Arrays

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  Data Structures and Program Design Using Java

  A Self-Teaching Introduction

  • D. Malhotra, N. Malhotra(Authors)
  • 2020(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  3

  ARRAYS

  3.1  Introduction

  In the previous chapter we studied the basics of programming in data structures and Java in which we aimed to design good programs, where a good program refers to a program which runs correctly and efficiently by occupying less space in the memory, and also takes less time to run and execute. Undoubtedly, a program is said to be efficient when it executes with less memory space and also in minimal time. In this chapter, we will learn about the concept of Arrays. An array is a user-defined data type that stores related information together. Arrays are discussed in detail in the following sections.

  3.2  Definition of an Array

  An array is a collection of homogeneous (similar) types of data elements in contiguous memory. An array is a linear data structure, because all elements of the array are stored in linear order. Let us take an example in which we have ten students in a class, and we have been asked to store the marks of all ten students; then we need a data structure known as an array.

  Figure 3.1. Representation of an array of ten elements.

  In the previous example, the data elements are stored in the successive memory locations and are identified by an index number (also known as the subscript), that is, Ai or A[i]. A subscript is an ordinal number which is used to identify an element of the array. The elements of an array have the same data type, and each element in an array can be accessed using the same name.

   

  Frequently Asked Questions

  1. What is an array? How can we identify an element in the array?

  Ans: An array is a collection of homogeneous (similar) types of data elements in contiguous memory. An element in an array can be identified by its index number, which is also known as a subscript.

  3.3  Array Declaration

  We know that all variables must be declared before they are used in the program. Therefore, the same concept also holds with array variables. An array must be declared before it is used. During the declaration of an array, the size of the array has to be specified. Declaring an array involves the following specifications:

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  Data Structures and Program Design Using C++

  • D. Malhotra, N. Malhotra(Authors)
  • 2019(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  3

  Arrays

  In This Chapter

  • Introduction

  • Definition of an array

  • Array declaration

  • Array initialization

  • Calculating the address of array elements

  • Analyzing an algorithm

  • Abstract data types

  • Declaration of two-dimensional Arrays

  • Operations on 2-D Arrays

  • Multidimensional Arrays/ N-dimensional arrayys

  • Calculating the address of 3-D Arrays

  • Arrays and pointers

  • Array of pointers

  • Arrays and their applications

  • Sparse matrices

  • Types of sparse matrices

  • Representation of sparse matrices

  • Summary

  • Exercises

  3.1Introduction

  We have already studied the basics of programming in data structures and C++ in the previous chapter in which we aimed to design good programs, where a good program refers to a program which runs correctly and efficiently by occupying less space in the memory, and also takes less time to run and execute. Undoubtedly, a program is said to be efficient when it executes with less memory space and also in minimal time. In this chapter, we will learn about the concept of Arrays. An array is a user-defined data type that stores related information together. Arrays are discussed in detail in the following sections.

  3.2Definition of an Array

  An array is a collection of homogeneous (similar) types of data elements in contiguous memory . An array is a linear data structure because all elements of the array are stored in linear order. Let us take an example in which we have ten students in a class, and we have been asked to store the marks of all ten students; then we need a data structure known as an array.

  FIGURE 3.1 .

  Representation of an array of 10 elements.

  In the previous example, the data elements are stored in the successive memory locations and are identified by an index number (also known as the subscript), that is, Ai or A[i]. A subscript is an ordinal number which is used to identify an element of the array

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  Data Structures and Program Design Using C

