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CS 31: Introduction To CS ITopic 3: Functions

9/2010 John A. RohrAll Rights Reserved

JAR 3-1

CS 31:

Introduction toComputer Science I

Topic 3

Functions

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JAR 3-2

Functions

Function Definition

A function is a single unit of computation

Other words for function

Procedure

Method Subprogram (that returns a value)

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Functions

Function Characterization

Accomplishes one thing

May use other functions

May produce a result

Sequence of statements

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Functions

Function Inputs

Called arguments or actual parameters

Provides values for calculation

Not needed by all functions

Display text

Generate random number

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Functions

Function Outputs

Called the return value

Reports the results of the processing

Not produced by all functions

Functions that perform an action only

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Functions

Function Processing

Apply defined algorithm

Use inputs

Generate outputs

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Functions

Function Example

Square Root

Input: Value: 9

Processing: Calculate square root

Output: Square root of value: 3

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Functions

Two Function Dichotomies

Function definition dichotomy

Predefined functions

Programmer-written functions

Function return value dichotomy

void

Typed (int, float, double, char, bool, etc.)

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Functions

Function Definition Types

Predefined functions

Function library

Commercial product

Other programmers

Programmer defined functions Written by programmer

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Functions

Function Return Value Types

Functions that return a value (typed)

Perform a calculation (e.g. Square root)

Deliver (return) the result

Functions that do not return a value (void)

Perform an action (e.g. set an output format)

Do not have a result to return

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Functions

C++ Predefined Functions

Provided by the compiler

Organized in libraries

Referenced by #include statements

Included in program using #include

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Functions

Some Predefined Libraries

iostream Stream input and output

cmath Mathematical functions

cstdlib Some standard functions

cctype Character operations

string String capabilities

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Functions

Some Predefined Functions

Library iostream (#include )

cin Stream input

cout Stream output

precision Stream precision

width Stream width setf Stream formatting

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Functions


Library cmath (#include )

double sqrt(double) Square root

double exp(double) Exponential (ex)

double sin(double) Trigonometric sine

double log(double) Natural logarithm (ln) double floor(double) Floor

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Functions


Library cstdlib (#include )

int abs(int) Absolute value

int rand() Random number

void srand(unsigned int) Seed random number

void exit(int) Exit program

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Functions


Library cctype (#include )

bool isdigit(char) Digit

bool isupper(char) Upper case

bool isspace (char) White space

bool ispunct(char) Punctuation int toupper(char) To upper case

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Functions


Library string (#include )

String declaration (with/without initialization)

String assignment

String input and output

String character selection Substring

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Functions

Function Call

Invokes the use of a function

Specifies input arguments

Return result value, if any

void function: No return value

Typed function: Return value

Exactly one value

Value is function type

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Functions

Function Call Syntax

name(arg1, arg2, arg3, . . . argn);

variable = name(arg1, arg2, arg3, . . . argn);

name: Function name

argi: Argument i

variable: Place to put function value

(if any)

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CS 31: Introduction To CS ITopic 3: Functions9/2010 John A. RohrAll Rights Reserved

JAR 3-20

Functions

Function Calls

void function: No value is returned

typed function: One value is returned Cannot be no value

Cannot be more than one value

Must be exactly one value

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Functions

Type Conversion

Input arguments: For literals only

Will be converted if necessary and possible

Return values

Always returned as function type

May be converted by an assignmentstatement after return

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Functions

Function Example

root = sqrt(value);

Function name: sqrt

Library location: cmath

Function action: Square root

Argument: value (e.g. 25) Output: Square root of value (e.g.5)

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Functions

Literal Argument

root = sqrt(64);

Argument is an integer

Parameter is a double

Automatic upconversion of literal value

from integer to double

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Functions

Variable Argument

double value = 64;

root = sqrt(value);Argument is a double

Argument must match type

No conversion

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Functions

Function Use#include

#include using namespace std;

int main()

{

double value;

double root;

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Functions

Function Usecout > value;root = sqrt(value);

cout

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Functions

Function Execution

Enter a value:5.76

The square root of "5.76" is "2.4"

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Functions

Exit Function

exit(integer);

Useful for stopping program early on error Takes integer value for identification

0 for special exit without error

1 or other for error exit In library cstdlib

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Functions

Exit Use

#include

using namespace std;int main()

{

exit(0);}

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Functions

Time Function

now = time(0);

