It is time to return to the problem of how to represent higher-dimensional arrays in terms of one-dimensional arrays. For simplicity, only two-dimensional arrays are discussed, but the techniques can be readily extended for higher dimensions. Two techniques will be studied: 1) rowwise and columnwise representation and 2) pointer array representation.
What exactly is meant by representing a two-dimensional array a in terms of a one-dimensional array (say, data), and why is it done? The idea is that the problem to be solved may involve the use of a, but the language being used may not provide two-dimensional arrays, or the programmer may choose not to use them for some other reason. Instead, the entries of a are stored in data. This must be done so that whenever reference is to be made to the entry in position (i,j) of a in the program, the corresponding position of data in which it is stored is referenced instead. For example, the check functions of Example 2.3 referred to a two-dimensional array a. If its information were stored in data, then the functions would have to be rewritten, replacing each reference to a[i][j] with a reference to the correct entry in data that corresponds to it. Of course, the declarations involving a would also have to be replaced by declarations involving data.
2.3.1 Rowwise and Columnwise Representation
2.3.2 Symmetric Array Representation
2.3.3 Pointer Array Representation