2-DataStrucs&ADTs.txt

1

II. Introduction to Data Structure and Abstract Data Types — C-Style Types
A. Introduction (§2.1)
One important aspect of the design phase is the selection and design of appropriate data types
to organize the data to be processed; indeed, this is the real essence of OOP (object-oriented
programming).
Example 1: Trans-Fryslan Airlines (pp. 30-31)
Attempt 1:
enum SeatStatus {OCCUPIED, UNOCCUPIED};
SeatStatus seat1, seat2, . . . , seat10;
Simple data organization, but horrible algorithms for the basic operations!
ALGORITHM TO LIST UNOCCUPIED SEATS
1. If seat1 is UNOCCUPIED
Display 1.
2. If seat2 is UNOCCUPIED
Display 2.
3. If seat3 is UNOCCUPIED
Display 3.
.
.
.

10. If seat10 is UNOCCUPIED
Display 10.
ALGORITHM TO RESERVE A SEAT
1. Set done to false.
2. If seat1 is UNOCCUPIED do the following:
a. Display "Do you wish to assign Seat #1?".
b. Get response from user.
c. If response is 'y' then to the following:
i. Set seat1 to OCCUPIED.
ii. Set done to true.
3. If not done and seat2 is UNOCCUPIED then do the following:
a. Display "Do you wish to assign Seat #2?".
b. Get response from user.
c. If response is 'y' then to the following:
i. Set seat2 to OCCUPIED.
ii. Set done to true.
.
.
.

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Attempt 2:
const int MAX_SEATS = 10; // upper limit on the number of seats
enum SeatStatus {OCCUPIED, UNOCCUPIED};
typedef SeatStatus SeatList[MAX_SEATS];
SeatList seat;
More complex data organization, but much nicer algorithms for the basic operations!
ALGORITHM TO LIST UNOCCUPIED SEATS
1. For number ranging from 0 to MAX_SEATS - 1 do the following:
If seat[number] is UNOCCUPIED
Display number
ALGORITHM TO RESERVE A SEAT
1. Read number of seat to be reserved.
2. If seat[number] is UNOCCUPIED
Set seat[number] to OCCUPIED.
Else
Display a message that the seat having this number has already been assigned.
→ Quite often there's a tradeoff:
simplicity of data organization ↔ simplicity/elegance of algorithms
Example 2: Searching an online phone directory
Linear search?
OK for Calvin College, but too slow for Grand Rapids or New York
→ Amount of data is an important factor. May have to restructure the data set for
efficient processing — e.g., keep it ordered and use binary search or an indexed
sequential search
Example3: Compiler lookup of an identifier's memory address, type, . . . in a symbol table
Linear search? No, too slow
Binary search? No, too much work to keep sorted
Use hash tables
→ Number of accesses & speed required is an important factor.
Example 4: Text processing
Store in an array / vector?
OK for text analysis — word counts, average word length, etc.
Not for word-processing — Too inefficient if many insertions & deletions
→ Static vs. dynamic nature of the data is an important factor

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Definitions
1. An abstract data type (ADT) is:
a collection of related data items
together with
basic relations between them and operations to be performed on them.
Why "abstract?" Data, operations, and relations are studied independently of how they
are going to be implemented.
What not how
Example:
Data items: seats for TFA
Basic operations: find unoccupied sets, reserve a set, cancel a seat assignment.
2. An implementation of an ADT consists of
storage structures (commonly called data structures) to store the data items
and
algorithms for the basic operations and relations.
Examples: Attempts 1 and 2 for TFA
3. Data abstraction: Separating the definition of a data type from its implementation.
An important concept in software design.
Usually the storage structures / data structures used in implementation are those provided in a
language or built from them. So we look first at those provided in C++. We begin by
reviewing the simple types — int, double, etc. — and then the structured ones.

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Diagram from p. 33
C++ Types

Fundamental Types

Arithmetic

Integral

Floating point
(reals)

Characters Enumerations Integers

char
unsigned char
signed char

void

bool

Structured Types

pointers

complex

float
double
long double

int
short int
long int
unsigned
unsigned short
unsigned long

array
struct
union
class
istream
ostream
iostream
ifstream
ofstream
fstream
string
vector
deque
list
stack
queue
priority_queue
map
multimap
set
multiset
bitset
valarray

B. Simple Data Types (§2.2)
Memory:
2-state devices ↔ bits 0 and 1
Organized into bytes (8 bits) and words (machine dependent — e.g., 4 bytes).
Each byte (or word) has an address making it possible to store and retrieve contents of
any given memory location.
Therefore:
• The most basic form of data: sequences of bits
• We can view simple data types (values are atomic — can't be subdivided) as ADTs.
• Implementations have:
Storage structures: memory words
Algorithms: system hardware/software to do basic operations.

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1. Boolean data
Data values: {false, true}
In C/C++: false = 0, true = 1 (or nonzero)
Could store 1 value per bit, but usually use a byte (or word)
Operations:

and:
&&
or: ||
not: !

