I don't know why I can't figure this out. I'm writing some code, and want to use this "mapping". As I am using arrays, it's not important if the output is 0 through 7, or 1 through 8. I just need the pairs to map correctly.
Also, I'm wondering if the first four should map to odds, and the last 4 to evens, but I don't know. So I'm writing it as I thought it would work.
r $\in (0,1)$, and c $\in (0,3)$
r,c
0,0 $\rightarrow$ 0
0,1 $\rightarrow$ 1
0,2 $\rightarrow$ 2
0,3 $\rightarrow$ 3
1,0 $\rightarrow$ 4
1,1 $\rightarrow$ 5
1,2 $\rightarrow$ 6
1,3 $\rightarrow$ 7
For more clarity it's something like
if r = 0 and c = 0 then fetch index(0) from someArray
if r = 0 and c = 1 then fetch index(1) from someArray
if ...
if r = 1 and c = 3 then fetch index(7) from someArray
where "fetch index(x)" is some $f(r,c) \rightarrow x$
I tried some binary power stuff with the r, and c, but nothing works. e.g. $2^r+c$, $2^{(r+1)} + (c+1) -2$
What should $f(r,c)$ be?
Try $f(r,c)=4 r + c$.
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