多维线性数组C

Question

I was reading this article: How to loop through multi-dimensional arrays quickly .

I would like to know more about "linear multidimensional arrays" but I can't find anything of relevance and would like to know if any of you have seen anything like it.

Specifically I would like to understand better how to access a multidimensional array (that's declared as single dimension) using math. It sounds awesome!

Answer 1

Statically allocate

In c, if you want to create a 3x4 array for example you need to do like following code:

int array1[3][4]; // statically allocate 3x4 integer in stack. The memory will be organize like this:
// [[0, 1, 2, 3] // first row
//  [4, 5, 6, 7] // second row
//  [8, 9, 10, 11]

It would be the same if you declare a 12 int array

int array2[12]; // memory will be
// [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]

So: array1[2][3] == array[2* (number of columns) + 3] = 11

Both are the same, the first one is easier to read than the second one. The compiler knows the dimension of the array, so it will calculate the address for you.

Dynamically allocate

In this case you don't know the dimension of the array, so. Create a 3x4 array will like this

int **array1 = (int **) malloc(rows * sizeof(int *)); // allocate 4 pointers
for (int i = 0; i < rows; i++) {
  array1[i] = (int *) malloc(columns * sizeof(int)); // allocate memory for each row.
}

// the memory will be organized like this
// array1 [row0pointer, row1pointer, row2pointer]
// some where else in the memory: ... row0 ... row1 ... row2 ..

It's not optimize because you need memory to store pointers, and when you access each member you have to access through pointers. So you can allocate a single array that has rows * columns member instead:

int *array2 = (int *) malloc(rows * columns * sizeof(int));

// then when you want to access array2[i][j] you can easily access 
array2[i * columns + j]

The same with n-dimensions array.