Lab # 7

(Function with output parameter and Recursive function)

© Manzur Ashraf

Objective:

Learn how to write user defined functions.

Scope:

The student should know the following:

1. void Functions with Input/Output Parameters

2. Recursive functions

Functions with output parameters using pointers :

Till now we used only the functions that returned zero or one value through the return statement. To return more than one value, we need to use the output parameters, which are pointers. Note that when we use output parameters in functions we declare those functions as void returning functions because they are not returning single value by return statement.

Solved Example (i) :

Consider the example of a function that accepts the radius of a circle from the main program and returns the area and circumference of a circle by using the output parameters:

#include <stdio.h>

void area_circum (float radius, float *area, float * circum) ; / function prototype */

void main (void)

{

float r, a, c ;

printf (“Enter the radius of the circle \n”) ;

scanf (“%f”, &r) ;

area_circum (r, &a, &c) ; /* function call that passes the address of the variables a and c */

printf (“The area is %f and circumference is %f\n”, a, c) ; /* output results */

} //end of main

void area_circum (float radius, float *area, float * circum) // function

{

*area = 3.14 * radius * radius ; /* indirect reference to variable a of main program */

*circum = 2 * 3.14 * radius ; /* indirect reference to variable c of main program */

} // end of function area_circum()

Here the variables area of function area_circum and a of main both refer to the same memory location. Similarly, the variables circum of function area circum and c of main both refer to the same memory location.

Note that when the function is called in the main program, the output parameters have & attached to them before their name. When the output parameters are used in the function, they are used with * attached to them before their name.

Recursion:

What is recursion?:

· So far, we have seen that a C program consists of the function main() and a zero or more other functions.

· That each of the other functions can be called by main() or by other functions.

· In addition, C also allows a function to call itself. Such a function is called a recursive function.

· Recursion is essentially another way of performing iteration.

· It is a very powerful tool for simplifying algorithms and coding of functions that involve repetitions

· It generally involves using the divide and conquer approach to problem solving.

· In this approach, a large problem is solved by breaking it into two or more sub-problems and solving the sub-problems. The sub-problems are solved by further sub-dividing them into more simpler problems. This sub-division continue until the simples form of the problem is obtained, the solution to which is obvious.

Examples of recursive functions:

• Recursive functions generally consists of two parts:

Base Case: Which provides a solution to the simplest form of a problem.

Recursive Case: Which solves a general form of the problem in terms of the next simpler

version of the problem.

Example 1:

• The function sum above can be computed as follows:

Iterative Solution	Recursive Solution
int sumton(int n) { int i, sum=0; for (i=1; i<=n; i++) sum+=i*i; return sum; }	int sumton(int n) { if (n ==1) return 1; else return (n*n+sumton(n-1)); }

Example2:

Fibonacci Sequence:

This is defined recursively as:

f₀ = 0, f₁ = 1 f_i+1 = f_i + f_i-1 for i=1,2, ..

i.e. except for f₀ and f₁, every element is the sum of its previous two elements:

0, 1, 1, 3, 5, . . .

• The following functions implements computes the nth Fibonacci number.

Iterative Solution	Recursive Solution
int fibonacci (int n) { int i,sum1=0, sum2=1, sum; if (n<=1) return n; else { for (i=2; i<=n; i++) { sum=sum1+sum2; sum1=sum2; sum2=sum; } return sum; } }	int fibonacci(int n) { if (n<=1) return n; else return (fibonacci(n-1) + fibonacci(n-2)); }

Exercises:

Problem # 1:

By taking help from Solved Example(i) Solve the following problem:

Write a function that takes 3 integers a, b , c from main program as input parameter

and returns the sum of the three, the product of the three, and the average by using

output parameter. Write a main program to test the function.

Problem #2 :

By taking help from above solved examples of recursive functions Solve the following problem:

Write a recursive function power that takes a float variable x, and an integer variable n, and returns the value of xⁿ . Write a main program to test the function.

Evaluation:

Your grade will depend on yours individual efforts in solving lab problems , your active participation and seriousness during the lab.