cpphtp4_PPT_03.ppt

 2003 Prentice Hall, Inc. All rights reserved.
1
Chapter 3 - Functions
Outline
3.1 Introduction
3.2 Program Components in C++
3.3 Math Library Functions
3.4 Functions
3.5 Function Definitions
3.6 Function Prototypes
3.7 Header Files
3.8 Random Number Generation
3.9 Example: A Game of Chance and Introducing enum
3.10 Storage Classes
3.11 Scope Rules
3.12 Recursion
3.13 Example Using Recursion: The Fibonacci Series
3.14 Recursion vs. Iteration
3.15 Functions with Empty Parameter Lists

2
Chapter 3 - Functions
Outline
3.16 Inline Functions
3.17 References and Reference Parameters
3.18 Default Arguments
3.19 Unary Scope Resolution Operator
3.20 Function Overloading
3.21 Function Templates

3
3.1 Introduction
• Divide and conquer
– Construct a program from smaller pieces or components
– Each piece more manageable than the original program

4
• Modules: functions and classes
• Programs use new and “prepackaged” modules
– New: programmer-defined functions, classes
– Prepackaged: from the standard library
• Functions invoked by function call
– Function name and information (arguments) it needs
• Function definitions
– Only written once
– Hidden from other functions

5
• Boss to worker analogy
– A boss (the calling function or caller) asks a worker (the
called function) to perform a task and return (i.e., report
back) the results when the task is done.

6
• Perform common mathematical calculations
– Include the header file <cmath>
• Functions called by writing
– functionName (argument);
or
– functionName(argument1, argument2, …);
• Example
cout << sqrt( 900.0 );
– sqrt (square root) function The preceding statement would
print 30
– All functions in math library return a double

7
• Function arguments can be
– Constants
• sqrt( 4 );
– Variables
• sqrt( x );
– Expressions
• sqrt( sqrt( x ) ) ;
• sqrt( 3 - 6x );

8
Method Desc ription Example
ceil( x ) rounds x to the smallest integer
not less than x
ceil( 9.2 ) is 10.0
ceil( -9.8 ) is -9.0
cos( x ) trigonometric cosine of x
(x in radians)
cos( 0.0 ) is 1.0
exp( x ) exponential function ex exp( 1.0 ) is 2.71828
exp( 2.0 ) is 7.38906
fabs( x ) absolute value of x fabs( 5.1 ) is 5.1
fabs( 0.0 ) is 0.0
fabs( -8.76 ) is 8.76
floor( x ) rounds x to the largest integer
not greater than x
floor( 9.2 ) is 9.0
floor( -9.8 ) is -10.0
fmod( x, y ) remainder of x/y as a floating-
point number
fmod( 13.657, 2.333 ) is 1.992
log( x ) natural logarithm of x (base e) log( 2.718282 ) is 1.0
log( 7.389056 ) is 2.0
log10( x ) logarithm of x (base 10) log10( 10.0 ) is 1.0
log10( 100.0 ) is 2.0
pow( x, y ) x raised to power y (xy) pow( 2, 7 ) is 128
pow( 9, .5 ) is 3
sin( x ) trigonometric sine of x
(x in radians)
sin( 0.0 ) is 0
sqrt( x ) square root of x sqrt( 900.0 ) is 30.0
sqrt( 9.0 ) is 3.0
tan( x ) trigonometric tangent of x
(x in radians)
tan( 0.0 ) is 0
Fig. 3.2 Math library func tions.

9
3.4 Functions
• Functions
– Modularize a program
– Software reusability
• Call function multiple times
• Local variables
– Known only in the function in which they are defined
– All variables declared in function definitions are local
variables
• Parameters
– Local variables passed to function when called
– Provide outside information

10
• Function prototype
– Tells compiler argument type and return type of function
– int square( int );
• Function takes an int and returns an int
– Explained in more detail later
• Calling/invoking a function
– square(x);
– Parentheses an operator used to call function
• Pass argument x
• Function gets its own copy of arguments
– After finished, passes back result

11
• Format for function definition
return-value-type function-name( parameter-list )
{
declarations and statements
}
– Parameter list
• Comma separated list of arguments
– Data type needed for each argument
• If no arguments, use void or leave blank
– Return-value-type
• Data type of result returned (use void if nothing returned)

12
• Example function
int square( int y )
{
return y * y;
}
• return keyword
– Returns data, and control goes to function’s caller
• If no data to return, use return;
– Function ends when reaches right brace
• Control goes to caller
• Functions cannot be defined inside other functions
• Next: program examples

 2003 Prentice Hall, Inc.
All rights reserved.
Outline
13
fig03_03.cpp
(1 of 2)
1 // Fig. 3.3: fig03_03.cpp
2 // Creating and using a programmer-defined function.
3 #include <iostream>
4
5 using std::cout;
6 using std::endl;
7
8 int square( int ); // function prototype
9
10 int main()
11 {
12 // loop 10 times and calculate and output
13 // square of x each time
14 for ( int x = 1; x <= 10; x++ )
15 cout << square( x ) << " "; // function call
16
17 cout << endl;
18
19 return 0; // indicates successful termination
20
21 } // end main
22
Parentheses () cause
function to be called. When
done, it returns the result.
Function prototype: specifies
data types of arguments and
return values. square
expects and int, and returns
an int.