(See bit tables on p. 34)

&&

||

x !x
0 1
1 0

2. Character Data
Store numeric codes (ASCII, EBCDIC, Unicode) in 1 byte for ASCII and EBCDIC,
2 bytes for Unicode (see examples on p. 35).

Basic operation: comparison to determine if =, <, >, etc. — use their numeric codes

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3. Integer Data
Nonegative (unsigned) integer: type unsigned (and variations) in C++
Store its base-two representation in a fixed number w of bits (e.g., w = 16 or w = 32)
88 = 00000000010110002

Signed integer:

type int (and variations) in C++

Store in a fixed number w of bits using one of the following:
a. Sign-magnitude representation
Save one bit for sign (0 = +, 1 = –) and use base-two representation in the other bits.
88 → 0000000001011000
↑

–88 → 1000000001011000

sign bit

↑

sign bit

→ Not good for arithmetic computations
b. Two's complement representation
For n ≥ 0 : Use ordinary base-two representation with leading (sign) bit 0
For –n:
(1) Find w-bit base-2 representation of n
(2) Complement each bit.
(3) Add 1
(From right, change all 1's up to first 0; change this 0 to a 1.)
Example: –88
1. 88 as a 16-bit base-two number
2. Complement this bit string
3. Add 1

0000000001011000
1111111110100111
1111111110101000

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→ Good for arithmetic computations

(see p. 38)

These work for both + and – integers
5 + 7:
111 ← carry bits
0000000000000101
+ 0000000000000111
0000000000001100
5 + –6:
0000000000000101
+ 1111111111111010
1111111111111111
c. Biased representation
Add a constant bias to the number (typically, 2w – 1);
then find its base-two representation.
Examples:
88 using w = 16 bits and bias of 215 = 32768
1. Add the bias to 88, giving 32856
2. Represent the result in base-two notation:

1000000001011000

Note: For n ≥ 0, just change leftmost bit of binary representation of n to 1
–88:
1. Add the bias to -88, giving 32680
2. Represent the result in base-two notation:

0111111110101000

→ Good for comparisons; so, it is commonly used for exponents in floating-point
representation of reals.
d. Problems:
→ Overflow: Too many bits to store.
→ Not a perfect representation of (mathematical) integers; can only store a finite
(sub)range of them.

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4. Real Data
Types float and double (and variations) in C++
IEEE Floating-Point Format
Single precision:
1. Write binary representation in floating-point form:
b1.b 2b3 . . . × 2 k with each bi a bit and b1 = 1 (unless number is 0)
↑
mantissa
exponent
or fractional part
2. Store:
— sign of mantissa in leftmost bit (0 = +, 1 = –)
— biased binary rep. of exponent in next 8 bits (bias = 127)
— bits b 2b3 . . . in rightmost 23 bits. (Need not store b1 — know it's 1)
Example: 22.625 = 10110.1012
(see p.41)
Floating point form: 1.01101012 × 24

Problems:
→ Exponent overflow/underflow (p. 41)
Only a finite range of reals can be stored exactly.

→ Roundoff error (pp. 41-42)
— Only a finite subset of this range of reals can be stored exactly.
(Most reals do not have terminating binary representations.)
Example: 0.7 = (0.101100110011001100110011001100110 . . .)2
— Roundoff error may be compounded in a sequence of operations.
(Some of the usual laws of arithmetic do not hold — associative, distributive)
— Be careful in comparing reals with == and !=.

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Assignment #2
→ Be able to answer the questions in Quick Quiz 2.2.
→ Write out the following to hand in next Wednesday, Feb. 10:
Exercises 2.2 1
10, 12 (Exers 2, 4 in sign-magnitude)
16, 18 (Exers 2, 4 in two's complement)
22, 24 (Exers 2, 4 in biased notation)
27, 32, 37, 38, 40, 43

We've been looking at simple types. Now we look at structured data types (also called data
structures) that store collections of data. We will first review/ introduce arrays and structs
from a "traditional" point of view (i.e., as used in C and many other languages). Classes will
be considered in detail very soon. A large part of this course will focus on how these (and
other) data types are used to construct other useful data types.

C. C-Style One-Dimensional Arrays (§2.3)
1. Def of an array as an ADT:
A fixed-size sequence (ordered set) of elements, all of the same type, where
the basic operation is direct access to each element in the array so values can
be retrieved from or stored in this element.
Properties:
• Fixed number of elements
• Must be ordered so there is a first element, a second one, etc.
• Elements must be the same type (and size);
∴ use arrays only for homogeneous data sets.
• Direct access: Access an element, just by giving its location — the time to access each
element is the same for all elements, regardless of position.
[In contrast to sequential access: To access an element, must first access all those that
precede it.]

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2. Declaring arrays in C++
element_type array_name[CAPACITY];
where
element_type is any type,
array_name is the name of the array — any valid identifier.
CAPACITY (a positive integer constant) is the number of elements in the array
→The compiler reserves a block of consecutive memory locations, enough to hold
CAPACITY values of type element_type. (These are consecutive memory locations,
except possibly if CAPACITY or the size of element_type objects is very large).
The elements (or positions) of the array, are indexed 0 , 1 , 2 ,

. . .,

CAPACITY - 1 .

