Arrays Structured Programming 256 Chapter 10 © 2000 Scott S Albert Arrays One-Dimensional initialize & display Arrays as Arguments Two-dimensional initialize

Arrays

Structured Programming 256

Chapter 10

© 2000 Scott S Albert

Arrays

One-Dimensionalinitialize & display

Arrays as Arguments

Two-dimensional initialize & display

Part I


Data Types

a simple or atomic

a structured

* *

char, int, float, double

array, struct, union, class


Structured Data Type - Array

• An array is a collection of data storage locations, each of which holds the same type of data. Each storage location is called an element of the array.

• Each element is referred to as an indexed or subscripted variable.


Array Declaration

• SyntaxdataType arrayName [[ ConstIntExpression ]]

• The number of elements in an array is • stated within square brackets, [ ][ ].

• Examplesdouble angle [4]; constant POLY = 8;int testScore [12]; double angle [POLY]; char password [8];


Array Storage

• Each array has sufficient memory reserved to hold the number of data items of the given type.

• Initializing an array sets up the address of the first element. Addresses of all other elements are offsets from the starting address.


Array Element Access

• Syntax• arrayName [ indexExpression ]

• Program access to each of the array elements is by referring to an offset from the array name. Array elements are counted beginning with zero.


Array Element Access

• double angle[4]; // declaration

• Exampleangle [0] = 6.21;angle [1] = 15.89;angle [2] = 7.5;angle [3] = -45.7;

angle sub zero = 6.21angle sub one = 15.89angle sub two = 7.5angle sub three = -45.7

* * *


Using Array Elementsa write the contents of an array element:

cout << angle[2];

a assign values to an array element:cin >> angle[3];angle[6] = pow(axis,4);

a use it as a parameter:y = sqrt(angle[0]);

a use it in an expression:x = 2.5 * angle[1] + 64;

* * * *


Array Component Access

• for(indexindex=0; index index < arraySize; indexindex++)myArray[indexindex] = 0.0;

100

* *

Zero out an entire array. (Initialize every element to 0.0.)


Off Set• memory

addresses

• starting address

• off set by one unit

• off set by two units

• off set by three units

[ 0 ]

[ 1 ]

[ 2 ]

[ 3]

@#$

@#$


Out-of-Bounds Array Index• memory

addresses

• angle[4] = 135;

cout << angle[5];

[ 0 ]

[ 1 ]

[ 2 ]

[ 3]

@#$

@#$


Declare an Array

• Syntaxtype arrayName[index];

Exampledouble dailyHigh[23] ;

int quizGrade[132] ;

char ASURiteID[5] ;

*


Initialize an Array Element

• SyntaxarrayName[index] = value;

ExampledailyHigh[18] = 16.7;

quizGrade[2] = 15;

ASURiteID[3] = ‘d’;

*


Initialize an Array

double angle[4] = {16.21, 15.89, 7.5, -45.7};

double ATtoCG[5] = {.64, .89, .76, .83, .65};

int scores[12] = {210, 198, 203, 188, 200, 224, 220, 217, 211, 194, 197, 189};

double iona[8] = {0.0};*


Initialize an Array

int scores[ ] = {210, 198, 203, 188, 200, 224, 220, 217, 211, 194, 197, 189};

char name[4] = {‘Z’, ‘o’, ‘l’, ‘a’};

char name[4] = “Zola”; // no braces or ,char phrase [ ] = “Hello World”;

* *


Initialize an Array

double angle[4]; // declaration

Exampleangle [0] = 6.21;angle [1] = 15.89;angle [2] = 7.5;angle [3] = -45.7;

angle sub zero = 6.21angle sub one = 15.89angle sub two = 7.5angle sub three = -45.7

*


Sequencing Through an Array

• Use the for statement to sequence through an array.

• Total the contents of an array:sum = 0;for(index=0; index < 7; index++)

sum = sum + grades[index];


Loading an Array

• double grade[10];

• int index;

• for(index=0; index < 10; index++){

cout<<“Enter a grade “;

• cin >> grade[index];

• }


Finding the Max/Min Value

• Set the max or min to element zero.

