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6

C Arrays

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Now go, write it before them in a table,�and note it in a book.

Isaiah 30:8

To go beyond is as wrong as to fall short.

Confucius

Begin at the beginning, …�and go on till you come to the end: then stop.

Lewis Carroll

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OBJECTIVES

In this chapter you will learn:

To use the array data structure to represent lists and tables of values.
To define an array, initialize an array and refer to individual elements of an array.
To define symbolic constants.
To pass arrays to functions.
To use arrays to store, sort and search lists and tables of values.
To define and manipulate multiple-subscripted arrays.

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6.1 Introduction

6.2 Arrays

6.3 Defining Arrays

6.4 Array Examples

6.5 Passing Arrays to Functions

6.6 Sorting Arrays

6.7 Case Study: Computing Mean, Median and Mode Using Arrays

6.8 Searching Arrays

6.9 Multiple-Subscripted Arrays

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6.1 Introduction

Arrays

Structures of related data items
Static entity – same size throughout program
Dynamic data structures discussed in Chapter 12

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6.2 Arrays

Array

Group of consecutive memory locations
Same name and type

To refer to an element, specify

Array name
Position number

Format:

arrayname[ position number ]

First element at position 0
n element array named c:

c[ 0 ], c[ 1 ]...c[ n – 1 ]

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Fig. 6.1 | 12-element array.

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6.2 Arrays

Array elements are like normal variables

c[ 0 ] = 3;

printf( "%d", c[ 0 ] );

Perform operations in subscript. If x equals 3

c[ 5 - 2 ] == c[ 3 ] == c[ x ]

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Common Programming Error 6.1

It is important to note the difference between the “seventh element of the array” and “array element seven.” Because array subscripts begin at 0, the “seventh element of the array” has a subscript of 6, while “array element seven” has a subscript of 7 and is actually the eighth element of the array. This is a source of “off-by-one” errors.

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Fig. 6.2 | Operator precedence.

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6.3 Defining Arrays

When defining arrays, specify

Name
Type of array
Number of elements

arrayType arrayName[ numberOfElements ];

Examples:

int c[ 10 ];

float myArray[ 3284 ];

Defining multiple arrays of same type

Format similar to regular variables
Example:

int b[ 100 ], x[ 27 ];

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6.4 Array Examples

Initializers

int n[ 5 ] = { 1, 2, 3, 4, 5 };

If not enough initializers, rightmost elements become 0

int n[ 5 ] = { 0 }

All elements 0

If too many initializers, a syntax error occurs
C arrays have no bounds checking

If size omitted, initializers determine it

int n[ ] = { 1, 2, 3, 4, 5 };

5 initializers, therefore 5 element array

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Outline

fig06_03.c

(1 of 2 )

for loop initializes each array element separately

for loop outputs all array elements

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fig06_03.c

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fig06_04.c

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initializer list initializes all array elements simultaneously

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fig06_04.c

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Common Programming Error 6.2

Forgetting to initialize the elements of an�array whose elements should be initialized.

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Common Programming Error 6.3

Providing more initializers in an array�initializer list than there are elements�in the array is a syntax error.

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Outline

fig06_05.c

(1 of 2 )

#define directive tells compiler to replace all instances of the word SIZE with 10

SIZE is replaced with 10 by the compiler, so array s has 10 elements

for loop initializes each array element separately

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fig06_05.c

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Common Programming Error 6.4

Ending a #define or #include preprocessor directive with a semicolon. Remember that preprocessor directives are not C statements.

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Common Programming Error 6.5

Assigning a value to a symbolic constant in�an executable statement is a syntax error.�A symbolic constant is not a variable. No�space is reserved for it by the compiler as with variables that hold values at execution time.

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Software Engineering Observation 6.1

Defining the size of each array as a symbolic constant makes programs more scalable.

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Good Programming Practice 6.1

Use only uppercase letters for symbolic constant names. This makes these constants stand out in a program and reminds you that symbolic constants are not variables.

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Good Programming Practice 6.2

In multiword symbolic constant names, use underscores to separate the words for readability.

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Outline

fig06_06.c

initializer list initializes all array elements simultaneously

for loop adds each element of the array to variable total

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fig06_07.c

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#define directives create symbolic constants

frequency array is defined with 11 elements

responses array is defined with 40 elements and its elements are initialized

subscript of frequency array is given by value in responses array

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fig06_07.c

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Good Programming Practice 6.3

Strive for program clarity. Sometimes it may be worthwhile to trade off the most efficient use of memory or processor time in favor of writing clearer programs.

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Performance Tip 6.1

Sometimes performance considerations�far outweigh clarity considerations.

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Common Programming Error 6.6

Referring to an element outside the array bounds.

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Error-Prevention Tip 6.1

When looping through an array, the array subscript should never go below 0 and should always be less than the total number of elements in the array (size – 1). Make sure the loop-terminating condition prevents accessing elements outside this range.

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Error-Prevention Tip 6.2

Programs should validate the correctness of all input values to prevent erroneous information from affecting a program’s calculations.

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Outline

fig06_08.c

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nested for loop prints n[ i ] asterisks on the ith line

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fig06_08.c

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fig06_09.c

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for loop uses one array to track number of times each number is rolled instead of using 6 variables and a switch statement

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fig06_09.c

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6.4 Array Examples

Character arrays

String “first” is really a static array of characters
Character arrays can be initialized using string literals

char string1[] = "first";

Null character '\0' terminates strings
string1 actually has 6 elements

It is equivalent to

char string1[] = { 'f', 'i', 'r', 's', 't', '\0' };

Can access individual characters

string1[ 3 ] is character ‘s’

Array name is address of array, so & not needed for scanf

scanf( "%s", string2 );

Reads characters until whitespace encountered
Be careful not to write past end of array, as it is possible to do so

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Common Programming Error 6.7

Not providing scanf with a character array large enough to store a string typed at the keyboard can result in destruction of data in a program and other runtime errors. This can also make a system susceptible to worm and virus attacks.