Outline
14
fig03_03.cpp
(2 of 2)
fig03_03.cpp
output (1 of 1)
23 // square function definition returns square of an integer
24 int square( int y ) // y is a copy of argument to function
25 {
26 return y * y; // returns square of y as an int
27
28 } // end function square
1 4 9 16 25 36 49 64 81 100
Definition of square. y is a
copy of the argument passed.
Returns y * y, or y squared.

Outline
15
fig03_04.cpp
(1 of 2)
1 // Fig. 3.4: fig03_04.cpp
2 // Finding the maximum of three floating-point numbers.
4
5 using std::cout;
6 using std::cin;
7 using std::endl;
8
9 double maximum( double, double, double ); // function prototype
10
11 int main()
12 {
13 double number1;
14 double number2;
15 double number3;
16
17 cout << "Enter three floating-point numbers: ";
18 cin >> number1 >> number2 >> number3;
19
20 // number1, number2 and number3 are arguments to
21 // the maximum function call
22 cout << "Maximum is: "
23 << maximum( number1, number2, number3 ) << endl;
24
Function maximum takes 3
arguments (all double) and
returns a double.

Outline
16
fig03_04.cpp
(2 of 2)
fig03_04.cpp
output (1 of 1)
26
27 } // end main
28
29 // function maximum definition;
30 // x, y and z are parameters
31 double maximum( double x, double y, double z )
32 {
33 double max = x; // assume x is largest
34
35 if ( y > max ) // if y is larger,
36 max = y; // assign y to max
37
38 if ( z > max ) // if z is larger,
39 max = z; // assign z to max
40
41 return max; // max is largest value
42
43 } // end function maximum
Enter three floating-point numbers: 99.32 37.3 27.1928
Maximum is: 99.32
Maximum is: 3.333
Maximum is: 88.99
Comma separated list for
multiple parameters.

17
• Function prototype contains
– Function name
– Parameters (number and data type)
– Return type (void if returns nothing)
– Only needed if function definition after function call
• Prototype must match function definition
– Function prototype
double maximum( double, double, double );
– Definition
double maximum( double x, double y, double z )
{
…
}

18
• Function signature
– Part of prototype with name and parameters
• double maximum( double, double, double );
• Argument Coercion
– Force arguments to be of proper type
• Converting int (4) to double (4.0)
cout << sqrt(4)
– Conversion rules
• Arguments usually converted automatically
• Changing from double to int can truncate data
– 3.4 to 3
– Mixed type goes to highest type (promotion)
• Int * double
Function signature

19
Data types
long double
double
float
unsigned long int (synonymous with unsigned long)
long int (synonymous with long)
unsigned int (synonymous with unsigned)
int
unsigned short int (synonymous with unsigned short)
short int (synonymous with short)
unsigned char
char
bool (false becomes 0, true becomes 1)
Fig. 3.5 Promotion hierarc hy for built-in data types.

20
3.7 Header Files
• Header files contain
– Function prototypes
– Definitions of data types and constants
• Header files ending with .h
– Programmer-defined header files
#include “myheader.h”
• Library header files
#include <cmath>

21
• rand function (<cstdlib>)
– i = rand();
– Generates unsigned integer between 0 and RAND_MAX
(usually 32767)
• Scaling and shifting
– Modulus (remainder) operator: %
• 10 % 3 is 1
• x % y is between 0 and y – 1
– Example
i = rand() % 6 + 1;
• “Rand() % 6” generates a number between 0 and 5 (scaling)
• “+ 1” makes the range 1 to 6 (shift)
– Next: program to roll dice

Outline
22
fig03_07.cpp
(1 of 2)
1 // Fig. 3.7: fig03_07.cpp
2 // Shifted, scaled integers produced by 1 + rand() % 6.
4
5 using std::cout;
6 using std::endl;
7
8 #include <iomanip>
9
10 using std::setw;
11
12 #include <cstdlib> // contains function prototype for rand
13
14 int main()
15 {
16 // loop 20 times
17 for ( int counter = 1; counter <= 20; counter++ ) {
18
19 // pick random number from 1 to 6 and output it
20 cout << setw( 10 ) << ( 1 + rand() % 6 );
21
22 // if counter divisible by 5, begin new line of output
23 if ( counter % 5 == 0 )
24 cout << endl;
25
26 } // end for structure
Output of rand() scaled and
shifted to be a number
between 1 and 6.

Outline
23
fig03_07.cpp
(2 of 2)
fig03_07.cpp
output (1 of 1)
27
29
30 } // end main
6 6 5 5 6
5 1 1 5 3
6 6 2 4 2
6 2 3 4 1

24
• Next
– Program to show distribution of rand()
– Simulate 6000 rolls of a die
– Print number of 1’s, 2’s, 3’s, etc. rolled
– Should be roughly 1000 of each

Outline
25
fig03_08.cpp
(1 of 3)
1 // Fig. 3.8: fig03_08.cpp
2 // Roll a six-sided die 6000 times.
4
5 using std::cout;
6 using std::endl;
7
9
10 using std::setw;
11
12 #include <cstdlib> // contains function prototype for rand
13
14 int main()
15 {
16 int frequency1 = 0;
22 int face; // represents one roll of the die
23

