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Lecture 21:Arrays
2
Lecture Contents:
Declaring and referencing arrays Array subscripts Using for/while loops for sequential access Demo programs Exercises
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Basic description
Data structure: composite of related data items stored in memory under the same name.
Typical data structures available in most PL:– Array: to be discussed today– Structure: (struct in C like PLs)– Class: structure with methods (OOP)– File (I/O processing aside keyboard and
screen)
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Basic description
Array: a collection of data items of the same type.
Reminder:Simple data type: Data type used to store a single value.
scalar variable stores a single value.
Therefore array may store many data items (scalar values) of the same type.
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Array: a collection of data items of the same type
How to define (declare) an array:
Using a definition statement to specify:– data type for all array elements– name of the array, i.e. identifier– size of the array, number of array elements
See next three slides
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Array: a collection of data items of the same type
How to define (declare) an array:
int a[6]; // array named a with size of 6 // a names a collection of 6 integer data items // where 6 integer values may store
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Array: a collection of data items of the same type
How to define (declare) an array:
float b[10]; // array named b with size of 10 // b names a collection of 10 real data items // where 10 real (float) values may store
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Array: a collection of data items of the same type
How to define (declare) an array:
char c[20]; // array named c with size of 20 // c names a collection of 20 char data items // where 20 symbols (char values) may store
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Array initialization: to set value at time of definition
Reminder: scalar variable initialization int pom = 56; double quantity = 77.8;
// size matches the list of initializersint prime1[10]={2,3,5,7,11,13,17,19,23,29};
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Array initialization: to set value at time of definition
Reminder: scalar variable initialization int pom = 56; double quantity = 77.8;
// size matches the list of initializersint prime1[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
// size omittedint prime2[ ] = { 2, 3, 5, 7, 11, 13 };
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Array initialization: to set value at time of definition
Reminder: scalar variable initialization int pom = 56; double quantity = 77.8;
// size matches the list of initializersint prime1[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
// size omittedint prime2[ ] = { 2, 3, 5, 7, 11, 13 };
// size is greater than the list of initializersint prime3[20] = { 2, 3, 5, 7 };
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Referencing array elements
The access to an array element:
Using subscript, also named index– Always integer valued
In What context:– assignment statements, – Input/Output (cin, cout) statements– arguments in function calling statement
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Referencing array elements
Subscripted /indexed/ variable:a variable followed by a subscript in brackets, designating an array element.
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Referencing array elementsArray subscript:
integer literal or integer variable or integer valued expression
enclosed in brackets after array name, specifying which element to access.
Examples on Array subscripts:Given: int x[10], I=5;
x[4] integer literal
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Referencing array elements
Array subscript: an integer literal, integer variable or integer valued expression enclosed in brackets after array name, specifying which element to access.
Examples on Array subscripts:Given: int x[10], I=5;
x[I] integer variable
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Referencing array elementsArray subscript: an integer literal, integer variable or
integer valued expression enclosed in brackets after array name, specifying which element to access.
Examples on Array subscripts:Given: int x[10], I=5;
x[I+1] x[2*I-3] x[I++] integer expression – 3 examples
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Array size & Array indexes
Array size of 10 Valid index values are 0, 1, 2, … , 9 Attention: Highest value is 9, but
not 10
int x[10];
x[0], x[1], … , x[9]
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Sequential access to array
Using for loops for sequential access Given: int x[10], i;
for(i=0; i<=9; i++) x[i] = i * 10;
for(i=9; i>=0; i--) cout << ‘\n’ << x[i] ;
Statistical computation using arrays: computing mean and standard deviations.
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Sequential access to array
Using while loops for sequential accessGiven: int x[10], i; i=0; while (i<=9){ x[i] = i*20; i++; }
i=9; while (i>=0) {
cout << ‘\n’ << x[i]; i--; }
Statistical computation using arrays: computing mean and standard deviations.
