Lecture 21: Arrays. 2 Lecture Contents: t Declaring and referencing arrays t Array subscripts t...

Lecture 21:Arrays

Lecture Contents:

Declaring and referencing arrays Array subscripts Using for/while loops for sequential access Demo programs Exercises

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)

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.

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

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

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

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

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 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 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 };

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

Subscripted /indexed/ variable:a variable followed by a subscript in brackets, designating an array element.

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

Array subscript: an integer literal, integer variable or integer valued expression enclosed in brackets after array name, specifying which element to access.

x[I] integer variable

Referencing array elementsArray subscript: an integer literal, integer variable or

integer valued expression enclosed in brackets after array name, specifying which element to access.

x[I+1] x[2*I-3] x[I++] integer expression – 3 examples

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]

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.

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.

More on arrays

Extract from Friedman/Koffman, chapter 9

Data Structures Arrays and Structs

Chapter 9

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

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

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

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)

Array Declaration

Type ofvalues in

BaseType Id [ SizeExp ] ;

Nameof list

Bracketedconstant

expressionindicatingnumber of

elements inlist

Sample Declarations Suppose

const int N = 20;const int M = 40;const int MaxStringSize = 80;const int MaxListSize = 1000;

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];

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]

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

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]

-- -- ---- -- --

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;

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

Inputting Into An Array int A[MaxListSize];int n = 0;int CurrentInput; while (n < MaxListSize){ cin >> CurrentInput; A[n] = CurrentInput; ++n;

Displaying An Array// List A of n elements has// already been setfor (int i = 0; i < n; ++i) {

cout << A[i] << " ";}cout << endl;

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

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

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;

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;}

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

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

Exchange.cpp

// FILE: Exchange.cpp// Exchanges two type float values

void exchange (float& a1, float& a2){ float temp;

temp = a1; a1 = a2; a2 = temp;}

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

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

Problem

To check two arrays for identity

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”;

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.

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]);}

Problem

To add two arrays (to add their corresponding elements)

Result saved to third array, same size

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}

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

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]

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"

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);

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;}

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).

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;

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; }}

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

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);

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;

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;}

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); }

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

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.

Before lecture end

Lecture:Arrays

More to read:Friedman/Koffman, Chapter 09

Chapter 9:Data Structures: Arrays and Structs

Problem Solving, Abstraction, and Design using C++ 5e

by Frank L. Friedman and Elliot B. Koffman

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

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

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

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

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];

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];

Figure 9.3 Arrays onVacation, vacationDays, and dayOff

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 ([ ])

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

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

Example of Sequential Access

int cube[10];for (int i = 0; i < 10; i++)

cube[i] = i * i * i;

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 )

9.3 Array Arguments

• Use <, ==, >, +, -, etc. to test and modify array elements individually

• Can pass array elements to functionsexchange (s[3], s[5]);

Listing 9.3 Function to exchange the contents of two floating-point memory locations

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

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;

Listing 9.4 Function sameArray

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);

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];}

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

Listing 9.7 Function readScoresFile

Listing 9.7 Function readScoresFile (continued)

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

Thank You For

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