Outline
26
fig03_08.cpp
(2 of 3)
24 // loop 6000 times and summarize results
25 for ( int roll = 1; roll <= 6000; roll++ ) {
26 face = 1 + rand() % 6; // random number from 1 to 6
27
28 // determine face value and increment appropriate counter
29 switch ( face ) {
30
31 case 1: // rolled 1
32 ++frequency1;
33 break;
34
36 ++frequency2;
37 break;
38
40 ++frequency3;
41 break;
42
44 ++frequency4;
45 break;
46
48 ++frequency5;
49 break;

Outline
27
fig03_08.cpp
(3 of 3)
50
52 ++frequency6;
53 break;
54
55 default: // invalid value
56 cout << "Program should never get here!";
57
58 } // end switch
59
60 } // end for
61
62 // display results in tabular format
63 cout << "Face" << setw( 13 ) << "Frequency"
64 << "n 1" << setw( 13 ) << frequency1
65 << "n 2" << setw( 13 ) << frequency2
66 << "n 3" << setw( 13 ) << frequency3
67 << "n 4" << setw( 13 ) << frequency4
68 << "n 5" << setw( 13 ) << frequency5
69 << "n 6" << setw( 13 ) << frequency6 << endl;
70
72
73 } // end main
Default case included even
though it should never be
reached. This is a matter of
good coding style

Outline
28
fig03_08.cpp
output (1 of 1)
Face Frequency
1 1003
2 1017
3 983
4 994
5 1004
6 999

29
• Calling rand() repeatedly
– Gives the same sequence of numbers
• Pseudorandom numbers
– Preset sequence of "random" numbers
– Same sequence generated whenever program run
• To get different random sequences
– Provide a seed value
• Like a random starting point in the sequence
• The same seed will give the same sequence
– srand(seed);
• <cstdlib>
• Used before rand() to set the seed

Outline
30
fig03_09.cpp
(1 of 2)
1 // Fig. 3.9: fig03_09.cpp
2 // Randomizing die-rolling program.
4
5 using std::cout;
6 using std::cin;
7 using std::endl;
8
10
11 using std::setw;
12
13 // contains prototypes for functions srand and rand
14 #include <cstdlib>
15
16 // main function begins program execution
17 int main()
18 {
19 unsigned seed;
20
21 cout << "Enter seed: ";
22 cin >> seed;
23 srand( seed ); // seed random number generator
24
Setting the seed with
srand().

Outline
31
fig03_09.cpp
(2 of 2)
fig03_09.cpp
output (1 of 1)
25 // loop 10 times
26 for ( int counter = 1; counter <= 10; counter++ ) {
27
28 // pick random number from 1 to 6 and output it
29 cout << setw( 10 ) << ( 1 + rand() % 6 );
30
31 // if counter divisible by 5, begin new line of output
32 if ( counter % 5 == 0 )
33 cout << endl;
34
35 } // end for
36
38
39 } // end main
Enter seed: 67
6 1 4 6 2
1 6 1 6 4
Enter seed: 432
4 6 3 1 6
3 1 5 4 2
Enter seed: 67
6 1 4 6 2
1 6 1 6 4
rand() gives the same
sequence if it has the same
initial seed.

32
• Can use the current time to set the seed
– No need to explicitly set seed every time
– srand( time( 0 ) );
– time( 0 );
• <ctime>
• Returns current time in seconds
• General shifting and scaling
– Number = shiftingValue + rand() % scalingFactor
– shiftingValue = first number in desired range
– scalingFactor = width of desired range

33
3.9 Example: Game of Chance and
Introducing enum
• Enumeration
– Set of integers with identifiers
enum typeName {constant1, constant2…};
– Constants start at 0 (default), incremented by 1
– Constants need unique names
– Cannot assign integer to enumeration variable
• Must use a previously defined enumeration type
• Example
enum Status {CONTINUE, WON, LOST};
Status enumVar;
enumVar = WON; // cannot do enumVar = 1

34
3.9 Example: Game of Chance and
Introducing enum
• Enumeration constants can have preset values
enum Months { JAN = 1, FEB, MAR, APR, MAY,
JUN, JUL, AUG, SEP, OCT, NOV, DEC};
– Starts at 1, increments by 1
• Next: craps simulator
– Roll two dice
– 7 or 11 on first throw: player wins
– 2, 3, or 12 on first throw: player loses
– 4, 5, 6, 8, 9, 10
• Value becomes player's "point"
• Player must roll his point before rolling 7 to win

Outline
35
fig03_10.cpp
(1 of 5)
1 // Fig. 3.10: fig03_10.cpp
2 // Craps.
4
5 using std::cout;
6 using std::endl;
7
8 // contains function prototypes for functions srand and rand
9 #include <cstdlib>
10
11 #include <ctime> // contains prototype for function time
12
13 int rollDice( void ); // function prototype
14
15 int main()
16 {
17 // enumeration constants represent game status
18 enum Status { CONTINUE, WON, LOST };
19
20 int sum;
21 int myPoint;
22
23 Status gameStatus; // can contain CONTINUE, WON or LOST
24
Function to roll 2 dice and
return the result as an int.
Enumeration to keep track of
the current game.

Outline
36
fig03_10.cpp
(2 of 5)
25 // randomize random number generator using current time
26 srand( time( 0 ) );
27
28 sum = rollDice(); // first roll of the dice
29
30 // determine game status and point based on sum of dice
31 switch ( sum ) {
32
33 // win on first roll
34 case 7:
35 case 11:
36 gameStatus = WON;
37 break;
38
39 // lose on first roll
40 case 2:
41 case 3:
42 case 12:
43 gameStatus = LOST;
44 break;
45
switch statement
determines outcome based on
die roll.

