A Textbook of Data Structures and Algorithms, Volume 1

3Arrays

3.1. Introduction

In Chapter 1, an abstract data type (ADT) was defined to be a set of data objects and the fundamental operations that can be performed on this set.

In this regard, an array is an ADT whose objects are a sequence of elements of the same type, and the two operations performed on it are store and retrieve. Thus, if a is an array, the operations can be represented as STORE (a, i, e) and RETRIEVE (a, i), where i is termed the index and e is the element that is to be stored in the array. These functions are equivalent to the programming language statements a[i ]:= e and a[i], where i is termed subscript and a is termed array variable name in programming language parlance.

Arrays can be one-dimensional, two-dimensional, three-dimensional or in general multidimensional. Figure 3.1 illustrates a one-dimensional and two-dimensional array. It may be observed that while one-dimensional arrays are mathematically likened to vectors, two-dimensional arrays are likened to matrices. In this regard, two-dimensional arrays also have the terminologies of rows and columns associated with them.

Figure 3.1. Examples of arrays

In Figure 3.1, A[1:5] refers to a one-dimensional array where 1 and 5 are referred to as the lower and upper indexes or the lower and upper bounds of the index range, respectively. Similarly, B[1:3, 1:2] refers to a two-dimensional array where 1, ...