  A Self-Teaching Introduction

  • D. Malhotra, N. Malhotra(Authors)
  • 2018(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  C H A P T E R 3 Arrays In This Chapter l Introduction l Definition of an array l Array declaration l Array initialization l Calculating the address of array elements l Analyzing an algorithm l Abstract data types l Declaration of two-dimensional Arrays l Operations on 2-D Arrays l Multidimensional Arrays/ N-dimensional arrayys l Calculating the address of 3-D Arrays l Arrays and pointers l Array of pointers l Arrays and their applications l Sparse matrices l Types of sparse matrices l Representation of sparse matrices l Summary l Exercises 78 • DATA STRUCTURES AND PROGRAM DESIGN USING C 3.1 Introduction We have already studied the basics of programming in data structures and C in the previous chapter in which we aimed to design good pro- grams, where a good program refers to a program which runs correctly and efficiently by occupying less space in the memory, and also takes less time to run and execute. Undoubtedly, a program is said to be efficient when it executes with less memory space and also in minimal time. In this chapter, we will learn about the concept of Arrays. An array is a user-defined data type that stores related information together. Arrays are discussed in detail in the following sections. 3.2 Definition of an Array An array is a collection of homogeneous (similar) types of data ele- ments in contiguous memory. An array is a linear data structure because all elements of the array are stored in linear order. Let us take an exam- ple in which we have ten students in a class, and we have been asked to store the marks of all ten students; then we need a data structure known as an array. In the previous example, the data elements are stored in the succes- sive memory locations and are identified by an index number (also known as the subscript), that is, A i or A[i]. A subscript is an ordinal number which is used to identify an element of the array.

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  Programming Logic and Design, Introductory

  • Joyce Farrell(Author)
  • 2017(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Each of these real-life Arrays helps you organize objects or information. You could store all your papers or receipts in one huge cardboard box, or find courses if they were printed randomly in one large book. However, using an organized storage and display system makes your life easier in each case. Similarly, an array provides an organized storage and display system for a program’s data. How Arrays Occupy Computer Memory When you declare an array, you declare a structure that contains multiple data items; each data item is one element of the array. Each element has the same data type, and each element occupies an area in memory next to, or contiguous to, the others. You can indicate the number of elements an array will hold—the size of the array—when you declare the array along with your other variables and constants. For example, you might declare an uninitialized, three-element numeric array named prices and an uninitialized string array of 10 employee names as follows: num prices[3] string employeeNames[10] When naming Arrays, programmers follow the same rules as when naming variables. That is, array names must start with a letter and contain no embedded spaces. Additionally, many programmers observe one of the following conventions when naming Arrays to make it more obvious that the name represents a group of items: • Arrays are often named using a plural noun such as prices or employeeNames. • Arrays are often named by adding a final word that implies a group, such as priceList, priceTable, or priceArray. 228 C H A P T E R 6 Arrays Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Each array element is differentiated from the others with a unique subscript, also called an index, which is a number that indicates the position of a particular item within an array.

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  Introduction to Computational Modeling Using C and Open-Source Tools

  • Jose M. Garrido(Author)
  • 2013(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  Chapter 8 Arrays 8.1 Introduction An array stores multiple values of data with a single name and most program-ming languages include facilities that support Arrays. The individual values in the array are known as elements . Many programs manipulate Arrays and each one can store a large number of values in a single collection. To refer to an individual element of the array, an integer value or variable known as the array index is used after the name of the array. The value of the index repre-sents the relative position of the element in the array. Figure 8.1 shows an array with 13 elements. This array is a data structure with 13 cells, and each cell contains an element value. In the C programming language, the index values start with 0 (zero). FIGURE 8.1: A simple array. To use Arrays in a C program the following steps are carried out: 1. Declare the array with appropriate name, size, and type 2. Assign initial values to the array elements 3. Access or manipulate the individual elements of the array In C, an array is basically a static data structure because once the array is de-clared, its size cannot be changed. The size of an array is the number of elements it can store. An array can also be created at execution time using pointers. A simple array has one dimension and is considered a row vector or a column vector. To manipulate the elements of a one-dimensional array, a single index is re-quired. A vector is a single-dimension array and by default it is a row vector. A matrix is a two-dimensional array and the typical form of a matrix is an array with data items organized into rows and columns. In this array, two indexes are used: one index to indicate the column and one index to indicate the row. Figure 8.2 shows 99 100 Introduction to Computational Modeling a matrix with 13 columns and two rows. Because this matrix has only two rows, the index values for the rows are 0 and 1. The index values for the columns are from 0 up to 12.

