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C subscripted value is neither array nor pointer nor vector

int * matrixsum(int *a,int *b,int n,int m)
{
    int *p=NULL,i,j;
    p=malloc(sizeof(int)*n*m);
    if(p==NULL)
    {
        printf("Error!\n");
        exit(1);
    }
    for(i=0;i<n;i++)
    {
        for(j=0;j<m;j++)
        {
            *(p+i*n+j)=*(a+i*n+j)+*(b+i*n+j);
        }
    }
    return p;
}

My question is about the line *(p+i*n+j)=*(a+i*n+j)+*(b+i*n+j); : if I replace it with p[i][j]=a[i][j]+b[i][j]; I get the following error 3 times:

error: subscripted value is neither array nor pointer nor vector

Why? From my knowledge they are the same thing.

My compiler is gcc version 4.6.3.

They're not the same thing at all — which is why the compiler is complaining! You could write:

p[i*n+j] = a[i*n+j] + b[i*n+j];

The type of p is int * ; therefore the type of p[i] is int , and you can't subscript an int . You'd have to be passing a 2D-array of int , or an array of pointers to int , to be able to use the p[i][j] notation. For example, in C99 (using variable-length arrays — and note the reordering of the parameters):

int *matrixsum(int n, int m, int a[m][n], int b[m][n])
{
    ...
    p[i][j] = a[i][j] + b[i][j];
    ...
}

Or, with some considerable care in the setup, you could use:

int *matrixsum(int **a, int **b, int m, int n)
{
    ...
    p[i][j] = a[i][j] + b[i][j];
    ...
}

Note that for this latter example, you can't simply write:

int a[4][4] = { ... };
int b[4][4] = { ... };
int r = matrixsum(a, b, 4, 4);

The memory allocation for the 2D array is quite different from what is required for the int ** notation.

The compiler is simply telling you that you can't de-reference an integer. p is only an int pointer - similarly for a , b , and c . You can simulate p[i][j] by doing the tricky pointer arithmetic into your buffer, but you can't de-reference an int .

These variables must be int ** before you can use them as a 2D array, using array subscripts.

from my knowledge they are the same thing

Yes, you've converted from linear indexing to subscripts correctly, but all 3 of those variables are of the wrong type to apply those subscripts. They need to be of type int ** for you to be able to do 2-D array indexing.

In the second form, how can the compiler guess that n is the length of the first dimension of YOUR tab (not his one) ? to compute &t[i][j] == *(t + i * n + j)

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