Outline
37
fig03_10.cpp
(3 of 5)
46 // remember point
47 default:
48 gameStatus = CONTINUE;
49 myPoint = sum;
50 cout << "Point is " << myPoint << endl;
51 break; // optional
52
53 } // end switch
54
55 // while game not complete ...
56 while ( gameStatus == CONTINUE ) {
57 sum = rollDice(); // roll dice again
58
59 // determine game status
60 if ( sum == myPoint ) // win by making point
61 gameStatus = WON;
62 else
63 if ( sum == 7 ) // lose by rolling 7
64 gameStatus = LOST;
65
66 } // end while
67

Outline
38
fig03_10.cpp
(4 of 5)
68 // display won or lost message
69 if ( gameStatus == WON )
70 cout << "Player wins" << endl;
71 else
72 cout << "Player loses" << endl;
73
75
76 } // end main
77
78 // roll dice, calculate sum and display results
79 int rollDice( void )
80 {
81 int die1;
82 int die2;
83 int workSum;
84
85 die1 = 1 + rand() % 6; // pick random die1 value
86 die2 = 1 + rand() % 6; // pick random die2 value
87 workSum = die1 + die2; // sum die1 and die2
88
Function rollDice takes no
arguments, so has void in
the parameter list.

Outline
39
fig03_10.cpp
(5 of 5)
fig03_10.cpp
output (1 of 2)
89 // display results of this roll
90 cout << "Player rolled " << die1 << " + " << die2
91 << " = " << workSum << endl;
92
93 return workSum; // return sum of dice
94
95 } // end function rollDice
Player rolled 2 + 5 = 7
Player wins
Player loses
Point is 6
Player wins

Outline
40
fig03_10.cpp
output (2 of 2)
Point is 4
Player loses

41
• Variables have attributes
– Have seen name, type, size, value
– Storage class
• How long variable exists in memory
– Scope
• Where variable can be referenced in program
– Linkage
• For multiple-file program (see Ch. 6), which files can use it

42
• Automatic storage class
– Variable created when program enters its block
– Variable destroyed when program leaves block
– Only local variables of functions can be automatic
• Automatic by default
• keyword auto explicitly declares automatic
– register keyword
• Hint to place variable in high-speed register
• Good for often-used items (loop counters)
• Often unnecessary, compiler optimizes
– Specify either register or auto, not both
• register int counter = 1;

43
• Static storage class
– Variables exist for entire program
• For functions, name exists for entire program
– May not be accessible, scope rules still apply (more later)
• static keyword
– Local variables in function
– Keeps value between function calls
– Only known in own function
• extern keyword
– Default for global variables/functions
• Globals: defined outside of a function block
– Known in any function that comes after it

44
3.11 Scope Rules
• Scope
– Portion of program where identifier can be used
• File scope
– Defined outside a function, known in all functions
– Global variables, function definitions and prototypes
• Function scope
– Can only be referenced inside defining function
– Only labels, e.g., identifiers with a colon (case:)

45
3.11 Scope Rules
• Block scope
– Begins at declaration, ends at right brace }
• Can only be referenced in this range
– Local variables, function parameters
– static variables still have block scope
• Storage class separate from scope
• Function-prototype scope
– Parameter list of prototype
– Names in prototype optional
• Compiler ignores
– In a single prototype, name can be used once

Outline
46
fig03_12.cpp
(1 of 5)
1 // Fig. 3.12: fig03_12.cpp
2 // A scoping example.
4
5 using std::cout;
6 using std::endl;
7
8 void useLocal( void ); // function prototype
9 void useStaticLocal( void ); // function prototype
10 void useGlobal( void ); // function prototype
11
12 int x = 1; // global variable
13
14 int main()
15 {
16 int x = 5; // local variable to main
17
18 cout << "local x in main's outer scope is " << x << endl;
19
20 { // start new scope
21
22 int x = 7;
23
24 cout << "local x in main's inner scope is " << x << endl;
25
26 } // end new scope
Declared outside of function;
global variable with file
scope.
Local variable with function
scope.
Create a new block, giving x
block scope. When the block
ends, this x is destroyed.

Outline
47
fig03_12.cpp
(2 of 5)
27
28 cout << "local x in main's outer scope is " << x << endl;
29
30 useLocal(); // useLocal has local x
31 useStaticLocal(); // useStaticLocal has static local x
32 useGlobal(); // useGlobal uses global x
33 useLocal(); // useLocal reinitializes its local x
34 useStaticLocal(); // static local x retains its prior value
35 useGlobal(); // global x also retains its value
36
37 cout << "nlocal x in main is " << x << endl;
38
40
41 } // end main
42

Outline
48
fig03_12.cpp
(3 of 5)
43 // useLocal reinitializes local variable x during each call
44 void useLocal( void )
45 {
46 int x = 25; // initialized each time useLocal is called
47
48 cout << endl << "local x is " << x
49 << " on entering useLocal" << endl;
50 ++x;
51 cout << "local x is " << x
52 << " on exiting useLocal" << endl;
53
54 } // end function useLocal
55
Automatic variable (local
variable of function). This is
destroyed when the function
exits, and reinitialized when
the function begins.

