Why is it allowed to omit the first dimension, but not the other dimensions when declaring a multi-dimensonal array?

Question

Why it is not necessary to mention first dimension of multidimensional array and necessary to mention other dimensions:

int A[][][2]={{{1,2},{3,4}},{{4,5},{5,6}}}; // error 
int A[][2][2]={{{1,2},{3,4}},{{4,5},{5,6}}}; // OK 

I am not able to understand the concept or logic behind this.

Answer 1

Because when using a multidimensional array, computing the actual index uses all dimension sizes except the first. For example for a 3D array declared as int arr[3][4][5];, arr[i][j][k] is by definition *(&(arr[0][0][0]) + k + 5 *(j + 4 * i))

So when the first dimension can be deduced from the context initialization, or may be ignored (when getting a parameter in a funtion) it can be omitted.

Examples:

int arr[][2] = { 1,2,3,4 };

void setArr(void *container, int arr[][4]);

Answer 2

It is necessary to mention both dimensions of 2D arrays except when it is in function's parameter or if an initializer is present then first dimension can be omitted.

When used as a parameter in a function, for example,

int 2D_arr[m][n]   

converted to

int (*2D_arr)[n]  

Therefore, first dimension can be omitted. But, second dimension must be there to tell the compiler that the pointer 2D_arr is a pointer to an array of n ints.

In second case, when initializer is present

int A[][2][2]={{{1,2},{3,4}},{{4,5},{5,6}}};    

the compiler uses the length of the initializer to calculate the first dimension only. The rest of the dimension must be explicitly specified at the time of declaration.