Example:
double score[100];
or better, use a named constant to specify the array capacity:
const int CAPACITY = 100;
double score[CAPACITY];

Note: Can use typedef with array declarations; for example,
const int CAPACITY = 100;
typedef double ScoresArray[CAPACITY];
ScoresArray score;
→ How well does this implement the general definition of an array:
As an ADT
In C++
ordered ←→ indices are numbered 0, 1, 2, . . ., CAPACITY - 1
fixed size ←→ CAPACITY specifies the capacity of the array
same type elements ←→ element_type is the type of elements
direct access ←→ Subscript operator []

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3. Subscript operator
The subscript operator [] is an actual operator and not simply a notation/punctuation as
in some other languages. Its two operands are an array variable and an integer index
(or subscript) and is written
array_name[i]
Here i is an integer expression with 0 ≤ i ≤ CAPACITY – 1. This subscript operator
returns a reference to (alias of) the element in location i in array_name; so it
is a variable, called an indexed (or subscripted) variable, whose type is the specified
element_type of the array.
This means that this array reference can be used on the left side of an assignment, in input
statements, etc. to store a value in a specified location in the array.
Examples:
// Zero out all the elements of score
for (int i = 0; i < CAPACITY; i++)
score[i] = 0.0;
// Read values into the first numScores elements of score
for (int i = 0; i < numScores; i++)
cin >> score[i];
// Display the values stored in the first numScores
// elements of score
for (int i = 0; i < numScores; i++ )
cout << score[i] << endl;
4. Array Initialization
In C++, arrays can be initialized when they are declared.
a. Numeric arrays:
element_type num_array[CAPACITY] = {list_of_initial_values};
Example:
double rate[5] = {0.11, 0.13, 0.16, 0.18, 0.21};
declares rate to be an array of 5 real values and intializes rate as follows:
0

rate

1

2

3

0.11 0.13 0.16 0.18

4

0.21

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Note 1: If fewer values are supplied than the declared capacity of the array,
the remaining elements are assigned 0.
double rate[5] = {0.11, 0.13, 0.16};
intializes rate as follows:
0

rate

1

2

0.11 0.13 0.16

3

4

0

0

Note 2: It is an error if more values are supplied than the declared size of the array,
How this error is handled, however, will vary from one compiler to another.
In Gnu C++ ???
Note 3: If no values are supplied, array elements are undefined (i.e., garbage values).
b. Character arrays:
They may be initialized in the same manner as numeric arrays.
Example:
char vowel[5] = {'A', 'E', 'I', 'O', 'U'};
declares vowel to be an array of 5 characters and initializes it as follows:

vowel

0

1

2

3

4

A

E

I

O

U

Note 1: If fewer values are supplied than the declared size of the array,
the zeros used to fill unitialized elements are interpreted
as the null character '\0' whose ASCII code is 0.
Example:
const int NAME_LENGTH = 10;
char collegeName[NAME_LENGTH] = {'C', 'a', 'l', 'v', 'i', 'n'};

initializes collegeName as follows:
0

1

2

3

4

5

6

7

8

9

collegeName C

a

l

v

i

n \0 \0 \0 \0

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Note 2: Character arrays may be initialized using string constants. For example, the
following declaration is equivalent to the preceding:
char collegeName[NAME_LENGTH] = "Calvin";
Note 3:The null character '\0' (ASCII code is 0) is used as an end-of-string mark.
Thus, character arrays used to store strings should be declared large enough to
store the null character. If it is not, one cannot expect some of the string
functions and operations to work correctly. If a character array is initialized with a ,
string constant, the end-of-string mark is added automatically, provided there is
room for it.
Example:
char collegeName[7] = {'C', 'a', 'l', 'v', 'i', 'n', '\0'};
char collegeName[7] = "Calvin";
c. Initializations with no array size specified
The array capacity may be omitted in an array declaration with an initializer list. In
this case, the number of elements in the array will be the number of values in
the initializer list.
Example:
double rate[] = {0.11, 0.13, 0.16};
Note: This explains the brackets in constant declarations such as
const char IN_FILE[] = "employee.dat";
5. Addresses
When an array is declared, the address of the first byte (or word) in the block of memory
associated with the array is called the base address of the array. Each array reference
is then translated into an offset from this base address.
For example, suppose each element of array score will be stored in 8 bytes and the base
address of score is 0x1396. A statement such as
cout << score[3] << endl;
requires that the array reference score[3] first be translated into a memory address:
score[3] → 0x1396 + 3 * sizeof(double)
= 0x1396 + 3 * 8
= 0x13ae

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The contents of the memory word with this address 0x13ae can then be retrieved and
displayed. An address translation like this is carried out each time an array element is
accessed.
For an array variable array_name, its value is actually the base address of
array_name and array_name + index is the address of array_name[index].
An array reference
array_name[index]
is equivalent to
*(array_name + index)
Here, * is the dereferencing operator;
*ref returns the contents of the memory location with address ref.
z

For example, the statement
cout << score[3] << endl;
could also be written
cout << *(score + 3) << endl;
Note: No bounds checking of indices is done!