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  An Object-Oriented Approach to Programming Logic and Design

  • Joyce Farrell(Author)
  • 2012(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Each array element occupies an area in memory next to, or contiguous to, the others. l When you use a variable as a subscript to an array, you can replace multiple nested decisions with many fewer statements. l Constants can be used to hold an array ’ s size or to represent its values. Using a named constant for an array ’ s size makes the code easier to understand and less likely to contain an error. Array values are declared as constant when they should not change during program execution. l Searching through an array to find a value you need involves initializing a subscript, using a loop to test each array element, and setting a flag when a match is found. l With parallel Arrays, each element in one array is associated with the element in the same relative position in the other array. l When you need to compare a value to a range of values in an array, you can store either the low-or high-end value of each range for comparison. l When you access data stored in an array, it is important to use a subscript containing a value that accesses memory occupied by the array. When you use a subscript that is not within the defined range of acceptable subscripts, your subscript is said to be out of bounds. l The for loop is a particularly convenient tool when working with Arrays because you frequently need to process every element of an array from beginning to end. Key Terms A data structure is a collection of data items that are grouped and organized so they can be used more efficiently. An array is a data structure that consists of a series or list of values in computer memory, whose members have the same name but are differentiated by special numbers called subscripts. An element is a single data item in an array. The size of the array is the number of elements it can hold. A subscript , also called an index , is a number that indicates the position of a particular item within an array. Populating an array is the act of assigning values to the array elements.

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  Fundamentals of Python

  Data Structures

  • Kenneth Lambert(Author)
  • 2018(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  This chapter examines the data organization and concrete details of processing that are particular to Arrays and linked structures. Their use in implementing various types of collections is discussed in later chapters. The Array Data Structure An array represents a sequence of items that can be accessed or replaced at given index positions. You are probably thinking that this description resembles that of a Python list. In fact, the data structure underlying a Python list is an array. Although Python programmers would typically use a list where you might use an array, the array rather than the list is the primary implementing structure in the collections of Python and many other programming languages. Therefore, you need to become familiar with the array way of thinking. Some of what this chapter has to say about Arrays also applies to Python lists, but Arrays are much more restrictive. A programmer can access and replace an array’s items at given positions, examine an array’s length, and obtain its string representation—but that’s all. The programmer cannot add or remove positions or make the length of the array larger or smaller. Typically, the length or capacity of an array is fixed when it is created. Python’s array module does include an array class, which behaves more like a list but is limited to storing numbers. For purposes of the discussion that follows, you will define a new class named Array that adheres to the restrictions mentioned earlier but can hold items of any type. Ironically, this Array class uses a Python list to hold its items. The class defines methods that allow clients to use the subscript operator [], the len function, the str function, and the for loop with array objects. The Array methods needed for these operations are listed in Table 4-1. The variable a in the left column refers to an Array object.

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  A Textbook of Data Structures and Algorithms, Volume 1

  Mastering Linear Data Structures

  • G. A. Vijayalakshmi Pai(Author)
  • 2022(Publication Date)
  • Wiley-ISTE

    (Publisher)

  3 Arrays 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 46 A Textbook of Data Structures and Algorithms 1 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, 3 and 1, 2 are the lower and upper indexes of the rows and columns, respectively. Additionally, each element of the array, namely, A[i] or B[i, j], resides in a memory location also called a cell. Here, the cell refers to a unit of memory and is machine dependent. 3.2. Array operations An array, when viewed as a data structure, supports only two operations, namely: (i) storage of values, that is, writing into an array (STORE (a, i, e)); (ii) retrieval of values, that is, reading from an array (RETRIEVE (a, i)).

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  Compact Data Structures

  A Practical Approach

  • Gonzalo Navarro(Author)
  • 2016(Publication Date)
  • Cambridge University Press

    (Publisher)

