Recursive solution of the exponential problem and it’s illustration in detail

This is very common problem that is asked in any interview. So that will be explained below:-

Before solving any recursive solution, we have to find the base case first and then the recursive portion. Here if we apply the power rule like a^(4) = a^(2) * a(^2) , then we can see one recursive pattern here. Now the base case will be a^0 or a^1, in both the case it will return 1 and the number itself, so we can easily consider a^1 as the base case.

But, what about the odd power number like, a^(5). Here also we can apply the power rule, like a^(4) * a^(1). So for the odd cases, we have to multiply with the number itself for one more time.

So, let’s check the solution in java-script. In the below mentioned code zero power value is not handled, please add this for your implementation.

//exponential recursive solution 

/*******

Here the approach is if , the n is 0 or 1 , we will return the number itself, this will be the base case, 
and for the logic we will use the power rule, like a^4 = a^2 * a^2 

************/
function exponentialRecursive( a , n )
{

         //base case define // zero value not handled intentionally
       if (n ===1) {
           return a;
       } else if  (n%2 ===0)       {

             // even number check 

           a = exponentialRecursive( a , n/2   ) * exponentialRecursive( a , n/2   );
            return a;
           
       }else if (n%2 ===1 ) {
           // odd number check 


               a = exponentialRecursive( a , Math.floor(n/2) ) * a * exponentialRecursive( a , Math.floor(n/2)   );
           return a;
               
           
       }



    
}

Illustration of the call stack:-

You can also check the below mentioned link, where it’s also explained with divide and conquer technique.

Recursive Exponential Function