What's the shortest way to calculate the position of item in flat 2D list by coordinates?

Question

I'm looking for the shortest equation to find the flattened position of an ordered pair.

Let's use a TicTacToe board for example.

|---|---|---|
| 0 | 1 | 2 |
|---|---|---|
| 3 | 4 | 5 |
|---|---|---|
| 6 | 7 | 8 |
|---|---|---|

Given (1, 1), how can I get 4? What about (2, 1) to get 5?

I would like the solution to be general and not language syntax-specific.

Not sure what you mean by "algorithm"? Isn't it just indexing on an array? — cs95, Oct 19 '17 at 00:54
@cᴏʟᴅsᴘᴇᴇᴅ More or less wanted an algebraic equation. — Jacob Birkett, Oct 19 '17 at 00:54
Given (x, y), `c * x + y` where c is the number of columns assuming row-major ordering. — cs95, Oct 19 '17 at 00:57

score 1 · Answer 1 · answered Oct 19 '17 at 00:55

1

Since you're numbering along rows first, the formula you need is row_number * column_count + column_number.

If you were numbering down columns first, or right-to-left, or any other variation, you would have to adjust that formula accordingly.

Keep in mind, also, that this works for zero-based indexing only.

answered Oct 19 '17 at 00:55

David Z

This seems like it was super simple for you guys. I probably need sleep. – Jacob Birkett Oct 19 '17 at 00:59
1

I've spent longer than I should have figuring out this exact thing in the past. – David Z Oct 19 '17 at 01:02

1 Answers1