Trinary operator

gagless12 · #1 04-Jun-2008, 19:45

I was looking at the following function definition and I'm not understanding how it works exactly.

CPP / C++ / C Code:

int F( int X )
{
	return (X<=0) ? 3 : F(X/2)+F(X-3);
}

I tested it out and put 0 and lower values into and got three, fine. But when I put in values greater than zero, like 2, it returned 9. 3 also returned 9. 4 returns 15.

ocicat · #2 04-Jun-2008, 20:31

Quote:

Originally Posted by gagless12

I tested it out and put 0 and lower values into and got three, fine. But when I put in values greater than zero, like 2, it returned 9. 3 also returned 9. 4 returns 14.

First of all, it is called the ternary operator.

Function F() as defined above is equivalent to the following:

CPP / C++ / C Code:

int f(int i) {
    int v;

    if (i <= 0)
        v = 3;
    else
        v = f(i / 2) + f(i - 3);

    return v;
}

Both forms are recursive -- the return value is determined by calling the same function again with differing arguments.

The sequence generated is:

Code:

 0        3       
 1        6       
 2        9       
 3        9       
 4       15     
 5       18  
 6       18  
 7       24  
 8       33  
 9       33
10       42 
11       51 
12       51 
13       60 
14       75 
15       75 
16       93 
17      108
18      108
19      126

The sequence is modestly interesting by virtue of its recurring plateaus, & you may be able to find a relation between the number of repeated plateau values, the value 3, & the fact that division by 2 is being done with integer division.

Otherwise, I do not recognize this sequence as being anything historically notable; it's just a sequence.

gagless12 · #3 04-Jun-2008, 22:34

Great. Thanks for the help.

gagless12 · #4 04-Jun-2008, 23:45

Have another question.

I'm trying to write a recursive function that takes one parameter ( an interger ) and returns how many of the digits are 3, recursively.

So if the parameter is 31337 the function returns 3, if its 0152, it returns 0.

I have the simple parts down, if x = 0 return 0 and if x = 3 return 1, but I can't figure out how to do the part where the function calls itself. Would I need to use an array? Or can it be done without one.

ocicat · #5 04-Jun-2008, 23:52

Quote:

Originally Posted by gagless12

Would I need to use an array?

To store the answer? I haven't worked out the solution yet, but no. You simply need the count.

fakepoo · #6 06-Jun-2008, 07:42

Here is how I would do it:

CPP / C++ / C Code:

void NumDigits( int i )
{
  // If the absolute value of i is zero, return 0
  // If the absolute value of i is less than 10, return 1
  // return 1 + NumDigits(i/10)

}

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