Question

Given inputs 1-32 how can I generate the below output?

in. out

1. 1
2. 1
3. 1
4. 1
5. 2
6. 2
7. 2
8. 2
9. 1
10. 1
11. 1
12. 1
13. 2
14. 2
15. 2
16. 2
    …

Edit Not Homework.. just lack of sleep.

I am working in C#, but I was looking for a language agnostic algorithm.

Edit 2 To provide a bit more background… I have an array of 32 items that represents a two dimensional checkerboard. I needed the last part of this algorithm to convert between the vector and the graph, where the index aligns on the black squares on the checkerboard.

Final Code:

 --Index;
 int row = Index >> 2;
 int col = 2 * Index - (((Index & 0x04) >> 2 == 1) ? 2 : 1);

Answer 1

Assuming that you can use bitwise operators you can check what the numbers with same output have in common, in this case I preferred using input 0-31 because it’s simpler (you can just subtract 1 to actual values)

What you have?

0x0000 -> 1
0x0001 -> 1
0x0010 -> 1
0x0011 -> 1
0x0100 -> 2
0x0101 -> 2
0x0110 -> 2
0x0111 -> 2
0x1000 -> 1
0x1001 -> 1
0x1010 -> 1
0x1011 -> 1
0x1100 -> 2
...

It’s quite easy if you notice that third bit is always 0 when output should be 1 and viceversa it’s always 1 when output should be 2

so:

char codify(char input)
{
     return ((((input-1)&0x04)>>2 == 1)?(2):(1));
}

EDIT

As suggested by comment it should work also with

char codify(char input)
{
     return ((input-1 & 0x04)?(2):(1));
}

because in some languages (like C) 0 will evaluate to false and any other value to true. I’m not sure if it works in C# too because I’ve never programmed in that language. Of course this is not a language-agnostic answer but it’s more C-elegant!