An in-depth look into Recursion in C

Reading time: 30 minutes

What is base condition in recursion?

In recursive program we have 2 conditions to be followed :

1. The solution of bigger problem are reduced into smaller problems or subproblems.
2. The solution is already available.

int fact(int n)
{
    if (n < = 1) // base case
        return 1;
    else    
        return n*fact(n-1);    
}

In the above example, base case for n < = 1 ( as the value for n < = 1 is always 1 )is defined and larger value of number can be solved by converting to smaller one till base case is reached.

Types of recursion

There are two types of recursion:

• Direct recursion
• Indirect recursion

Direct Recursion :

A function fun is called direct recursive if it calls the same function fun.

void directFun()
{
    // Some code....

    directFun();

    // Some code...
}

Indirect Recursion

A function fun is called indirect recursive if it calls another function say fun_new and fun_new calls fun directly or indirectly.

void indirectFun1()
{
    // Some code...

    indirectFun2();

    // Some code...
}
void indirectFun2()
{
    // Some code...

    indirectFun1();

    // Some code...
}

How recursion works?

Recursive functions use something called “the call stack.” When a program calls a function, that function goes on top of the call stack. This similar to a stack of books. You add things one at a time. Then, when you are ready to take something off, you always take off the top item.

I will show you the call stack in action with the factorial function. factorial(4) is written as 4! and it is defined like this: 4! = 4 * 3 * 2 * 1. Here is a recursive function to calculate the factorial of a number:

function fact(x) {
  if (x == 1) {  
    return 1;  
  } else {      
    return x * fact(x-1);
  }
}

Now let’s see what happens if you call fact(4) The illustration bellow shows how the stack changes, line by line. The topmost box in the stack tells you what call to fact you’re currently on.

Conversion of a loop into recursion

Key points:

• Any loop can be converted into recursion
• Any recursion can be converted into loops like for loop

The following code uses the while loop to compute the Greatest Common Divisor (GCD) of two numbers:

unsigned greatest_common_divisor (unsigned a, unsigned b)
{
      while (a != b)
      {
        if (a > b)
        {
          a -= b;
        }
        else if (b > a)
        {
          b -= a;
        }
      }
}

The above while loop is converted to a recursion in the following code:

unsigned greatest_common_divisor (unsigned a, unsigned b)
{
      if (a > b)
      {
        return greatest_common_divisor ( a-b, b );
      }
      else if (b > a)
      {
        return greatest_common_divisor ( a, b-a );
      }
      else // (a == b)
      {
        return a; 
      }
}

Disadvantages of using recursion

1. Requires more space as all functions remains in STACK till reaches the base class.
2. It also has greater time requirements because of function calls and return overhead.

Difference between recursion and iterations

• A conditional statement decides the termination of recursion while a control variable’s value decide the termination of the iteration statement (except in the case of a while loop).

• Infinite recursion can lead to system crash whereas, infinite iteration consumes CPU cycles.

• Recursion repeatedly invokes the mechanism, and consequently the overhead, of method calls. This can be expensive in both processor time and memory space while iteration doesn’t.

• Recursion makes code smaller while iteration makes it longer.

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