What is recursion and when should I use it?

Answer 1

"If I have a hammer, make everything look like a nail."

Recursion is a problem-solving strategy for huge problems, where at every step just, "turn 2 small things into one bigger thing," each time with the same hammer.

Example

Suppose your desk is covered with a disorganized mess of 1024 papers. How do you make one neat, clean stack of papers from the mess, using recursion?

1. Divide: Spread all the sheets out, so you have just one sheet in each "stack".
2. Conquer:
   2. Go around, putting each sheet on top of one other sheet. You now have stacks of 2.
   3. Go around, putting each 2-stack on top of another 2-stack. You now have stacks of 4.
   4. Go around, putting each 4-stack on top of another 4-stack. You now have stacks of 8.
   5. ... on and on ...
   6. You now have one huge stack of 1024 sheets!

Notice that this is pretty intuitive, aside from counting everything (which isn't strictly necessary). You might not go all the way down to 1-sheet stacks, in reality, but you could and it would still work. The important part is the hammer: With your arms, you can always put one stack on top of the other to make a bigger stack, and it doesn't matter (within reason) how big either stack is.