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fig06_10.c

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string2 array is defined with one element for each character, so 15 elements including null character /0

for loop prints characters of string1 array with spaces in between

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fig06_10.c

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Performance Tip 6.2

In functions that contain automatic arrays where the function is in and out of scope frequently, make the array static so it is not created each time the function is called.

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fig06_11.c

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fig06_11.c

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static array is created only once, when staticArrayInit is first called

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fig06_11.c

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automatic array is recreated every time automaticArrayInit is called

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fig06_11.c

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Common Programming Error 6.8

Assuming that elements of a local static�array are initialized to zero every time the function in which the array is defined is called.

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6.5 Passing Arrays to Functions

Passing arrays

To pass an array argument to a function, specify the name of the array without any brackets

int myArray[ 24 ];

myFunction( myArray, 24 );

Array size usually passed to function

Arrays passed call-by-reference
Name of array is address of first element
Function knows where the array is stored

Modifies original memory locations

Passing array elements

Passed by call-by-value
Pass subscripted name (i.e., myArray[ 3 ]) to function

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6.5 Passing Arrays to Functions

Function prototype

void modifyArray( int b[], int arraySize );

Parameter names optional in prototype

int b[] could be written int []
int arraySize could be simply int

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Performance Tip 6.3

Passing arrays by reference makes sense for performance reasons. If arrays were passed by value, a copy of each element would be passed. For large, frequently passed arrays, this would be time consuming and would consume considerable storage for the copies of the arrays.

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fig06_12.c

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Software Engineering Observation 6.2

It is possible to pass an array by value (by�using a simple trick we explain in Chapter 10).

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fig06_13.c

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Function prototype indicates function will take an array

Array a is passed to modifyArray by passing only its name

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fig06_13.c

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Array element is passed to modifyElement by passing a[ 3 ]

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fig06_13.c

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fig06_14.c

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const qualifier tells compiler that array cannot be changed

Any attempts to modify the array will result in errors

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fig06_14.c

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Software Engineering Observation 6.3

The const type qualifier can be applied to an array parameter in a function definition to prevent the original array from being modified in the function body. This is another example of the principle of least privilege. Functions should not be given the capability to modify an array unless it is absolutely necessary.

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6.6 Sorting Arrays

Sorting data

Important computing application
Virtually every organization must sort some data

Bubble sort (sinking sort)

Several passes through the array
Successive pairs of elements are compared

If increasing order (or identical ), no change
If decreasing order, elements exchanged

Repeat

Example:

original: 3 4 2 6 7
pass 1: 3 2 4 6 7
pass 2: 2 3 4 6 7
Small elements "bubble" to the top

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Performance Tip 6.4

Often, the simplest algorithms perform poorly. Their virtue is that they are easy to write, test and debug. However, more complex algorithms are often needed to realize maximum performance.

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fig06_15.c

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fig06_15.c

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If any two array elements are out of order, the function swaps them

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6.7 Case Study: Computing Mean, Median and Mode Using Arrays

Mean – average
Median – number in middle of sorted list

1, 2, 3, 4, 5
3 is the median

Mode – number that occurs most often

1, 1, 1, 2, 3, 3, 4, 5
1 is the mode

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fig06_16.c

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fig06_16.c

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fig06_16.c

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Once the array is sorted, the median will be the value of the middle element

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fig06_16.c

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fig06_16.c

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fig06_16.c

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6.8 Searching Arrays

Search an array for a key value
Linear search

Simple
Compare each element of array with key value
Useful for small and unsorted arrays

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fig06_18.c

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fig06_18.c

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fig06_18.c

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Linear search algorithm searches through every element in the array until a match is found

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6.8 Searching Arrays

Binary search

For sorted arrays only
Compares middle element with key

If equal, match found
If key < middle, looks in first half of array
If key > middle, looks in last half
Repeat

Very fast; at most n steps, where 2ⁿ > number of elements

30 element array takes at most 5 steps

2⁵ > 30 so at most 5 steps

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fig06_19.c

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fig06_19.c

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fig06_19.c

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If value is found, return its index

If value is too high, search the left half of array

If value is too low, search the right half of array

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fig06_19.c

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fig06_19.c

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fig06_19.c

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6.9 Multiple-Subscripted Arrays

Multiple subscripted arrays

Tables with rows and columns (m by n array)
Like matrices: specify row, then column

Initialization

int b[ 2 ][ 2 ] = { { 1, 2 }, { 3, 4 } };
Initializers grouped by row in braces
If not enough, unspecified elements set to zero

int b[ 2 ][ 2 ] = { { 1 }, { 3, 4 } };

Referencing elements

Specify row, then column

printf( "%d", b[ 0 ][ 1 ] );

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Common Programming Error 6.9

Referencing a double-subscripted array element as a[ x, y ] instead of a[ x ][ y ]. C interprets a[ x, y ] as a[ y ], and as such it does not cause a syntax error.

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Fig. 6.20 | Double-subscripted array with three rows and four columns.

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fig06_21.c

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array1 is initialized with both rows full

array2 and array3 are initialized only partially

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fig06_21.c

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fig06_22.c

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Each row in the array corresponds to a single student’s set of grades

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fig06_22.c

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average function is passed a row of the array

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fig06_22.c

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fig06_22.c

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fig06_22.c

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fig06_22.c

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