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More on arrays
Extract from Friedman/Koffman, chapter 9
Data Structures Arrays and Structs
Chapter 9
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9.1 The Array Data Type Array elements have a common name
– The array as a whole is referenced through the common name
Array elements are of the same type — the base type
Individual elements of the array are referenced by sub_scripting the group name
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Arrays Analogies
– Egg carton– Apartments– Cassette carrier
More terminology– Ability to refer to a particular element
• Indexing or sub_scripting– Ability to look inside an element
• Accessing value
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Arrays Language restrictions
– Subscripts are denoted as expressions within brackets: [ ]
– Base type can be • any fundamental type, or• library-defined type, or• programmer-defined type
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Arrays– The index type is always integer and the
index range must be0 ... n-1• where n is a programmer-defined constant
expression.– Parameter passing style
• Always call by reference (no indication necessary)
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Array Declaration
Type ofvalues in
list
BaseType Id [ SizeExp ] ;
Nameof list
Bracketedconstant
expressionindicatingnumber of
elements inlist
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Sample Declarations Suppose
const int N = 20;const int M = 40;const int MaxStringSize = 80;const int MaxListSize = 1000;
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Sample Declarations Then the following are all correct array
declarations.int A[10]; char B[MaxStringSize]; float C[M*N]; int Values[MaxListSize];Rational D[N-15];
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Subscripting Suppose
int A[10]; // array of 10 ints To access an individual element we must
apply a subscript to array name A– A subscript is a bracketed expression
• The expression in the brackets is known as the index– First element of A has index 0A[0]
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Subscripting– Second element of A has index 1, and so onA[1]
– Last element has an index one less than the size of the arrayA[9]
Incorrect indexing is a common error
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Array Elements Suppose
int A[10]; // array of 10 uninitialized ints
To access an individual element we must apply a subscript to array name A
-- -- ----AA[4] A[5] A[6]A[3]A[0] A[2] A[8] A[9]A[7]A[1]
-- -- ---- -- --
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Array Element Manipulation Given the following:
int i = 7, j = 2, k = 4;A[0] = 1;A[i] = 5;A[j] = A[i] + 3;A[j+1] = A[i] + A[0];A[A[j]] = 12;
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Array Element Manipulation
cin >> A[k]; // where the next input value is 3
-- 8 61AA[4] A[5] A[6]A[3]A[0] A[2] A[8] A[9]A[7]A[1]
-- -- 53 --12
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Inputting Into An Array int A[MaxListSize];int n = 0;int CurrentInput; while (n < MaxListSize){ cin >> CurrentInput; A[n] = CurrentInput; ++n;
}
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Displaying An Array// List A of n elements has// already been setfor (int i = 0; i < n; ++i) {
cout << A[i] << " ";}cout << endl;
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Remember Arrays are always passed by reference
– Artifact of C Can use const if array elements are not to be
modified You do not need to include the array size within
the brackets when defining an array parameter Initialize array with 0 or some other known value
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9.2 Sequential Access to Array Elements
Random Access– Access elements in random order
Sequential Access– Process elements in sequential order starting
with the first– ShowDiff.cpp a program that looks at values
and calculates a difference between the element and the average
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ShowDiff.cpp#include <iostream>#include <iomanip>using namespace std;int main(){ const int MAX_ITEMS = 8; float x[MAX_ITEMS], average, sum; // Enter the data. cout << "Enter " << MAX_ITEMS << " numbers: "; for (int i = 0; i < MAX_ITEMS; i++) cin >> x[i];// Compute the average value. sum = 0.0; for (int i = 0; i < MAX_ITEMS; i++) sum += x[i]; average = sum / MAX_ITEMS; cout << "The average value is " << average << endl;
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ShowDiff.cpp
// Display the difference between each item// and the average.