Outline
49
fig03_12.cpp
(4 of 5)
56 // useStaticLocal initializes static local variable x only the
57 // first time the function is called; value of x is saved
58 // between calls to this function
59 void useStaticLocal( void )
60 {
61 // initialized only first time useStaticLocal is called
62 static int x = 50;
63
64 cout << endl << "local static x is " << x
65 << " on entering useStaticLocal" << endl;
66 ++x;
67 cout << "local static x is " << x
68 << " on exiting useStaticLocal" << endl;
69
70 } // end function useStaticLocal
71
Static local variable of
function; it is initialized only
once, and retains its value
between function calls.

Outline
50
fig03_12.cpp
(5 of 5)
fig03_12.cpp
output (1 of 2)
72 // useGlobal modifies global variable x during each call
73 void useGlobal( void )
74 {
75 cout << endl << "global x is " << x
76 << " on entering useGlobal" << endl;
77 x *= 10;
78 cout << "global x is " << x
79 << " on exiting useGlobal" << endl;
80
81 } // end function useGlobal
local x in main's outer scope is 5
local x in main's inner scope is 7
local x in main's outer scope is 5
local x is 25 on entering useLocal
local x is 26 on exiting useLocal
local static x is 50 on entering useStaticLocal
local static x is 51 on exiting useStaticLocal
global x is 1 on entering useGlobal
global x is 10 on exiting useGlobal
This function does not declare
any variables. It uses the
global x declared in the
beginning of the program.

Outline
51
fig03_12.cpp
output (2 of 2)
local x is 25 on entering useLocal
local x is 26 on exiting useLocal
local static x is 51 on entering useStaticLocal
local static x is 52 on exiting useStaticLocal
global x is 10 on entering useGlobal
global x is 100 on exiting useGlobal
local x in main is 5

52
3.12 Recursion
• Recursive functions
– Functions that call themselves
– Can only solve a base case
• If not base case
– Break problem into smaller problem(s)
– Launch new copy of function to work on the smaller
problem (recursive call/recursive step)
• Slowly converges towards base case
• Function makes call to itself inside the return statement
– Eventually base case gets solved
• Answer works way back up, solves entire problem

53
3.12 Recursion
• Example: factorial
n! = n * ( n – 1 ) * ( n – 2 ) * … * 1
– Recursive relationship ( n! = n * ( n – 1 )! )
5! = 5 * 4!
4! = 4 * 3!…
– Base case (1! = 0! = 1)

Outline
54
fig03_14.cpp
(1 of 2)
1 // Fig. 3.14: fig03_14.cpp
2 // Recursive factorial function.
4
5 using std::cout;
6 using std::endl;
7
9
10 using std::setw;
11
12 unsigned long factorial( unsigned long ); // function prototype
13
14 int main()
15 {
16 // Loop 10 times. During each iteration, calculate
17 // factorial( i ) and display result.
18 for ( int i = 0; i <= 10; i++ )
19 cout << setw( 2 ) << i << "! = "
20 << factorial( i ) << endl;
21
23
24 } // end main
Data type unsigned long
can hold an integer from 0 to
4 billion.

Outline
55
fig03_14.cpp
(2 of 2)
fig03_14.cpp
output (1 of 1)
25
26 // recursive definition of function factorial
27 unsigned long factorial( unsigned long number )
28 {
29 // base case
30 if ( number <= 1 )
31 return 1;
32
33 // recursive step
34 else
35 return number * factorial( number - 1 );
36
37 } // end function factorial
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10! = 3628800
The base case occurs when
we have 0! or 1!. All other
cases must be split up
(recursive step).

56
3.13 Example Using Recursion: Fibonacci
Series
• Fibonacci series: 0, 1, 1, 2, 3, 5, 8...
– Each number sum of two previous ones
– Example of a recursive formula:
• fib(n) = fib(n-1) + fib(n-2)
• C++ code for Fibonacci function
long fibonacci( long n )
{
if ( n == 0 || n == 1 ) // base case
return n;
else
return fibonacci( n - 1 ) +
fibonacci( n – 2 );
}

57
Series
f( 3 )
f( 1 )
f( 2 )
f( 1 ) f( 0 ) return 1
return 1 return 0
return +
+
return

58
Series
• Order of operations
– return fibonacci( n - 1 ) + fibonacci( n - 2 );
• Do not know which one executed first
– C++ does not specify
– Only &&, || and ?: guaranteed left-to-right evaluation
• Recursive function calls
– Each level of recursion doubles the number of function calls
• 30th number = 2^30 ~ 4 billion function calls
– Exponential complexity

Outline
59
fig03_15.cpp
(1 of 2)
1 // Fig. 3.15: fig03_15.cpp
2 // Recursive fibonacci function.
4
5 using std::cout;
6 using std::cin;
7 using std::endl;
8
9 unsigned long fibonacci( unsigned long ); // function prototype
10
11 int main()
12 {
13 unsigned long result, number;
14
15 // obtain integer from user
16 cout << "Enter an integer: ";
17 cin >> number;
18
19 // calculate fibonacci value for number input by user
20 result = fibonacci( number );
21
22 // display result
23 cout << "Fibonacci(" << number << ") = " << result << endl;
24
The Fibonacci numbers get
large very quickly, and are all
non-negative integers. Thus,
we use the unsigned
long data type.