  CHAPTER 3 Arrays An array A[1, n] is a sequence of elements that can be read and written at arbitrary positions. That is, the array is an abstract data type that supports the operations: read(A, i ): returns A[i], for any 1 ≤ i ≤ n. write(A, i, x): sets A[i] ← x, for any 1 ≤ i ≤ n and any x. Unlike the classical array programming construct, we are interested in space- efficient array representations, which hopefully store only the useful bits of each num- ber A[i]. In some cases the array values are uniform and it is reasonable to use the same number of bits for all. In others, the numbers are very different and we prefer to allocate a variable number of bits for each. Example 3.1 If we are storing the number of days per month worked by employees, then 5 bits are sufficient, and usually necessary too. On the other hand, if we store the number of children of employees, although in principle the number is not bounded, 1–3 bits will be sufficient for most of them. It is not space-efficient to allocate the maximum number of bits for everyone. As seen in Chapter 2, variable-length elements also appear frequently as a result of compression, and compression will generally not work if we allocate the maximum number of bits to every element. In Chapter 2 we described ways to encode the variable- length elements so that the sequences can be decoded from the beginning. In this chap- ter we are more ambitious: to support read on Arrays efficiently, we need to directly extract the bits corresponding to any arbitrary element. In this chapter we discuss how to store Arrays in compact form, using ideally only the bits needed for each element, while providing efficient read operations. We will also provide efficient write operations on Arrays of fixed-length cells. On variable-length cells, a write operation may change the length of the cell, which introduces other com- plications that will be dealt with later (in Chapter 12).

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  Programming in Visual Basic 2010

  The Very Beginner's Guide

  • Jim McKeown(Author)
  • 2010(Publication Date)
  • Cambridge University Press

    (Publisher)

  10 Arrays and Structures – Organizing Data VB Quip [By the end of the 20th Century there will be a generation] to whom it will not be injurious to read a dozen quire of newspapers daily, to be constantly called to the telephone [and] to live half their time in a railway carriage or in a flying machine. – Max Nordau in 1895 So far you have seen how a sequence of steps lets you build a program that will do your bidding. You’ve seen how decision structures give the computer the ability to make decisions. You’ve learned how to get the computer to repeat instructions, giving it the ability to do the same task over and over. And, you’ve taught it how to read and write. Well, it can’t read and write, but it can access and store data in a file. All of these give the computer the ability to access and process data at remarkable speed. But, you’ve been limited to only a handful of names and numbers – only what you could hold in your hand and keep track of in your head. You’ve been forced to discard one thing in order to grab the next. It’s as if the world was a full-screen movie and you’re stuck looking at stills in the family photo album. Enter Arrays. With an array you can grab an armful of data and process it as you wish. Instead of stills on Grandma’s porch, you’ve got a DVD on HD and control of the remote. You can run it forward, backward, and rewind and pause. With your data in Arrays, you can manipulate it as you like. You can sort your data and search through it, find what you want, and pull it out to look at it. You’ll learn new controls to display your data on the screen. And you’ll learn how to create structures – think of them as boxes – to store your containers. Data runs the world and you’re in control of the data. Arrays – Order by the Numbers An array is a series of related variables. All have the same name and all share the same data type. The only difference is their index , an integer that is unique to each item in the array.

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  Big C++

  Late Objects

  • Cay S. Horstmann(Author)
  • 2017(Publication Date)
  • Wiley

    (Publisher)

  In this chapter, you will learn about Arrays, vectors, and common algorithms for processing them. 6.1 Arrays We start this chapter by introducing the array data type. Arrays are the fundamental mechanism in C++ for collecting multiple values. In the following sections, you will learn how to define Arrays and how to access array elements. 6.1.1 Defining Arrays Suppose you write a program that reads a sequence of values and prints out the sequence, marking the largest value, like this: 32 54 67.5 29 34.5 80 115 <= largest value 44.5 100 65 You do not know which value to mark as the largest one until you have seen them all. After all, the last value might be the largest one. Therefore, the program must first store all values before it can print them. Could you simply store each value in a separate variable? If you know that there are ten inputs, then you can store the values in ten variables value1, value2, value3, …, value10. However, such a sequence of variables is not very practical to use. You would values = 10 Figure 1 An Array of Size 10 6.1 Arrays 181 have to write quite a bit of code ten times, once for each of the variables. To solve this problem, use an array: a structure for storing a sequence of values. Here we define an array that can hold ten values: double values[10]; This is the definition of a variable values whose type is “array of double”. That is, val- ues stores a sequence of floating-point numbers. The [10] indicates the size of the array. (See Figure 1.) The array size must be a constant that is known at compile time. When you define an array, you can specify the initial values. For example, double values[] = { 32, 54, 67.5, 29, 34.5, 80, 115, 44.5, 100, 65 }; When you supply initial values, you don’t need to specify the array size. The com- piler determines the size by counting the values. Table 1 Defining Arrays int numbers[10]; An array of ten integers.

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