Question

I have been looking at the current problem on Coding Bat:

“We have triangle made of blocks. The topmost row has 1 block, the next row down has 2 blocks, the next row has 3 blocks, and so on. Compute recursively (no loops or multiplication) the total number of blocks in such a triangle with the given number of rows.”

I understand what the problem is asking for, and I understand how recursion works. For example, if I am given a recursion function I can work it out by hand and show what the output will be.

The problem is actually creating the recursion function from a given problem, such as this one. I’m not sure how to actually set this up and do it recursively. Are there some sort of rules to follow when actually setting up a recursion problem? I can only find examples that show you how recursion works, not showing you how to actually solve a recursion problem. Any help understanding how to get ready to write the actually recursion algorithm would be appreciated.

Answer 1

Roughly:

1. Always look at the problem and try to find out if it can be divided
   into subproblems of the same type. That’s a first hint that you can
   possibly use a recursion. Essentially you are looking for a smaller
   instances/versions of an actual problem.

   Recursion takes therefore a top down approach(from the more complex to simpler problem cases).

2. When you can find such cases then you should find out what is the
   relation between the “bigger” case and the “smaller” case and you
   have your recursion step.

3. The final thing is to find out the terminating condition or what
   is the smallest or last case where you want to stop.

You probably know about this but if not it might help you.