cout << "Table of differences between x[i] and the average." << endl;
cout << setw (4) << "i" << setw (8) << "x[i]" << setw (14) << "difference" << endl; for (int i = 0; i < MAX_ITEMS; i++) cout << setw (4) << i << setw (8) << x[i] << setw (14) << (x[i] - average) << endl; return 0;}
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ShowDiff.cpp
Program OutputEnter 8 numbers: 16 12 6 8 2.5 12 14 -54.5The average value is 2.0Table of differences between x[i] and the averageI x[I] difference0 16.0 14.01 12.0 10.02 6.0 4.03 8.0 6.0etc etc
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9.3 Array Arguments
Use <, ==, >, +, - to test and modify array elements
At times it might benefit you to pass an entire array to a function
Can pass array elements to functions– actual function callexchange (s[3], s[5]);
Examples follow
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Exchange.cpp
// FILE: Exchange.cpp// Exchanges two type float values
void exchange (float& a1, float& a2){ float temp;
temp = a1; a1 = a2; a2 = temp;}
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Arrays as Function Arguments Remember arrays are pass by reference
– Passing the array address Remember these points when passing arrays to
functions– The formal array argument in a function is not itself an
array but rather is a name that represents an actual array argument. Therefore in the function definition, you need only inform the compiler with [] that the actual argument will be an array
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Arrays as Function Arguments Remember these points when passing arrays
to functions– Formal array arguments that are not to be
altered by a function should be specified using the reserved word const. When this specification is used, any attempt to alter the contents will cause the compiler generate an error message
SameArray.cpp example
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Problem
To check two arrays for identity
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SameArray.cpp
// FILE: SameArray.cpp// COMPARES TWO FLOAT ARRAYS FOR EQUALITY BY// COMPARING CORRESPONDING ELEMENTS
bool sameArray (float a[], float b[], const int size); void main(){
float ar1[20], float ar2[20];// assgn values to ar1 and ar2bool flag; flag = sameArray(ar1, ar2, 20);if (flag) cout << “Two identical arrays”;else cout << “Two non identical arrays”;
}
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SameArray.cpp
// FILE: SameArray.cpp// COMPARES TWO FLOAT ARRAYS FOR EQUALITY BY// COMPARING CORRESPONDING ELEMENTS
// Pre: a[i] and b[i] (0 <= i <= size-1) are// assigned values.// Post: Returns true if a[i] == b[i] for all I// in range 0 through size - 1; otherwise, // returns false.
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SameArray.cpp
bool sameArray (float a[], float b[], const int size){ int i; i = 0;
while ((i < size-1) && (a[i] == b[i])) i++; return (a[i] == b[i]);}
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Problem
To add two arrays (to add their corresponding elements)
Result saved to third array, same size
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AddArray.cpp
// to add two arrays// Post: c[i] = a[i] + b[i] (0 <= i <= size-1)void addArray (int size, const float a[],
const float b[], float c[]);
void main(){ float x[40], y[40], z[40]; // assgn values to arrays x, y addArray( 40, x, y, z); // display array z}
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AddArray.cpp
// Array elements with subscripts ranging from// 0 to size-1 are summed element by element.// Pre: a[i] and b[i] are defined // (0 <= i <= size-1// Post: c[i] = a[i] + b[i] (0 <= i <= size-1)void addArray (int size, const float a[],
const float b[], float c[]){// Add corresponding elements of a and b and store in c. for (int i = 0; i < size; i++) c[i] = a[i] + b[i];} // end addArray
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9.4 Reading Part of an Array
Sometimes it is difficult to know how many elements will be in an array
Scores example– 150 students– 200 students
Always allocate enough space at compile time
Remember to start with index [0]
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ReadScoresFile.cpp
POSTPONE TO LECTURE ON FILESSkip 6 coming slides
// File: ReadScoresFile.cpp// Reads an array of exam scores for a lecture// section of up to max_size students.
#include <iostream>#include <fstream>using namespace std;
#define inFile "Scores.txt"
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ReadScoresFile.cpp
void readScoresFile (ifstream& ins,int scores[], const int MAX_SIZE, int& sectionSize);
int main(){ int scores[100]; int size; ifstream ins;
ins.open(inFile);
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ReadScoresFile.cpp
if (ins.fail()) { cout << "Error" << endl; return 1; } readScoresFile(ins, scores, 5, size); for (int i = 0; i < size; i++) cout << scores[i] << " " ; cout << endl;
return 0;}
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ReadScoresFile.cpp
// File: ReadScoresFile.cpp// Reads an array of exam scores for a lecture // section of up to MAX_SIZE students from a// file.
