----\n\n");               // this is a simple message as stated in the output of the question
       printf("\n1 - int Factorial(int n);\n\n");               // for calculating the factorial of number n
       printf("2 - int Fibonacci(int n);\n\n");               // for finding the nth fibonacci number
       printf("3 - int Gcd(int x, int y);\n\n");               // for finding the gcd of both x and y
       printf("4 - double Power(int a, int b);\n\n");               // for calculating pow(a,b)
       printf("5 - int digProduct (int x);\n\n");               // for finding the product of digits in the x
       printf("0 - QUIT\n\n");               // for quiting the menu by user
              
       int choice;                   // this variable will store the choice value of the user
       printf("Please enter a selection: ");               // asking for the choice of the user
       scanf("%d",&choice);               // taking input of the choice of the user
      
       if(choice==1)           // if choice is 1, we'll call Factorial(n)
       {
           int n;  
           printf("\nEnter a positive integer : ");               // asking for the input of n
           scanf("%d",&n);                   // taking input of n
          
           if(n>=0)           // if requirement is ok, then call Factorial(n)
           {
               int result = Factorial(n);
               printf("\nAnswer: %d",result);
           }
           else               // otherwise printing the error message
           printf("\nError! please enter a positive integer.");
          
       }
       else if(choice==2)           // if choice is 2, we'll call Fibonacci(n)
       {
           int n;
           printf("\nEnter a positive integer : ");               // asking for the input of positive integer
           scanf("%d",&n);                   // taking input of positive integer
          
           if(n>=0)           // if requirement is ok, then call Fibonacci(n)
           {
               int result = Fibonacci(n);
               printf("\nAnswer: %d",result);
           }
           else               // otherwise printing the error message
           printf("\nError! please enter a positive integer.");
       }
       else if(choice==3)           // if choice is 3, we'll call Gcd(x,y)
       {
           int x,y;
           printf("\nEnter the first positive integer : ");
           scanf("%d",&x);
           printf("\nEnter the second positive integer : ");
           scanf("%d",&y);
          
           if(x>0 && y>0)           // if requirement is ok, then call Gcd(x,y)
           {
               int result = Gcd(x,y);
               printf("\nAnswer: %d",result);
           }
           else               // otherwise printing the error message
           printf("\nError! please enter positive integers.");
       }
       else if(choice==4)           // if choice is 4, we'll call Power(a,b)
       {
           int a,b;
           printf("\nEnter the first positive integer : ");
           scanf("%d",&a);                               // taking input of first positive integer
           printf("\nEnter the second positive integer : ");
           scanf("%d",&b);               // taking input of second positive integer
          
           if(a>0 && b>0)           // if requirement is ok, then call Power(a,b)
           {
               double result = Power(a,b);
               printf("\nAnswer: %lf",result);
           }
           else               // otherwise printing the error message
           printf("\nError! please enter positive integers.");
       }
       else if(choice==5)           // if choice is 5, we'll call digProduct(x)
       {
           unsigned int x;
           printf("\nEnter a positive integer : ");
           scanf("%d",&x);               // taking input of positive integer
          
           if(x>0)           // if requirement is ok, then call digProduct(x)
           {
               int result = digProduct(x);
               printf("\nAnswer: %d",result);
           }
           else               // otherwise printing the error message
           printf("\nError! please enter a positive integer.");
       }
       else if(choice==0)               // if user wants to exit the program
       {
           printf("\nGoodbye!");               // printing goodbye
           break;               // breaking the while loop for exiting the program
       }
       else               // if user's choice is invalid
       printf("\nInvalid Input.\n");               // printing invalid input by user
   }
}

Output :