(See pp. 50-51)

D. C-Style Multidimensional Arrays
1. Introduction
Example: Suppose we wish to store and process a table of test scores for several different
students on several different tests:
Test 1
Test 2 Test 3 Test 4
Student 1
99.0
93.5
89.0
91.0
Student 2
66.0
68.0
84.5
82.0
Student 3
88.5
78.5
70.0
65.0
:
:
:
:
:
:
:
:
:
:
Student-n
100.0
99.5 100.0
99.0
Use a two-dimensional array.

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2. Declaring two-dimensional arrays
a. Usual form of declaration:
element_type array_name[NUM_ROWS][NUM_COLUMNS];
Example:
const int NUM_ROWS = 30,
NUM_COLUMNS = 5;
double scoresTable[NUM_ROWS][NUM_COLUMNS];
or using a typedef:
const int NUM_ROWS = 30,
NUM_COLUMNS = 5;
typedef double TwoDimArray[NUM_ROWS][NUM_COLUMNS];
TwoDimArray scoresTable;
b. Initializing
List the initial values in braces, row by row; may use internal braces for each row to
improve readability.
Example:
double
rates[2][3] = {{0.50, 0.55, 0.53},
// first row
{0.63, 0.58, 0.55} }; // second row
3. Processing two-dimensional arrays
Use doubly-indexed variables:
Example:
scoresTable[2][3] is the entry in row 2 (numbered from 0) and
↑
↑
column 3 (numbered from 0)
row index column index
Typically use nested loops to vary the two indices, most often in a rowwise manner.

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Example:
int numStudents, numTests,
i, j;
// indices;
cout >> "# students and # of tests? ";
cin >> numStudents >> numTests;
cout << "Enter " << numTests << " test scores for student\n";
for (i = 0; i < numStudents; i++)
{
cout << '#' << i + 1 << ':';
for (j = 0; j < numTests; j++)
cin >> scoresTable[i][j];
}

4. Higher-Dimensional Arrays
The methods for two-dimensional arrays extend in the obvious way.
a. Example: To store and process a table of test scores for several different students on
several different tests for several different semesters:
const int RANKS = 10, ROWS = 30, COLUMNS = 5;
typedef double ThreeDimArray[RANKS}[ROWS][COLUMNS;
ThreeDimArray gradeBook;
gradeBook[4][2][3]

is the score on page 4 (numbered from 0)
for student 2 (numbered from 0)
on test 3 (numbered from 0)

b. Still higher dimensions
Example like the automobile-inventory example on pp. 54-5
enum BrandType {Levi, Wrangler, CalvinKlein, Lee, BigYank, NUM_BRANDS};
enum StyleType {baggy, tapered, straightleg, designer, NUM_STYLES};
enum WaistType {w28, w29, w30, w31, w32, w33, w34, w35, w36,
w37, w38, w39, w40, w41, w42, w43, w44, w45,
w46, w47, w48, NUM_WAIST_SIZES};
enum InseamType {i26, i27, i28, i29, i30, i31, i32, i33, i34, i34, i36,
NUM_INSEAM_SIZES};
typdef int
JeansArray[NUM_BRANDS][NUM_STYLES][NUM_WAIST_SIZES][NUM_INSEAM_SIZES];
JeansArray jeansInStock;

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The value of
jeansInStock[Levi][Designer][w32][i31]

is the number of Levi's designer 32 × 31 jeans that are in stock. The statement
jeansInStock[brand][style][waist][inseam]--;

might be used to record the sale (i.e., decrement the inventory) of one pair of jeans of
brand brand, style style, waist size waist, and inseam length inseam.
5. Arrays of Arrays
Consider again the declaration
double scoresTable[30][4];
This is really a declaration of a one-dimensional array having 30 elements, each of which
is a one-dimensional array of 4 real numbers; that is, scoresTable is a one-dimensional
array of rows, each of which has 4 real values. This declaration is thus equivalent to a
declaration like
typedef double RowOfTable[4];
RowOfTable scoresTable[30];
or, since typedef is used once, why not use it twice:
typedef double RowOfTable[4];
typedef RowOfTable TwoDimArray[30];
TwoDimArray scoresTable;
With any of the declarations, we can always view a two-dimensional array like
scoresTable as an array of rows of a table. In fact,
scoresTable[i] is the i-th row of the table.
Then, scoresTable[i][j] should be thought of as (scoresTable[i])[j], that
is, as finding the j-th element of scoresTable[i].
Address Translation:
This array-of-arrays structure of multidimensional arrays also explains how address
translation is carried out. Suppose the base address of scoresTable is 0x12345:
scoresTable[10][3]
→ 0x12345 + 10 * sizeof(RowOfTable) + 3 * sizeof(double)
= 0x12345 + 10 * 4 * sizeof(double) + 3 * sizeof(double)
= 0x12345 + (10 * 4 + 3) * 8
= 0x1249d
What about higher-dimensional arrays?
An n-dimensional array should be viewed (recursively) as a one-dimensional
array whose elements are (n - 1)-dimensional arrays.

