Question 3: a) Write a C function count_digits() which takes an integer n as parameter and retums the number of digits in that integer. For example if n=12345 then your function should retum 5. Write appropriate main function to check your code. b) Write the above function count_digits() by using recursion.

Recursion

• Recursion is the process of repeating items in a self-similar way. In programming languages, if a program allows you to call a function inside the same function, then it is called a recursive call of the function.

• The C programming language supports recursion, i.e., a function to call itself. But while using recursion, programmers need to be careful to define an exit condition from the function, otherwise it will go into an infinite loop.

• Recursive functions are very useful to solve many mathematical problems, such as calculating the factorial of a number, generating Fibonacci series, etc.
• A function in C can be called either with arguments or without arguments.
• These function may or may not return values to the calling functions.
• All C functions can be called either with arguments or without arguments in a C program.

Function with no argument and no return value : 

When a function has no arguments, it does not receive any data from the calling function.

Similarly when it does not return a value, the calling function does not receive any data from the called function.

Function declaration : void function();
Function call : function();
Function definition :
                      void function()
                      {
                        statements;
                      }
Function with arguments but no return value : When a function has arguments, it receive any data from the calling function but it returns no values.

Syntax :

Function declaration : void function ( int );
Function call : function( x );
Function definition:
             void function( int x )
             {
               statements;
             }
Function with no arguments but returns a value : There could be occasions where we may need to design functions that may not take any arguments but returns a value to the calling function. A example for this is getchar function it has no parameters but it returns an integer an integer type data that represents a character.

Function declaration : int function();
Function call : function();
Function definition :
                 int function()
                 {
                     statements;
                      return x;
                  }