• Use a for loop to cycle through the array.

• Compare each element to the max/min.

• If necessary, assign a new value to max/min.

How would you do this?

*


Finding the Maximum Value

• double find_max(int temp[30])• {• max = temp[0];

• for(index=0; index < 30; index++)if (temp[index] > max)

max = temp[index];• return (max);• }

*


Finding the Minimum Value

• double find_min(int temp[30])• {

• min = temp[0];

• for(index = 1; index < 30; index++)if (temp[index] << min)

min = temp[index];• return ( min );• }

*


Aggregate Assignment - NOT!

• There are no aggregate assignments with arrays. That is, you may not assign one array to another.

• int x[5] = {11, 22, 33, 44, 55};

• int y[5];

• y = x; y[ ] = x[ ];


Arrays as Arguments

• void find_max(int temp[ ]temp[ ])• {

• max = temp[0];

• for(index = 1; index < 30; index++)if (temp[index] > max)

max = temp[index];

• }

double find_max(int temp[ ]temp[ ])

*

return max;


Passing an Array/Element

• find_max(temptemp); // no [ ]

• inventory(priceprice, quantityquantity, amountamount); // 3 arrays

• words(cupletcuplet);

find_max(temp[3]temp[3]); inventory(priceprice, quantity[4]quantity[4], amount[12]amount[12]);words(cupletcuplet);

*


Passing an Array

• formal parameterformal parameter formal parameterformal parameterdeclaration fordeclaration for declaration fordeclaration for

parameterparameter Pass-by-ValuePass-by-Value Pass-by-ReferencePass-by-Reference

•simple var. int cost int& pricearray impossible int myArray[ ]

•array const int source[ ]


1-D Array Review• An array is a structured data type• 1st element is “arrayName subzero”

• Array Declarationint myArray [9];

• Array Initializationint myArray [9 ] = { 9, 9, 9, 8, 7, 6, 5, 4,

3};

• Array Element ReferencemyArray [7]; // value = 4 *

99


1-D Array Review• Arrays are always passed by reference, unless

const added to the formal parameter.

• Array in a Function Prototype• void myFunction(int [9]);

• Array in a Function CallmyFunction(myArray);

• Array in a Function Headervoid myFunction(int anyArrayName[9])

optional


Two Dimensional Arrays

a everything about one dimensional arrays applies

a sometimes referred to as a table

a has rows and columnsex. multiplication table

•


2-D Array Declaration• Syntax• dataType arrayName [[ ConstIntExpression ]]

[[ ConstIntExpression ]]

• Example• int highTemp [52] [7];

double matrix [8] [8]; // checker boardint roomSchedule [237] [13];


2-D Array Initialization

• int nums [3] [2] = {7, 4, 1, 8, 5, 2}

• int roomsPSF[3] [7] = { {17, 18,19, 110, 111, 112, 113},

{27, 28, 29, 210, 211,212, 213},{37, 38, 39, 310, 311, 312, 313} };



• double ATtoCG[2] [3] = {.74, .79, .76, .83, .65, .89};

• double ATtoCG[2] [3] = { {.74, .79, .76}},

{.83, .65, .89} };

• int scores[4] [3] = {210, 198, 203, 188, 200, 224, 220, 217, 211, 194, 197, 189};



• You can assign values to individual elements:

• ATtoGC [0] [0] = 0.74;

ATtoGC [0] [1] = 0.79;

ATtoGC [0] [2] = 0.76;

ATtoGC [1] [0] = 0.83;

ATtoGC [1] [1] = 0.65;

*

ATtoCG [1] [2] = 0.89;


Accessing a 2-D Array

a very similar to creating a multiplication table.

a use nested loops.outer for loop was for the rowsinner for loop was for the columns


Loading a 2-D Array

a The Multiplication Table

• for (row =1; row <=10; row++)• {• cout <<setw(5)<<row<<" ";• forfor (column=1; column <= 10;

column++)• cout << setw(5)<< column*row;• cout << endl;• }


Loading a 2-D Array

• int scores [4][3];