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6. Arrays as Parameters
Passing an array to a function actually passes the base address of the array. Thus the
parameter has the same address as the argument, so modifying the parameter will modify
the corresponding array argument.
This also means that the array capacity is not available to the function unless passed as a
separate parameter.
Example: In void Print(theArray[100], int theSize);
can just as well use:
void Print(theArray[], int theSize);

Now, what about multidimensional arrays?
void Print(double table[][], int rows, int cols)
doesn't work. Best to use a typedef to declare a global type identifier and use it to declare
the types of the parameters.:
For example,
typedef double TwoDimArray[30][4];
TwoDimArray scoresTable;
void Print(TwoDimArray table, int rows, int cols)
. . .
Assignment #2:

Due: Friday., Feb. 19

Be able to answer questions in Quick Quiz 2.3
P. 61:

1, 3, 5, 6, 8, 10, 11, 13, 15, 17, 19

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Problems with C-Style Arrays
a. Capacity cannot change.
b. Vrtually no predefined operations or functions on non-char arrays.
→ Must pass size (and/or capacity) to array-processing functions.
c. Deeper Problem: In OOP, objects should be self-contained .
→ C-style arrays aren't.
Solution (OOP): Encapsulate array, capacity, size, and operations in a class.
→ vector

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E. Intro. to Structs
1. When is a structure needed?
Up to now, our approach to designing a program (and software in general) has been:
1. Identify the objects in the problem.
1a. . . .
2. Identify the operations in the problem.
1a. If the operation is not predefined, write a function to perform it.
1b. If the function is useful for other problems, store it in a library.
3. Organize the objects and operations into an algorithm.
4. Code the algorithm as a program.
5. Test, execute, and debug the program.
6. Maintain the program
Since predefined types may not be adequate, we add:
1a. If the predefined types are not adequate to model the object,
create a new data type to model it (e.g., enumerations).
Now, suppose the object being modeled has multiple attributes.
Examples :
A temperature has:
— a degrees attribute
— a scale attribute (Fahrenheit, Celsius, Kelvin)
32
degrees

F
scale

A date has:
— a month attribute
— a day attribute
— a year attribute
September 23 1998
month
day year
C++ provides structs and classes to create new types with multiple attributes.
might add to our design methodology:

So we

1. Identify the objects in the problem.
1a. If the predefined types are not adequate to model the object,
create a new type to model it.
1b. If the object has multiple attributes, create a struct or class to represent
objects of that type.

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2. As an ADT, a structure (usually abbreviated to struct and sometimes called a record) is
like an array in that it is has a fixed size, it is ordered, and the basic operation is direct
access to its members so that items can be stored in / retrieved from them; but it differs
from an array in that its elements may be of different types.
3. Declaration (C-style):
struct TypeName
{
declarations of members
};
4. Examples:
a. Temperature:
32
degrees

//of any types

F
scale
struct Temperature
{
double degree; // number of degrees
char scale;
// temp. scale (F, C, K, ...)
};
Temperature temp;

b. Date:
September 23 1998
month
day year

struct Date
{
string month;
int day,
year;
};
Date birthDay,
currentDate;

// name of month
// day number
// year number

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c. Phone Listing:
John Q. Doe 12345 Calvin Rd. Grand Rapids, MI

name

street

city & state

9571234

phone #

struct DirectoryListing
{
string name,
street,
cityAndState;

// name of person
// street address
// city, state (no zip)

unsigned phoneNumber;

// 7-digit phone number

};
DirectoryListing entry,
// entry in phone book
group[20]; // array of directory listings

d. Coordinates of a point:
3.73 –2.51
x coord. y coord.

(Members need not have different types.)

struct Point
{
double xCoord,
yCoord;
};
Point p, q;

e. Test scores:
012345
83 79 92 85
id-number
list of scores

(Members may be structured types — e.g., arrays.)

struct TestRecord
{
unsigned idNumber,
score[4];
};
TestRecord studentRecord, gradeBook[30];

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Heirarchical (or nested) structs
Since the type of a member may be any type, it may be another struct. For example,
John Q. Doe 12345 Calvin Rd. Grand Rapids, MI 9571234 June 17 1975 3.95 92.5
name
street
city & state
phone # month day year gpa credits
\__________________________ DirectoryListing ______________________/ \____ Date _____/ real real

struct PersonalInfo
{
DirectoryListing ident;
Date birth;
double cumGPA,
credits;
};
PersonalInfo student;
6. The scope of a member identifier is the struct in which it is defined.
Consequences:
— A member identifier may be used outside the struct for some other purpose.
— A member cannot be accessed outside the struct just by giving its name.
7. Direct access to members of a struct (or class) is implemented using member access
operators: one of these is the dot operator (.)
struct_var.member_name
Examples:
Input a value into the month member of birthday:
cin >> birthDay.month;
Calculate y coordinate of a point on y = 1/x:
if (p.xCoord != 0.0)
p.yCoord = 1.0 / p.xCoord;
Sum the scores in studentRecord:
double sum = 0;
for (int i = 0; i < 4; i++)
sum += studentRecord.score[i];
Output the name stored in student:
cout << student.ident.name << endl;

