Multi-Dimensional Arrays in C: are they jagged?

Question

A simple question about the C programming language (ANSI-C):

Are the multi-dimensional arrays in C jagged?

I mean - are we talking about "array of arrays" (one array of pointers to other addresses in the memory) , or this is just "long one-dimensional array" (which is stored sequentially in the memory)?

What that bothers me is that I'm kinda sure that:

matrix[i][j] is equivalent to * ( * (matrix + i) + j)

Answer 1

A multidimensional array in C is contiguous. The following:

int m[4][5];

consists of 4 int[5]s laid out next to each other in memory.

An array of pointers:

int *m[4];

is jagged. Each pointer can point to (the first element of) a separate array of a different length.

m[i][j] is equivalent to *(*(m+i)+j). See the C11 standard, section 6.5.2.1:

The definition of the subscript operator [] is that E1[E2] is identical to (*((E1)+(E2)))

Thus, m[i][j] is equivalent to (*(m+i))[j], which is equivalent to *(*(m+i)+j).

This equivalence exists because in most contexts, expressions of array type decay to pointers to their first element (C11 standard, 6.3.2.1). m[i][j] is interpreted as the following:

• m is an array of arrays, so it decays to a pointer to m[0], the first subarray.
• m+i is a pointer to the ith subarray of m.
• m[i] is equivalent to *(m+i), dereferencing a pointer to the ith subarray of m. Since this is an expression of array type, it decays to a pointer to m[i][0].
• m[i][j] is equivalent to *(*(m+i)+j), dereferencing a pointer to the jth element of the ith subarray of m.

Note that pointers to arrays are different from pointers to their first element. m+i is a pointer to an array; it is not an expression of array type, and it does not decay, whether to a pointer to a pointer or to any other type.