# recursive function without intermediate variables

The question was to convert this recursive code with intermediate variables to a functional program code without any intermediate variables.

product(p,q){
r=0
if(q==1)
return r
else{
if(q%2!=0){
r=r+p
q--
product(p,q)
}
else{
r=r+2p
q=q/2
product(p,q)
}
}
}

The code without intermediate variables that I wrote,

product(p,q){
if(q==1)
return r
else{
if(q%2!=0){
product(p,q--)
return r+p
}
else{
product(p,q/2)
return r+2p
}
}
}

Is this code correct?

For example if we take (5,3) it will output 15 as following if we use the first recursive code.

(p,q-1) --> (5,2)   as p=3 is odd       r=r+p=0+5=5

(p,q/2) --> (5,1)   as p=2 is even      r=r+2p=5+10=15

at this point it returns r which is equal to 15.

In the code without intermediate variables the return values are stored in the stack separately and they return r values separately. How can I add the r values without storing them in an intermediate variable?

(p,q-1) --> (5,2)   as p=3 is odd      return r+p=0+5=5

(p,q/2) --> (5,1)   as p=2 is even     return r+2p=0+10=10

I am new to learning recursion and I am really sorry if the question is not very clear.

• The code wont compile in any language since you haven't defined what $r$ is Jan 15 at 11:26
• If I declare r=0 before the function starts will it be okay? @nirshahar Jan 15 at 12:08
• Is the code correct? Run it on a few inputs and see if you get the same answer as the original code. Jan 15 at 12:13
• @SanduniAaloka of course not, since you never modify $r$ - it will always be $0$. It will technically compile, but would it really result in the answer you want? Jan 15 at 14:01
• @nirshahar No it doesn't give the answer I want. It wouldn't even return 0 for r and I have no idea of how to add those two r values in the if-else condition. Jan 15 at 16:02