• for(row=0; row<4; row++)• for(col=0; col<3; col++)• {• cout<<"Enter the value :";• cin>>scores[row][col];• }


Loading a 2-D Array

• scores [0][0] [2][0] [0][1] [2][1] [0][2] [2][2]

• [1][0] [3][0] [1][1] [3][1] [1][2] [3][2]

[row][col] = somevalue;


Displaying a 2-D Array• int scores [4] [3];

• for(row=0; row<4; row++)• {• for(col=0; col<3; col++)• cout << setw(6) << scores[row][col];• cout << endl; // new line for each row• }


Displaying a 2-D Array

• Output• 210 198 203

188 200 224220 217 211194 197 189


Functions and 2-D Arrays

• int test[7][19]; // declaration

• find_min(test); // function call

• int find_min(int num [7][19]) // funct. header

* * * *

char code[26][10];char code[26][10];

obtain(code);obtain(code);

char obtain(char key [26][10])char obtain(char key [26][10])


Local vs. Global

• No difference


Arrays

Multi-dimensional initialize & display

Sorting

Part II


Multidimensional Arrays

a everything about one dimensional arrays applies

a all elements of the same data type

a just need additional sets of [ ][ ]

a a 3-D array has rows, columns, and rank


Multidimensional Arrays• int scores [4] [3] [2]; // assume loaded with 1-24

• for(row=0; row<4; row++)• {• for(col=0; col<3; col++)• {• for(rank=0; rank<2; rank++)• cout<<setw(6)<<scores[row][col][rank];• cout<<endl; // new line for each row• }


Multidimensional Arrays

• {• cout <<endl; // start a new line• • { •• cout<<setw(6)<<nums[row][col][rank]nums[row][col][rank];• cout<<endl;// start a new line• }• }

for(rank=0; rank < 2; rank++)

for(col=0; col < 3; col++)

for(row=0; row < 4; row++)


A

B

C

D

E

28

40

29

9

14

• parallel arrays = two or more arrays in which elements with corresponding indexes are related

Parallel Arrays

Used when related data is of different data types.grade % of class

*


Parallel Arrays

• for(row…

• for(col…{ cout >> “Enter id#”;

cin >> id[row][col];

• cout >> “Enter grade”;cin >> grade[row][col];

}


Sum a Row• void main(void)• {• double nums [3][4] = {1, 2, 3, 4, 5, 6, 7, 8,

9, 10, 11, 12};• double sumRow(double [3] [4]); // prototype•• cout << “The sum of row 3 is “• << sumRow(nums)<<endl; //function

call• }


Sum a Row• double sumRow(double ary[3][4])

{ int col; double total=0;

for(col = 0; col < 4; col++)total += ary[ ][col];

return total;}

•

* *

total += ary[2][col]; //enter row #-1

output The sum of row 3 is 42The sum of row 3 is 42


Sum a Column• void main(void)• {• double nums [3][4] = {1, 2, 33, 4, 5, 6, 77, 8,

9, 10, 1111, 12};• double sumCol(double [3] [4]); // prototype•• cout << “The sum of column 3 is “• << sumCol(nums) << endl; //function

call• }


Sum a Column• double sumCol(double ary[3][4])

{ int row; double total=0;

• for(row = 0; row<3; row++)total += ary[row][ ];

return total;}

*

total += ary[row][2]; //enter col #-1

output The sum of column 3 is 21The sum of column 3 is 21


Sum All Rows• void sumRow(double ary[3][4])

{ int row, col;double total=0;

for(row = 0; row < 3; row++) { total = 0; // each row total begins at 0

for(col = 0; col<4; col++)total += ary[row][col]; // enter row #

cout << "The sum of row "<<row+1 << " is "<<total<<endl;

}cout<<endl;

}}

*

1

X


Sum All Columns• void sumCol(double ary[3][4])

{ int row, col;double total=0;

• for(col = 0; col < 4; col++){

total = 0; // each col. total begins at 0 for(row = 0; row < 3; row++)

total += ary[row][col]; //enter col #cout << "The sum of col " << col+1 << " is " << total << endl;

}}• cout<<endl;

}}*

1 3

X X

• Just for fun!• A 2-D array has the same number of rows as

col.