// Pre: None// Post: The data values are read from a file // and stored in array scores.// The number of values read is stored in // sectionSize.(0 <= sectionSize < MAX_SIZE).
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ReadScoresFile.cpp
void readScoresFile (ifstream& ins, int scores[],const int MAX_SIZE, int& sectionSize)
{ // Local data ... int tempScore;
// Read each array element until done. sectionSize = 0; ins >> tempScore; while (!ins.eof() && (sectionSize < MAX_SIZE)) { scores[sectionSize] = tempScore;
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ReadScoresFile.cpp
sectionSize++; ins >> tempScore; } // end while
// End of file reached or array is filled. if (!ins.eof()) { cout << "Array is filled!" << endl; cout << tempScore << " not stored" << endl; }}
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Strings and Arrays of Characters
String object uses an array whose elements are type char
First position of a string object is 0– example string find function ret of position 0
Can use the find function to locate or search an array
We will study some various search functions
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12.4 Recursive Functions with Array Arguments
// File: findSumTest.cpp// Program and recursive function to sum an// array's elements
#include <iostream>using namespace std;
// Function prototype int findSum(int[], int);int binSearch(int[], int, int, int);
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FindSumTest.cpp
int main(){ const int SIZE = 10; int x[SIZE]; int sum1; int sum2;
// Fill array x for (int i = 0; i < SIZE; i++) x[i] = i + 1;
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FindSumTest.cpp
// Calulate sum two ways sum1 = findSum(x, SIZE); sum2 = (SIZE * (SIZE + 1)) / 2;
cout << "Recursive sum is " << sum1 << endl; cout << "Calculated sum is " << sum2 << endl;
cout << binSearch(x, 10, 10, SIZE-1) << endl; return 0;}
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FindSumTest.cpp
// Finds the sum of integers in an n-element// arrayint findSum(int x[], int n){ if (n == 1) return x[0]; else return x[n-1] + findSum(x, n-1); }
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9.9 Common Programming Errors
Watch non int subscripts (ASCII value) Enumerated types can be used Out of range errors
– C++ no range error checking Lack of subscript to gain access Subscript reference to non-array variable Type mixing when using with functions Initialization of arrays
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Exercise 21.1-21.5
Build programs using arraysArrays as actual arguments and formal parameters: function to add two same size arrays (values associated
to all array elements); function to evaluate the first 20 elements of Fibonacci
series; sum (product) of the elements of an initialized array; average value of the sum of array elements entered as
input values; count the number of digit characters in the input stream.
