How to dynamically allocate a contiguous block of memory for a 2D array

Question

If I allocate a 2D array like this int a[N][N]; it will allocate a contiguous block of memory.

But if I try to do it dynamically like this :

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Answer 1

Say you want to dynamically allocate a 2-dimensional integer array of ROWS rows and COLS columns. Then you can first allocate a continuous chunk of ROWS * COLS integers and then manually split it into ROWS rows. Without syntactic sugar, this reads

int *mem = malloc(ROWS * COLS * sizeof(int));
int **A = malloc(ROWS * sizeof(int*));
for(int i = 0; i < ROWS; i++) 
   A[i] = mem + COLS*i;
// use A[i][j]

and can be done more efficiently by avoiding the multiplication,

int *mem = malloc(ROWS * COLS * sizeof(int));
int **A = malloc(ROWS * sizeof(int*));
A[0] = mem;
for(int i = 1; i < ROWS; i++) 
   A[i] = A[i-1] + COLS;
// use A[i][j]

Finally, one could give up the extra pointer altogether,

int **A = malloc(ROWS * sizeof(int*));
A[0] = malloc(ROWS * COLS * sizeof(int));
for(int i = 1; i < ROWS; i++) 
   A[i] = A[i-1] + COLS;
// use A[i][j]

but there's an important GOTCHA! You would have to be careful to first deallocate A[0] and then A,

free(A[0]);
free(A);              // if this were done first, then A[0] would be invalidated

The same idea can be extended to 3- or higher-dimensional arrays, although the code will get messy.