• 1. How to sum the diagonals - upper left to lower right?

• 2. How to sum the diagonals - upper right to lower left?

Sum Each Diagonal


Sorting

• Internal Sorts [for small data sets]selectionbubble (exchange)

• External Sorts [for large data sets]


Selection Sort

index (k) sm_index

0 2swap 21, 9

1 1swap 13, 13

2 3swap 21, 15

3 4swap 21, 17

21 159 13 17

15 179 13 21

99 152121 13 17

15 21219 13 1717

2121 15159 13 17


Selection Sort

• void sort(double [5]);• void swap(double [5], int, int); // prototypes

• void main(void)• { int index;• double my_list[ ] = {21, 13, 9, 15, 17};

• sort(my_list); // function call

• cout<<"\nThe sorted array is: \n";• for(index=0; index<5; index++)• cout<<'\t'<<my_list[index]<<endl;• }


Selection Sort• void sort(double testArray[5])• { int n, k, sm_index, moves=0; double smallest;•• for(k=0; k<4; k++) // size-1 = number of passes• { smallest=testArray[k];• sm_index=k;• for(n=k+1; n<5; n++) // size = # elem. to look at• if(testArray[n]<smallest)• { smallest=testArray[n];• sm_index=n;• }• swap(testArray, sm_index, k); // call to

swap()• }• }


Selection Sort• void swap(double testArray[5], int smaller, int pass)• { // pass = current

position: k• int moves;• double temp;

• temp=testArray[pass];• testArray[pass]=testArray[smaller];• testArray[smaller]=temp;

• moves++; // not needed for swap• }


Bubble Sort

• Put smaller first


• No change

• Put smaller first21 252513 9 1717

2121 252513 9 17

99 252121 13 17

9 2513 21 17


Bubble Sort

• Begin again and put smaller first

• No change


21 179 13 25

17 21219 13 2525

2121 171313 9 25

2121 17179 13 25

A Bubble Sort Function• void bubble_sort(int array[ ], int length)• {• int j, k, flag=1, temp;• for(j=1; j<=length && flag; j++)• {• flag=0; // false• for(k=0; k < (length-j); k++)• {• if (array[k+1] > array[k]) // > low to high• {• temp=array[k+1]; // swap• array[k+1]= array[k];• array[k]=temp;• flag=1; // indicates a swap• }} }} }} }} // has

occurred


Array Reviewa is an ordered sequence of data

of the same type

a can be of any valid data type

a can be 1-, 2-, or multidimensional

a must be declared before used

a can be assigned and initialized

a element numbering starts at zero


Array Review

a use for loops to access (nested for multidimentional)

a can be passed back and forth between functions

a when sent to functions the actual values are manipulated - not a copy

• (passed by reference)


Array Review -1 • Write a C++ program that adds equivalent

elements of the two-dimensional arrays named first and second. Both arrays should have two rows and three columns. For example, element [1][2] of the resulting array should be the sum of first[1][2] and second[1][2].

first second16 18 23 24 52 7754 91 11 16 19 59

sum40 70 10070 110 70

*


• Write a C++ program that finds and displays the maximum value in a two-dimensional array of integers. It should also show the maximum value’s subscripts. The array should be declared as a four-by-five array of integers and initialized.

• data: 16, 22, 99, 4, 18, -258, 4, 101, 5, 98,• 105, 6, 15, 2, 45, 33, 88, 72, 46, 3

Array Review - 2


Array Review - 3

• Write a program which picks the elements in ascending order from a two dimensional matrix (4 by 5) and puts them in a single dimensional array. Display the single dimensional array.


• There is a 3 by 5 array of grades. Write a program which reads the 15 grades and displays the number of grades below 60, number of grades in the 60's, number or grades in the 70's, number of grades in the 80's, and number of grades 90 or better.