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Before lecture end
Lecture:Arrays
More to read:Friedman/Koffman, Chapter 09
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Chapter 9:Data Structures: Arrays and Structs
Problem Solving, Abstraction, and Design using C++ 5e
by Frank L. Friedman and Elliot B. Koffman
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 68
9.1 The Array Data Type• Array elements have a common name
– The array as a whole is referenced through the common name
• Array elements are of the same type — the base type
• Individual elements of the array are referenced by sub-scripting the group name– element’s relative position used, beginning with 0
• Array stored in consecutive memory locations
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 69
Additional Array Details
• Subscripts are denoted as expressions within brackets: [ ]
• Base type can be any fundamental, library-defined, or programmer -defined type
• The index type is integer and the index range must be 0 ... n-1, for array of size n
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 70
Array Declaration
element-type array-name [array-size];
Type of all the values in the array
Name of the entire collection of values
Integer expression indicating number of elements in the array
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 71
Example 1
element-type array-name [array-size] = {initialization-list};
float x[8] = {16.0, 12.0, 6.0, 8.0, 2.5, 12.0, 14.0, -54.5};
16.0 12.0 6.0 8.0 2.5 12.0 14.0 -54.5
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 72
Example 1 (con’t)
cout << x[0];x[3] = 25.0;sum = x[0] + x[1];sum += x[2];x[3] += 1.0;x[2] = x[0] + x[1];
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 73
Example 2
const int NUM_EMP = 10;bool onVacation[NUM_EMP];int vacationDays[NUM_EMP];enum day {sunday, monday, tuesday, wednesday,
thursday, friday, saturday};day dayOff[NUM_EMP];float plantHours[7];
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 74
Figure 9.3 Arrays onVacation, vacationDays, and dayOff
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Array Initialization• List of initial values enclosed in braces ({ })
following assignment operator (=)• Values from initialization list are assigned in order
to array elements• Length of initialization list cannot exceed size of
the array• If too few values, value assigned is system
dependent• Size of array can be automatically set to number
of initializing values using empty brackets ([ ])
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 76
Array Subscripts• Enclosed in brackets ([ ])• Indicates which element is referenced by
position• Array subscript value is different than array
element value• Subscript can be an expression of any
integral type• To be valid, subscript must be a value
between 0 and one less than the array size
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 77
9.2 Sequential Access to Array Elements
• Random Access– Access elements is any order
• Sequential Access– Process elements in sequential order starting
with the first
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Example of Sequential Access
int cube[10];for (int i = 0; i < 10; i++)
cube[i] = i * i * i;
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 79
Strings and Arrays of Characters
• string object uses an array of char• Can reference individual character of a
string object in different ways– name[ i ]– name.at( i )
• Other member functions of string class– message.length( i )
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 80
9.3 Array Arguments
• Use <, ==, >, +, -, etc. to test and modify array elements individually
• Can pass array elements to functionsexchange (s[3], s[5]);
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Listing 9.3 Function to exchange the contents of two floating-point memory locations
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Passing an Array Argument
• Arrays are always passed by reference• Pass entire array to a function by writing
just its name (no subscripts or brackets) in the argument list of the function call
• In function definition and prototype, user empty brackets ([ ]) to identify array
• Use keyword const to indicate that array argument cannot be changed by function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 83
Example 1
const int MAX_SIZE = 5;float x[MAX_SIZE ];float y[MAX_SIZE ];. . .if (sameArray(x, y, MAX_SIZE))
cout << “Arrays are identical.” << endl;else
cout << “Arrays are different.” << endl;
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Listing 9.4 Function sameArray
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Example 2
const int MAX_SIZE = 5;float x[MAX_SIZE ] = {1.8, 2.2, 3.4, 5.1, 6.7};float y[MAX_SIZE ] = {2.0, 4.5, 1.3, 4.0, 5.5};float z[MAX_SIZE];. . .addArray(MAX_SIZE, x, y, z);
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 86
Listing 9.5 Function addArray// File: addArray.cpp// Stores the sum of a[i] and b[i] in c[i]
// Sums pairs of array elements with subscripts ranging from 0// to size – 1// Pre: a[i] and b[i] are defined (0 <= i <= size-1)// Post: c[i] = a[i] + b[i] (0 <= i <= size-1)
void addArray (int size, // IN: the size of the arrays const float a[], // IN: the first array const float b[], // IN: the second array float c[]) // OUT: result array{ // Add corresponding elements of a and b and store in c for (int i = 0; i < size; i++) c[i] = a[i] + c[i];}
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 87
9.4 Reading Part of an Array
• Sometimes it is difficult to know how many elements will be in an array– 150 students in one section– 200 students in another section
• Always allocate enough space for largest possible amount needed
• Remember to start reading with index [0]• Must keep track of how many elements used
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Listing 9.7 Function readScoresFile
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Listing 9.7 Function readScoresFile (continued)
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9.10 Common Programming Errors• Arrays
– Out-of-range subscript references– Unsubscripted array references– Subscripted references to nonarray variables– Mixing types in passing arrays to functions
91
Thank You For
Your Attention!