If I'm using a 1d array to represent a square board, how can I take my index and check the sqaures above, below and to its sides?

Question

If I have a 4x4 gameboard which I'm representing in my program as a 1d integer array of size 16.

How can I get the indexs of the squares above, below, to the left and to the right any given index?

So, for example:

A = { 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 }

Which represents this board

 0   1   2   3
 4   5   6   7
 8   9  10  11
12  13  14  15  

Lets say I am currently on index #8 in the board (value = 7). How can I get the index for 4 (value = 3) , 5 (value = 6), 10 (value = 11) and realize that there is no right square because it is on the right hand edge of the board.

I know I need to use some modulus math but I'm failing to come up with the right way to get the indexes for adjacent squares.

I'm thinking something like...

if ((i % 4) + 1 < 3) right = i + 1;
if ((i % 4) - 1 > 0) left = i - 1;
if ((i % 4) + 4 < 15) bottom = i + 4;
if ((i % 4) - 4 > 0 ) top = i - 4;

Does this seem like it is the right approach?

Answer 1

To get row,column from your index, use the following:

row = index/num_columns;
column = index % num_columns;

to get back to the index, use

index = row * num_columns + column;

One you're in rows and columns, it's easy to get the surrounding positions.

above = (row-1, column)
left = (row, column-1)
etc...