Question

I’m new to programming and have had a hard time understanding recursion. There’s a problem I’ve been working on but can’t figure out. I really just don’t understand how they are solvable.

“Define a procedure plus that takes two non-negative integers and returns their sum. The only procedures (other than recursive calls to plus) that you may use are: zero?, sub1, and add1.

I know that this is a built in functions in scheme, so I know they’re possible to solve, I just don’t understand how. Recursion is so tricky!

Any help would be greatly appreciated!
=] Thanks

I’m working in Petite Chez Scheme (with the SWL editor)

Answer 1

Recursion is a very important concept in software development. I don’t know (petit chez) scheme so I will approach this from a general angle.

The concept of a recursive function is to repeat the same task over and over again until you reach some limiting boundary. Taking your first question, you have two numbers and you need to add them together. However, you only have the ability to add 1 to a number or subtract 1 from a number. You also have the literal value zero.

So. consider you numbers as two buckets. They each have 10 stones in them. You want to “add” those two buckets together. You are only permitted to move one stone at a time (i.e. you can’t grab a handful or tip one bucket into the other).

Lets say you want to move everything from the left bucket into the right bucket, one stone at a time. What are you going to have to do?

First, you have to take 1 stone from the left bucket, i.e. you are using sub1 to remove one stone from the bucket. You then add that same stone to the right bucket, i.e. you add1 to the right bucket.

Now you could do this in a loop, but you don’t know how many stones there will be in any given solution. What you really want to do is say “Take one stone from the left bucket, put it in the right bucket and repeat until there are no stones in the left bucket.’ This case of there being no stones in the left bucket is called you “Base Case”. It’s the point at which you say OK, I’m done now.

A pseudocode example of this situation would be (using your plus, add1, sub1 and zero):

plus(leftBucket, rightBucket)
{
  if(leftBucket == zero) // check if the left bucket is empty yet
  {
    // the left bucket is empty, we've moved all the stones
    return rightBucket; // the right bucket must be full
  }
  else 
  {
    // we still have stones in the left bucket, remove 1, 
    // put it in the right bucket, repeat.
    return plus(sub1(leftBucket), add1(rightBucket)); 
  }
}

If you still need more help, let me know, I can run through other examples but this looks like it’s probably a homework problem for you and recursion is incredibly important to understand so I don’t want to just give you all the answers.