24

F. A Quick Look at Unions (p. 68)
1. A union has a definition like that of a struct, with "struct" replaced by "union":
union TypeName ← TypeName is optional
{
declarations of members //of any types
};

2. A union differs from a struct in that the members share memory. Memory is
(typically) allocated for the largest member, and all the other members share this memory.
Example:
#include <iostream>
using namespace std;
struct Struct
{
int i;
double d;
bool b;
};
union Union
{
int i;
double d;
bool b;
};
int main()
{
Struct s;
Union u;
s.i = 123456789;
u.i = 123456789;
cout << "Structure: "
<< (s.b ? "true"
cout << "Union:
"
<< (u.b ? "true"

<< s.i << " and " << s.d << "
: "false") << endl;
<< u.i << " and " << u.d << "
: "false") << endl;

"

s.d = 0.123;
u.d = 0.123;
cout << "Structure: "
<< (s.b ? "true"
cout << "Union:
"
<< (u.b ? "true"

<< s.i << " and " << s.d << "
: "false") << endl;
<< u.i << " and " << u.d << "
: "false") << endl;

"

s.b = true;
u.b = true;
cout << "Structure: "
<< (s.b ? "true"
cout << "Union:
"
<< (u.b ? "true"

<< s.i << " and " << s.d << "
: "false") << endl;
<< u.i << " and " << u.d << "
: "false") << endl;

"

}

"

"

"

25

Execution:
Structure:
Union:
Structure:
Union:
Structure:
Union:

123456789 and 6.95336e-310 false
123456789 and 3.21193e-273 true
123456789 and 0.123 false
1069513965 and 0.123 true
123456789 and 0.123 true
97517 and 2.06932e-309 true

Note: If data is stored in a union using one member and accessed using another member of
a different type, the results are implementation dependent.
3. Example: Suppose a file contains:
John Doe 40 M
<——— name, age, marital status (married)
January 30 1980
<——— wedding date
Mary Smith Doe 8
<——— spouse, # dependents
Fred Jones 17 S
<——— name, age, marital status (single)
T
<——— available
Jane VanderVan 24 D <——— name, age, marital status (divorced)
February 21 1998 N <——— divorce date, remarried (No)]
Peter VanderVan 25 W <——— name, age, marital status (widower)
February 22 1998 Y <——— date became a widower, remarried (Yes)
:
:
Since there are three types of records, we would need three types of structs:
struct MarriedPerson
{
string name;
short age;
char marStatus;
Date wedding;
string spouse;
short dependents;
};
struct SinglePerson
{
string name;
short age;
char marStatus;
bool available;
};

//
//
//
//

S = single, M = married, W = was married
date s/he was married
name of spouse
number of dependents

// true if person is available, else false

struct WasMarriedPerson
{
string name;
short age;
char marStatus;
Date divorceOrDeath;// date s/he was divorced/widow(er)ed
char remarried;
// Y or N
};

26

4. Structs like these with some common members — fixed part — but other fields that are different
can be combined into a single structure by using a union — to add a variant part.
struct Date
{
string month;
short day, year;
};
struct MarriedInfo
{
Date wedding;
string spouse
short dependents;
};
struct SingleInfo
{
bool available;
};
struct WasMarriedInfo
{
Date divorceOrDeath;
char remarried;
};
struct PersonalInfo
{
string name;
short age;
char marStatus; // Tag: S = single, M = married, W = was married
union
{
MarriedInfo married;
SingleInfo single;
WasMarriedInfo wasMarried;
};
};
PersonalInfo person;

Typically process such a structure using a switch for the variant part: e.g.,
cin >> person.name >> person.age >> person.marStatus;
switch(Person.marStatus)
{
case 'M': cin >> person.married.wedding.month
>> person.married.wedding.day
>> person.married.wedding.year
>> person.married.spouse
>> person.married.dependents;
break;
case 'S': cin >> available;
break;
case 'W': cout << "Enter . . . ";
cin >> person.wasMarried.divorceOrDeath.month
>> person.wasMarried.divorceOrDeath.day
>> person.wasMarried.divorceOrDeath.year
>> person.wasMarried.remarried;
}

27

5. Address translation for structs and unions:

(p. 70)

enum YearInSchool {fresh, soph, jun, sen, spec};
struct StudentRecord
{
int number;
char name[21];
double score[3];
YearInSchool year;
}
//PersonalInfo as before
StudentRecord s;
PersonalInfo p;

Addresses:
s = 0x33a18
p = 0x339d8
Struct S:
0x33a18 number
0x33a1c name
0x33a38 score
0x33a50 year
Struct P:
0x339d8 name
0x339ee age
0x339f0 marStatus
0x339f2 married.wedding.month
0x339fc married.wedding.day
0x339fe married.wedding.year
0x33a00 married.spouse
0x33a16 married.dependents
0x339f2 wasMarried.divorceOrDeath.month
0x339fc wasMarried.divorceOrDeath.Day
0x339fe wasMarried.divorceOrDeath.year
0x33a00 wasMarried.remarried

If a struct s has fields f1, ..., f n, requiring w1, ..., w n cells of storage, respectively:
Address of s.f k = base address of s + offset
k–1

= base address of s +

∑wi

i=1

For structs like p that contain unions: Allocate space for the largest variant, and then
overlay variants in this space.

