Base case in a recursive method

Question

A theoretical question here about the base or halting case in a recursive method, what\'s its standards?

I mean, is it normal not to have body in it, just a retu

Answer 1

The base case is to terminate the loop (avoid becoming an infinite recursion). There's no standard in the base case, any input that is simple enough to be solved exactly can be chosen as one.

For example, this is perfectly valid:

int factorial (int n) {
  if (n <= 5) {
    // Not just a return statement
    int x = 1;
    while (n > 0) {
      x *= n;
      -- n;
    }
    return x;
  } else {
    return n * factorial(n-1);
  }
}

Answer 2

It depends entirely on the particular recursive function. In general, it can't be an empty return; statement, though - for any recursive function that returns a value, the base case should also return a value of that type, since func(base) is also a perfectly valid call. For example, a recursive factorial function would return a 1 as the base value.

Answer 3

The pattern for recursive functions is that they look something like this:

f( value ) 
   if ( test value )
      return value
   else
      return f( simplify value )

I don't think you can say much more than that about general cases.

Answer 4

In some cases, your base case is

return literal

In some cases, your base case is not simply "return a literal".

There cannot be a "standard" -- it depends on your function.

The "Syracuse Function" http://en.wikipedia.org/wiki/Collatz_conjecture for example, doesn't have a trivial base case or a trivial literal value.

"Do you have different thoughts about it??" Isn't really a sensible question.

The recursion has to terminate, that's all. A trivial tail recursion may have a "base case" that returns a literal, or it may be a calculation. A more complex recursion may not have a trivial "base case".