Outline
60
fig03_15.cpp
(2 of 2)
fig03_15.cpp
output (1 of 2)
26
27 } // end main
28
29 // recursive definition of function fibonacci
30 unsigned long fibonacci( unsigned long n )
31 {
32 // base case
33 if ( n == 0 || n == 1 )
34 return n;
35
36 // recursive step
37 else
38 return fibonacci( n - 1 ) + fibonacci( n - 2 );
39
40 } // end function fibonacci
Enter an integer: 0
Fibonacci(0) = 0
Enter an integer: 1
Fibonacci(1) = 1
Enter an integer: 2
Fibonacci(2) = 1
Enter an integer: 3
Fibonacci(3) = 2

Outline
61
fig03_15.cpp
output (2 of 2)
Enter an integer: 4
Fibonacci(4) = 3
Enter an integer: 5
Fibonacci(5) = 5
Enter an integer: 6
Fibonacci(6) = 8
Enter an integer: 10
Fibonacci(10) = 55
Fibonacci(20) = 6765
Fibonacci(30) = 832040
Fibonacci(35) = 9227465

62
3.14 Recursion vs. Iteration
• Repetition
– Iteration: explicit loop
– Recursion: repeated function calls
• Termination
– Iteration: loop condition fails
– Recursion: base case recognized
• Both can have infinite loops
• Balance between performance (iteration) and good
software engineering (recursion)

63
3.15 Functions with Empty Parameter Lists
• Empty parameter lists
– void or leave parameter list empty
– Indicates function takes no arguments
– Function print takes no arguments and returns no value
• void print();
• void print( void );

Outline
64
fig03_18.cpp
(1 of 2)
1 // Fig. 3.18: fig03_18.cpp
2 // Functions that take no arguments.
4
5 using std::cout;
6 using std::endl;
7
8 void function1(); // function prototype
9 void function2( void ); // function prototype
10
11 int main()
12 {
13 function1(); // call function1 with no arguments
14 function2(); // call function2 with no arguments
15
17
18 } // end main
19

Outline
65
fig03_18.cpp
(2 of 2)
fig03_18.cpp
output (1 of 1)
20 // function1 uses an empty parameter list to specify that
21 // the function receives no arguments
22 void function1()
23 {
24 cout << "function1 takes no arguments" << endl;
25
26 } // end function1
27
28 // function2 uses a void parameter list to specify that
29 // the function receives no arguments
30 void function2( void )
31 {
32 cout << "function2 also takes no arguments" << endl;
33
34 } // end function2
function1 takes no arguments
function2 also takes no arguments

66
3.16 Inline Functions
• Inline functions
– Keyword inline before function
– Asks the compiler to copy code into program instead of
making function call
• Reduce function-call overhead
• Compiler can ignore inline
– Good for small, often-used functions
• Example
inline double cube( const double s )
{ return s * s * s; }
– const tells compiler that function does not modify s
• Discussed in chapters 6-7

Outline
67
fig03_19.cpp
(1 of 2)
1 // Fig. 3.19: fig03_19.cpp
2 // Using an inline function to calculate.
3 // the volume of a cube.
5
6 using std::cout;
7 using std::cin;
8 using std::endl;
9
10 // Definition of inline function cube. Definition of function
11 // appears before function is called, so a function prototype
12 // is not required. First line of function definition acts as
13 // the prototype.
14 inline double cube( const double side )
15 {
16 return side * side * side; // calculate cube
17
18 } // end function cube
19

Outline
68
fig03_19.cpp
(2 of 2)
fig03_19.cpp
output (1 of 1)
20 int main()
21 {
22 cout << "Enter the side length of your cube: ";
23
24 double sideValue;
25
26 cin >> sideValue;
27
28 // calculate cube of sideValue and display result
29 cout << "Volume of cube with side "
30 << sideValue << " is " << cube( sideValue ) << endl;
31
33
34 } // end main
Enter the side length of your cube: 3.5
Volume of cube with side 3.5 is 42.875

69
• Call by value
– Copy of data passed to function
– Changes to copy do not change original
– Prevent unwanted side effects
• Call by reference
– Function can directly access data
– Changes affect original

70
• Reference parameter
– Alias for argument in function call
• Passes parameter by reference
– Use & after data type in prototype
• void myFunction( int &data )
• Read “data is a reference to an int”
– Function call format the same
• However, original can now be changed

Outline
71
fig03_20.cpp
(1 of 2)
1 // Fig. 3.20: fig03_20.cpp
2 // Comparing pass-by-value and pass-by-reference
3 // with references.
5
6 using std::cout;
7 using std::endl;
8
9 int squareByValue( int ); // function prototype
10 void squareByReference( int & ); // function prototype
11
12 int main()
13 {
14 int x = 2;
15 int z = 4;
16
17 // demonstrate squareByValue
18 cout << "x = " << x << " before squareByValuen";
19 cout << "Value returned by squareByValue: "
20 << squareByValue( x ) << endl;
21 cout << "x = " << x << " after squareByValuen" << endl;
22
Notice the & operator,
indicating pass-by-reference.

Outline
72
fig03_20.cpp
(2 of 2)
23 // demonstrate squareByReference
24 cout << "z = " << z << " before squareByReference" << endl;
25 squareByReference( z );
26 cout << "z = " << z << " after squareByReference" << endl;
27
29 } // end main
30
31 // squareByValue multiplies number by itself, stores the
32 // result in number and returns the new value of number
33 int squareByValue( int number )
34 {
35 return number *= number; // caller's argument not modified
36
37 } // end function squareByValue
38
39 // squareByReference multiplies numberRef by itself and
40 // stores the result in the variable to which numberRef
41 // refers in function main
42 void squareByReference( int &numberRef )
43 {
44 numberRef *= numberRef; // caller's argument modified
45
46 } // end function squareByReference
Changes number, but
original parameter (x) is not
modified.
Changes numberRef, an
alias for the original
parameter. Thus, z is
changed.

