How do you create c program for matrix using pointer without array?

Answer 1

An array offers the most efficient method of implementing a matrix (an n-dimensional array). All arrays implicitly convert to pointers, so a pointer can be treated as an array even when it doesn't actually refer to one (so long as you don't access memory that doesn't actually belong to your program, of course).

If you don't want to use an array, use linked lists instead. Each node is a member of two or more lists, so each node requires at least one node pointer per list. If you require bi-directional traversal, each node requires at least two node pointers per list. For a two-dimensional, bi-directional matrix, each node requires up, down, left and right node pointers. For a three-dimensional, bi-directional matrix, each node requires forward and backward node pointers. For a generalised n-dimensional, bi-directional matrix, each node requires an array of n pairs of pointers, one pair for each dimension.

There are very few reasons to resort to linked lists to implement a matrix. For any given number of dimensions and elements, arrays will use far less memory and are much quicker to navigate than a linked list. One of the few exceptions is when you need to slice the matrix (to insert or extract rows or columns, for instance). In these cases it is generally more efficient to break or create a sequence of links than it is to move elements in order to remove or create gaps in the array, not to mention the reallocation of the entire matrix whenever an insert is required. However, this can be largely alleviated by implementing the matrix as separately allocated arrays. E.g., for a three-dimensional array of type T, use a T*** to refer to an array of type T**, where each pointer in that array refers to separately allocated arrays of type T*, where each pointer in those arrays refers to separately allocated arrays of type T. The pointer arithmetic is exactly the same as it would be if the matrix were allocate contiguously as a single block.

Another reason we might prefer a linked list implementation is when the array is sparse and largely contains no data. In this case, each node pointer refers to the nearest neighbouring node that holds data -- the non-data nodes in between can be omitted completely, thus reducing memory consumption and speeding up traversal.

Note that space and time complexities only give us a general sense of an algorithm's performance. Only a real-world performance test will tell us which algorithm is most suitable for a given task. There is no one-size-fits-all solution, hence C does not provide a built-in matrix type.