first and last elements respectively. For a vector with linear addressing, the element with index i is located at the address , where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride. If the valid element indices begin at 0, the constant B is simply the address of the first element of the array. For this reason, the C programming language specifies that array indices always begin at 0; and many programmers will call that element "zeroth" rather than "first". However, one can choose the index of the first element by an appropriate choice of the base address B. For example, if the array has five elements, indexed 1 through 5, and the base address B is replaced by , then the indices of those same elements will be 31 to 35. If the numbering does not start at 0, the constant B may not be the address of any element. Multidimensional arrays For a multidimensional array, the element with indices i,j would have address B + c · i + d · j, where the coefficients c and d are the row and column address increments, respectively. More generally, in a k-dimensional array, the address of an element with indices i1, i2, ..., ik is B + c1 · i1 + c2 · i2 + … + ck · ik. For example: int a[2][3]; This means that array a has 2 rows and 3 columns, and the array is of integer type. Here we can store 6 elements they will be stored linearly but starting from first row linear then continuing with second row. The above array will be stored as a11, a12, a13, a21, a22, a23. This formula requires only k multiplications and k additions, for any array that can fit in memory. Moreover, if any coefficient is a fixed power of 2, the multiplication can be replaced by bit shifting. The coefficients ck must be chosen so that every valid index tuple maps to the address of a distinct element. If the minimum legal value for every index is 0, then B is the address of the element whose indices are all zero. As in the one-dimensional case, the element indices may be changed by changing the base address B. Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20,