Outline
73
fig03_20.cpp
output (1 of 1)
x = 2 before squareByValue
Value returned by squareByValue: 4
x = 2 after squareByValue
z = 4 before squareByReference
z = 16 after squareByReference

74
• Pointers (chapter 5)
– Another way to pass-by-refernce
• References as aliases to other variables
– Refer to same variable
– Can be used within a function
int count = 1; // declare integer variable count
Int &cRef = count; // create cRef as an alias for count
++cRef; // increment count (using its alias)
• References must be initialized when declared
– Otherwise, compiler error
– Dangling reference
• Reference to undefined variable

Outline
75
fig03_21.cpp
(1 of 1)
fig03_21.cpp
output (1 of 1)
1 // Fig. 3.21: fig03_21.cpp
2 // References must be initialized.
4
5 using std::cout;
6 using std::endl;
7
8 int main()
9 {
10 int x = 3;
11
12 // y refers to (is an alias for) x
13 int &y = x;
14
15 cout << "x = " << x << endl << "y = " << y << endl;
16 y = 7;
18
20
21 } // end main
x = 3
y = 3
x = 7
y = 7
y declared as a reference to x.

Outline
76
fig03_22.cpp
(1 of 1)
fig03_22.cpp
output (1 of 1)
1 // Fig. 3.22: fig03_22.cpp
2 // References must be initialized.
4
5 using std::cout;
6 using std::endl;
7
8 int main()
9 {
10 int x = 3;
11 int &y; // Error: y must be initialized
12
14 y = 7;
16
18
19 } // end main
Borland C++ command-line compiler error message:
Error E2304 Fig03_22.cpp 11: Reference variable 'y' must be
initialized in function main()
Microsoft Visual C++ compiler error message:
D:cpphtp4_examplesch03Fig03_22.cpp(11) : error C2530: 'y' :
references must be initialized
Uninitialized reference –
compiler error.

77
3.18 Default Arguments
• Function call with omitted parameters
– If not enough parameters, rightmost go to their defaults
– Default values
• Can be constants, global variables, or function calls
• Set defaults in function prototype
int myFunction( int x = 1, int y = 2, int z = 3 );
– myFunction(3)
• x = 3, y and z get defaults (rightmost)
– myFunction(3, 5)
• x = 3, y = 5 and z gets default

Outline
78
fig03_23.cpp
(1 of 2)
1 // Fig. 3.23: fig03_23.cpp
2 // Using default arguments.
4
5 using std::cout;
6 using std::endl;
7
8 // function prototype that specifies default arguments
9 int boxVolume( int length = 1, int width = 1, int height = 1 );
10
11 int main()
12 {
13 // no arguments--use default values for all dimensions
14 cout << "The default box volume is: " << boxVolume();
15
16 // specify length; default width and height
17 cout << "nnThe volume of a box with length 10,n"
18 << "width 1 and height 1 is: " << boxVolume( 10 );
19
20 // specify length and width; default height
22 << "width 5 and height 1 is: " << boxVolume( 10, 5 );
23
Set defaults in function
prototype.
Function calls with some
parameters missing – the
rightmost parameters get their
defaults.

Outline
79
fig03_23.cpp
(2 of 2)
fig03_23.cpp
output (1 of 1)
24 // specify all arguments
26 << "width 5 and height 2 is: " << boxVolume( 10, 5, 2 )
27 << endl;
28
30
31 } // end main
32
33 // function boxVolume calculates the volume of a box
34 int boxVolume( int length, int width, int height )
35 {
36 return length * width * height;
37
38 } // end function boxVolume
The default box volume is: 1
The volume of a box with length 10,
width 1 and height 1 is: 10

80
3.19 Unitary Scope Resolution Operator
• Unary scope resolution operator (::)
– Access global variable if local variable has same name
– Not needed if names are different
– Use ::variable
• y = ::x + 3;
– Good to avoid using same names for locals and globals

Outline
81
fig03_24.cpp
(1 of 2)
1 // Fig. 3.24: fig03_24.cpp
2 // Using the unary scope resolution operator.
4
5 using std::cout;
6 using std::endl;
7
9
10 using std::setprecision;
11
12 // define global constant PI
13 const double PI = 3.14159265358979;
14
15 int main()
16 {
17 // define local constant PI
18 const float PI = static_cast< float >( ::PI );
19
20 // display values of local and global PI constants
21 cout << setprecision( 20 )
22 << " Local float value of PI = " << PI
23 << "nGlobal double value of PI = " << ::PI << endl;
24
Access the global PI with
::PI.
Cast the global PI to a
float for the local PI. This
example will show the
difference between float
and double.