28

6. These kinds of variant structures aren't used much anymore.

(p. 69)

Instead, in OOP languages:
• Encapsulate the common information in a base class
• Use inheritance to build derived classes for the variants
(Derived classes inherit all of the non-private members of the base class.)

base class

derived classes

PersonalInfo
name
age
marStatus

name
age
marStatus

name
age
marStatus

name
age
marStatus

wedding
spouse
dependents

available

divorceOrDeath
remarried

SinglePerson

WasMarriedPerson

MarriedPerson

G. A commercial for OOP
Two programming paradigms:
Procedural: commonly used withprocedural languages such as C, FORTRAN, and Pascal
Action-oriented — concentrates on the verbs of a problem's specification
Programmers:
• Identify basic tasks to be performed to solve problem
• Implement the actions required to do these tasks as subprograms
(procedures/functions/subroutines)
• Group these subprograms into programs/modules/libraries, which together make up a
complete system for solving the problem
Object-oriented: Uses in OOP languages like C++, Java, and Smalltalk
Focuses on the nouns of a problem's specification
Programmer:
• Determine what objects are needed for a problem and how they should work together to
solve the problem.
• Create types called classes made up ofdata members and function members to operate
on the data. Instances of a type (class) are called objects.

29

An Example — Creating a Data Type in a procedural (C-type) language

(pp. 74-78)

Problem: Create a type Time for processing times in standard hh:mm AM/PM form
and in military-time form.
Data Members:
Hours (0, 1, ..., 12)
Minutes (0, 1, 2, ..., 59)
AM or PM indicator ('A' or 'P')
MilTime (military time equivalent)
Some Operations :
1. Set the time
2. Display the time
3. Advance the time
4. Determine if one time is less than another time.
Implementation:
1. Need storage for the data members — use a struct
2. Need functions for the operations.
3. "Package" declarations of these together in a header file.

/** Time.h ---------------------------------------------------------This header file defines the data type Time for processing time.
Basic operations are:
Set:
To set the time
Display: To display the time
Advance: To advance the time by a certain amount
LessThan: To determine if one time is less than another
---------------------------------------------------------------------*/
#include <iostream>
using namespace std;
struct Time
{
unsigned hour,
minute;
char AMorPM;
unsigned milTime;
};

// 'A' or 'P'
// military time equivalent

30

/* Set sets the time to a specified values.
*
* Receive:
Time object t
*
hours, the number of hours in standard time
*
minutes, the number of minutes in standard time
*
AMPM ('A' if AM, 'P' if PM
* Pass back: The modified Time t with data members set to
*
the specified values
******************************************************************/
void Set(Time & t, unsigned hours, unsigned minutes, char AMPM);
/* Display displays time t in standard and military format using
* output stream out.
* Receive:
Time t and ostream out
* Output:
The time T to out
* Pass back: The modified ostream out
******************************************************************/
void Display(const Time & t, ostream & out);
/* Advance increments a time by a specified value.
*
* Receive:
Time object t
*
hours, the number of hours to add
*
minutes, the number of minutes to add
* Pass back: The modified Time t with data members incremented
*
by the specified values
******************************************************************/
void Advance(Time & t, unsigned hours, unsigned minutes);
/* Determine if one time is less than another time.
*
* Receive: Times t1 and t2
* Return:
True if t1 < t2, false otherwise.
******************************************************************/
bool LessThan(const Time & t1, const Time & t2);

31

//========= Time.cpp -- implements the functions in Time.h =========
#include "Time.h"
/*** Utility functions -- might be added as basic operations later ***/
int ToMilitary(unsigned hours, unsigned minutes, char AMPM);
void ToStandard(unsigned military,
unsigned & hours, unsigned & minutes, char& AMPM);
void Set(Time & t, unsigned hours, unsigned minutes, char AMPM)
{
if (hours >= 1 && hours <= 12 &&
minutes >= 0 && minutes <= 59 &&
(am_pm == 'A' || am_pm == 'P'))
{
t.hour = hours;
t.minute = minutes;
t.AMorPM = AMPM;
t.milTime = ToMilitary(hours, minutes, AMPM);
}
else
cout << "*** Can't set time with these values ***\n";
// t remains unchanged
}
void Display(const Time & t, ostream & out)
{
out << t.hour << ':'
<< (t.minute < 10 ? "0" : "") << t.minute
<< ' ' << t.AMorPM << ".M. ("
<< t.milTime << " mil. time)";
}
void Advance(Time & t, unsigned hours, unsigned minutes)
{
// Advance using military time
t.milTime += 100 * hours + minutes;
unsigned milHours = t.milTime / 100,
milMins = t.milTime % 100;
// Adjust to proper format
milHours += milMins / 60;
milMins %= 60;
milHours %= 24;
t.milTime = 100 * milHours + milMins;
// Now set standard time
ToStandard(t.milTime, t.hour, t.minute, t.AMorPM);
}
bool LessThan(const Time & t1, const Time & t2)
{
return (t1.milTime < t2.milTime);
}

