c - Performance of 2-dimensional array vs 1-dimensional array

Question

In C, is there a difference in time and space between an m×n 2-dimensional array vs a 1-dimensional array of length m×n (for large values of m and n)? Will accessing elements be faster with a 1-dimensional array?

question from:https://stackoverflow.com/questions/1242705/performance-of-2-dimensional-array-vs-1-dimensional-array

Answer 1

In C, 2-dimensional arrays are just a neat indexing scheme for 1-dimensional arrays. Just like with a 1D array, 2D arrays allocate a single block of contiguous memory, and the A[row][col] notation is similar to saying A[row*NCOLS+col].

Usually if you were to implement your own multidimensional arrays using single dimensional arrays, you'd write an indexing function:

int getIndex(int row, int col) { return row*NCOLS+col; }

Assuming your compiler inlines this function, the performance here would be precisely the same as if you used the built in 'indexing function' of 2D arrays.

To illustrate:

#define NROWS 10
#define NCOLS 20

This:

int main(int argc, char *argv[]) {
    int myArr[NROWS*NCOLS];
    for (int i=0; i<NROWS; ++i) {
       for (int j=0; j<NCOLS; ++j) {
          myArr[getIndex(i,j)] = i+j;
       }
    }
    return 0;
}

Should perform the same as this:

int main(int argc, char *argv[]) {
    int myArr[NROWS][NCOLS];
    for (int i=0; i<NROWS; ++i) {
       for (int j=0; j<NCOLS; ++j) {
          myArr[i][j] = i+j;
       }
    }
    return 0;
}

Though as AraK pointed out, if you are jumping around rows a lot, and the rows are very large, you could hit a lot of page faults... in that case the custom indexing function (with rows and cols switched around) could help, but so could simply changing which of the dimensions in a 2-dimensional array you treat as the rows and which you treat as the columns.