Outline
82
fig03_24.cpp
(2 of 2)
fig03_24.cpp
output (1 of 1)
26
27 } // end main
Borland C++ command-line compiler output:
Local float value of PI = 3.141592741012573242
Global double value of PI = 3.141592653589790007
Microsoft Visual C++ compiler output:
Local float value of PI = 3.1415927410125732
Global double value of PI = 3.14159265358979

83
3.20 Function Overloading
• Function overloading
– Functions with same name and different parameters
– Should perform similar tasks
• I.e., function to square ints and function to square floats
int square( int x) {return x * x;}
float square(float x) { return x * x; }
• Overloaded functions distinguished by signature
– Based on name and parameter types (order matters)
– Name mangling
• Encodes function identifier with parameters
– Type-safe linkage
• Ensures proper overloaded function called

Outline
84
fig03_25.cpp
(1 of 2)
1 // Fig. 3.25: fig03_25.cpp
2 // Using overloaded functions.
4
5 using std::cout;
6 using std::endl;
7
8 // function square for int values
9 int square( int x )
10 {
11 cout << "Called square with int argument: " << x << endl;
12 return x * x;
13
14 } // end int version of function square
15
16 // function square for double values
17 double square( double y )
18 {
19 cout << "Called square with double argument: " << y << endl;
20 return y * y;
21
22 } // end double version of function square
23
Overloaded functions have
the same name, but the
different parameters
distinguish them.

Outline
85
fig03_25.cpp
(2 of 2)
fig03_25.cpp
output (1 of 1)
24 int main()
25 {
26 int intResult = square( 7 ); // calls int version
27 double doubleResult = square( 7.5 ); // calls double version
28
29 cout << "nThe square of integer 7 is " << intResult
30 << "nThe square of double 7.5 is " << doubleResult
31 << endl;
32
34
35 } // end main
Called square with int argument: 7
Called square with double argument: 7.5
The square of integer 7 is 49
The square of double 7.5 is 56.25
The proper function is called
based upon the argument
(int or double).

Outline
86
fig03_26.cpp
(1 of 2)
1 // Fig. 3.26: fig03_26.cpp
2 // Name mangling.
3
4 // function square for int values
5 int square( int x )
6 {
7 return x * x;
8 }
9
10 // function square for double values
11 double square( double y )
12 {
13 return y * y;
14 }
15
16 // function that receives arguments of types
17 // int, float, char and int *
18 void nothing1( int a, float b, char c, int *d )
19 {
20 // empty function body
21 }
22

Outline
87
fig03_26.cpp
(2 of 2)
fig03_26.cpp
output (1 of 1)
23 // function that receives arguments of types
24 // char, int, float * and double *
25 char *nothing2( char a, int b, float *c, double *d )
26 {
27 return 0;
28 }
29
30 int main()
31 {
33
34 } // end main
_main
@nothing2$qcipfpd
@nothing1$qifcpi
@square$qd
@square$qi
Mangled names produced in
assembly language.
$q separates the function
name from its parameters. c
is char, d is double, i is
int, pf is a pointer to a
float, etc.

88
• Compact way to make overloaded functions
– Generate separate function for different data types
• Format
– Begin with keyword template
– Formal type parameters in brackets <>
• Every type parameter preceded by typename or class
(synonyms)
• Placeholders for built-in types (i.e., int) or user-defined types
• Specify arguments types, return types, declare variables
– Function definition like normal, except formal types used

89
• Example
template < class T > // or template< typename T >
T square( T value1 )
{
return value1 * value1;
}
– T is a formal type, used as parameter type
• Above function returns variable of same type as parameter
– In function call, T replaced by real type
• If int, all T's become ints
int x;
int y = square(x);

Outline
90
fig03_27.cpp
(1 of 3)
1 // Fig. 3.27: fig03_27.cpp
2 // Using a function template.
4
5 using std::cout;
6 using std::cin;
7 using std::endl;
8
9 // definition of function template maximum
10 template < class T > // or template < typename T >
11 T maximum( T value1, T value2, T value3 )
12 {
13 T max = value1;
14
15 if ( value2 > max )
16 max = value2;
17
18 if ( value3 > max )
19 max = value3;
20
21 return max;
22
23 } // end function template maximum
24
Formal type parameter T
placeholder for type of data to
be tested by maximum.
maximum expects all
parameters to be of the same
type.

Outline
91
fig03_27.cpp
(2 of 3)
25 int main()
26 {
27 // demonstrate maximum with int values
28 int int1, int2, int3;
29
30 cout << "Input three integer values: ";
31 cin >> int1 >> int2 >> int3;
32
33 // invoke int version of maximum
34 cout << "The maximum integer value is: "
35 << maximum( int1, int2, int3 );
36
37 // demonstrate maximum with double values
38 double double1, double2, double3;
39
40 cout << "nnInput three double values: ";
41 cin >> double1 >> double2 >> double3;
42
43 // invoke double version of maximum
44 cout << "The maximum double value is: "
45 << maximum( double1, double2, double3 );
46
maximum called with various
data types.

Outline
92
fig03_27.cpp
(3 of 3)
fig03_27.cpp
output (1 of 1)
47 // demonstrate maximum with char values
48 char char1, char2, char3;
49
50 cout << "nnInput three characters: ";
51 cin >> char1 >> char2 >> char3;
52
53 // invoke char version of maximum
54 cout << "The maximum character value is: "
55 << maximum( char1, char2, char3 )
56 << endl;
57
59
60 } // end main
Input three integer values: 1 2 3
The maximum integer value is: 3
Input three double values: 3.3 2.2 1.1
The maximum double value is: 3.3
Input three characters: A C B
The maximum character value is: C

cpphtp4_PPT_03.ppt

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