Array Review - 4


• Write a program that finds and displays the maximum value and its indicies in a two-dimensional array of integers. The array should be declared as a 10-row by 20-column array of integers in main().

Array Review - 5


Array Review - 6a

• There is an array of three students each with four exam scores. Assume the scores are known and are: {77, 68, 86, 73}, {96, 87, 89, 78}, {70, 90, 86, 81}. Create a program which will display the lowest grade, the highest grade and the average of the grades to two decimal places.


Array Review - 6b• #include <iostream.h>• #include <iomanip.h>

• const int STUDENTS = 3;• const int EXAMS = 4;

• int mini (int [][EXAMS], int, int);• int maxi (int [][EXAMS], int, int);• float average(int [], int);• void printArray(int [][EXAMS], int, int);

Array Review - 6c• void main(void)• { int studentGrades[STUDENTS][EXAMS] = • {{77, 68, 86, 73}, {96, 87, 89, 78}, {70, 90, 86, 81}};

• cout << "The array is:" << endl;• printArray(studentGrades, STUDENTS, EXAMS);• cout<<endl<<endl<<"Lowest grade: "• << mini (studentGrades, STUDENTS, EXAMS)• << endl << "Highest grade: " • << maxi (studentGrades, STUDENTS,

EXAMS)<<endl;

• for (int person = 0; person < STUDENTS; person++)• cout << "The average grade for student " << person << " is " • <<setiosflags(ios::fixed | ios::showpoint)<<setprecision(2) • << average(studentGrades[person], EXAMS) << endl;• }


Array Review - 6d• int mini(int grades[][EXAMS],• int pupils, int

tests)• { • int lowGrade = 100;• for (int i = 0; i < pupils; i++)• for (int j = 0; j < tests; j++)• if (grades[i][j] < lowGrade)• lowGrade = grades[i][j];• return lowGrade; • }

int maxi(int grades[][EXAMS], int pupils, int tests)

{ int highGrade = 0; for (int i = 0; i < pupils; i++) for (int j = 0; j < tests; j++) if (grades[i][j] > highGrade) highGrade = grades[i][j]; return highGrade; }


Array Review - 6e• float average(int

setOfGrades[],• int tests)• { • int total = 0;• for (int i = 0; i < tests; i++)• total += setOfGrades[i];• return (float) total / tests; • }

void prtArray(int grades[][EXAMS], int pupils, int tests){ cout << " [0] [1] [2] [3]"; for (int i = 0; i < pupils; i++) { cout << endl<< "studentGrades["

<< i << "] ";

for (int j = 0; j < tests; j++) cout << setiosflags(ios::left)

<< setw(5) << grades[i][j];}


Array Review - 6f• function call:• average(studentGrades[person],

EXAMS)

• float average(int setOfGrades[], int tests)• { int total = 0;

• for (int i = 0; i < tests; i++)• total += setOfGrades[i];

• return total• }


Common Errors

Not declaring the arrayNot declaring the array First element is called First element is called zerozero; last element ; last element

is one less than the number of elementsis one less than the number of elements Out of rangeOut of range subscripts - no warning subscripts - no warning Error in the Error in the forfor loop - check the counter loop - check the counter Not initializing the arrayNot initializing the array


Common Errors

Aggregate operations not allowedAggregate operations not allowed Omitting array size - permitted only Omitting array size - permitted only

when declared as a formal parameter when declared as a formal parameter initialized in the declarationinitialized in the declaration

If array is /* in */ only, declare the If array is /* in */ only, declare the formal parameter as formal parameter as constconst to prevent to prevent accidental modificationaccidental modification


Debugging

array subscriptsarray subscripts

recheck array size in declaration, recheck array size in declaration, initialization, and initialization, and forfor loops loops

Prevention - plan first!Prevention - plan first!Valuation tablesValuation tablesDisplay values with coutDisplay values with cout

Documents

Arrays Structured Programming 256 Chapter 10 © 2000 Scott S Albert Arrays One-Dimensional initialize & display Arrays as Arguments Two-dimensional initialize