32

/***** UTILITY FUNCTIONS *****/
/* ToMilitary converts standard time to military time.
*
* Receive: hours, minutes, AMPM
* Return: The military time equivalent
******************************************************************/
int ToMilitary (unsigned hours, unsigned minutes, char AMPM)
{
if (hours == 12)
hours = 0;
return hours * 100 + minutes + (AMPM == 'P' ? 1200 : 0);
}
/* ToStandard converts military time to standard time.
*
* Receive: military, a time in military format
* Return: hours, minutes, AMPM -- equivalent standard time
*******************************************************************/
void ToStandard(unsigned military,
unsigned & hours, unsigned & minutes, char & AMPM)
{
hours = (military / 100) % 12;
if (hours == 0)
hours = 12;
minutes = military % 100;
AMPM = (military / 100) < 12 ? 'A' : 'P';
}

33

//========= Test driver =========
#include <iostream>
#include "Time.h"
uses namespace std;
int main()
{
Time mealTime,
goToWorkTime;
Set(mealTime, 5, 30, 'P');
cout << "We'll be eating at ";
Display(mealTime, cout);
cout << endl;
Set(goToWorkTime, 5, 30, 'P');
// Try other values also: 'A' -> 'P'
cout << "You leave for work at ";
Display(goToWorkTime, cout);
cout << endl;
if (LessThan(MealTime. goToWorkTime))
cout << "If you hurry, you can eat first.\n";
else
cout << "Sorry you can't eat first.\n";
Advance(goToWorkTime, 0, 30);
// Try other values also: 0 -> 12)
cout << "You go into work later at ";
Display(goToWorkTime, cout);
cout << endl;
if (LessThan(MealTime. goToWorkTime))
cout << "If you hurry, you can eat first.\n";
else
cout << "Sorry you can't eat with us.\n";
cout << endl;
}

Execution:
We'll be eating at 5:30 P.M. (1730 mil. time)
You leave for work at 5:30 P.M. (1730 mil. time)
Sorry you can't eat first.
You go into work later at 6:00 P.M. (1800 mil. time)
If you hurry, you can eat first.

34

7. Problems with C-Style Arrays
a. The capacity of a C-style array cannot change.
Solution 1 (non-OOP): Use run-time arrays.
— Construct B to have required capacity
— Copy elements of A into first part of B
— Deallocate A
Solution 2 (OOP): Use vectors which do this automatically.
b. There are virtually no predefined operations or functions on non-char arrays.
Basic reason for this disparity:
There is no numeric equivalent of the NUL character that can be used to mark the end
of a sequence of numbers.
Start
processing
here

name

Quit
processing
here

J

o

h

n

D

[0]

[1]

[2]

[3]

[4]

Start
processing
here

intArray

[5]

o

e

\0

\0

[6]

[7]

[8]

[9]

0

0

0

0

[6]

[7]

Quit
processing
where???

6

2

0

1

5

2

[0]

[1]

[2]

[3]

[4]

[5]

[8]

[9]

35

Solution 1 (non-OOP): In addition to the array, pass its size (and perhaps its
capacity) to functions.
Example: Function to output an array of doubles:
void Print(ostream & out, double theArray[], int itsSize)
{
for (int i = 0; i < itsSize; i++)
out << theArray[i] << endl;
}

Function call:

Print(cout, dubArray, dubArraySize);

Example: Function to input an array of doubles:
void Read(istream & in, double theArray[],
const int ITS_CAPACITY, int & itsSize)
{
itsSize = 0;
for (;;)
{
in >> theArray[itsSize];
if (in.eof()) break;
itsSize++;
if (itsSize >= ITS_CAPACITY) // prevent out-of-range error
{
cerr << "\nRead warning: array is full!\n";
return;
}
}
}

Function call:

int mySize;
Read(cin, dubArray, CAPACITY, mySize);

• The Deeper Problem.
One of the principles of object-oriented programming is that an object should be
autonomous (self-contained), which means that it should carry within itself all of the
information necessary to describe and operate upon itself.
C-style arrays violate this principle. In particular, they carry neither their size nor
their capacity within them, and so C-style arrays are not self-contained objects.
Solution 2 (OOP): Encapsulate all three pieces of information — the array, its capacity
and its size — within a class. This is the approach used by the vector<T> class
template.