Returns current time Seconds since January 1, 1970

Useful to obtain a random number

In library ctime

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Functions

Time Use#include

#include using namespace std;int main(){

cout

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Functions

Random Number Generation

Sequence of pseudorandom numbers

Not completely random Generated by algorithm

Initialized by an integer seed number

Will repeat same sequence for same seed

Use random seed for random sequence

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Functions

Random Number Function

rand();

Does not take any argument Generates a pseudorandom number

Value is between 0 and RAND_MAX (>=32,767)

Can be scaled for other ranges Function and RAND_MAX in library cstdlib

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Functions

Random Number Use#include

#include using namespace std;int main(){

cout

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Functions

Random Number Scaling

rand() value is between 0 and RAND_MAX

Value can be scaled to any range

Select number of values using modulus

Shift range by addition

Scale by multiplication

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Functions

Scaling Example

Find result of throwing two dice

Minimum value is 2

Maximum value is 12

count = (rand() % 11) + 2;

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Functions

Another Scaling Example

Find a probability

Minimum value is 0

Maximum value is 1.0

count = (RAND_MAX - rand()) /

(RAND_MAX * 1.0);

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Functions

Seeded Random Numbers

srand(seed);

Initializes random number generator

Used unsigned integer for seed

Generate same sequence for same seed

Generate different numbers

with different seed

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CS 31: Introduction To CS I

Topic 3: Functions


Functions

Seeded Random Numbers

#include

#include #include using namespace std;int main(){

srand(time(0));cout

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Topic 3: Functions


C++ Strings

string Library

#include

Provides C++ strings

Not part of language itself

Cannot be used without #include

One of many extensions to the language

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Topic 3: Functions


C++ Strings

C++ String Declaration

string st1;

string st2 = "Initial string"; String is initialized to empty string by default

String can be initialized with declaration

Characters are numbered beginning with 0

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Topic 3: Functions9/2010 John A. Rohr

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C++ Strings

C++ String Length

string st = "Example text";

st.length() or st.size() (Integer 12) Length of the string

Function with no parameters

Return value is integer

Syntax uses string name followed by period

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C++ Strings

C++ String Access


st[3] (Character m) One character of the string

Position can be any integer expression

Must not access past last character

Syntax uses position in square brackets

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C++ Strings

Alternate C++ String Access


st[3] (Character m) st.at(3) (Character m)

Both access one character

atchecks for beyond end of string

atthrows an exception on error

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C++ Strings

C++ Substring


st.substr(8) (String "text") Part of the string

Position can be any integer expression

Must not begin past last character

Result is string from position specified

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C++ Strings

C++ Substring


st.substr(2, 5) (String "ample") Part of the string

Start can be any integer expression

Length can be any integer expression Must not extend past last character

Result string from position with length given

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C++ Strings

C++ String Comparison

Strings can be compared like numbers

Operators are ==, !=, >, =, and

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C++ Strings


Comparisons are character by character

First differing character determines result Comparisons also depend on length

Longer string is greater than shorter string

if identical up to the end of the shorter

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C++ Strings


string st1 = "On";

string st2 = "Once"; string st3 = "Once more";

st1 == st2 is false

st1 == st2.substr(0,2) is true

st2 != st3 is true

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C++ Strings


string st1 = "On";

string st2 = "Once"; string st3 = "Once more";

st2 < st3 is true

st2 >= st3.substr(0,4) is true

st1 > st3 is false

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C++ Strings

C++ String Concatenation

string st1 = "One string";

string st2 = " extended"; st1 + st2 ("One string extended")

First string followed by second

No characters inserted between

Plus sign (+) defined by #include

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C++ Strings

C++ String Insertion


string st2 = " more"; string st3, st4;

st3 = st1.insert(3, st2); ("One more string")

st4 = st1.insert(3, st2, 1, 2 ) ("Onemo string")

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C++ Strings

C++ String Removal


string st2 = "op"; string st3, st4, st5;

st2 = st1.erase(3); ("One")

st3 = st1.erase(0, 6); ("ring")

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C++ Strings

C++ String Replacement


string st2 = "person"; string st3 = "weather";

string st4, st5;

st4 = st1.replace(4, 6, st2); ("One person")

st5 = st1.replace(0, 7, st3, 3, 2); ("thing")

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C++ Strings

C++ String Find

string st = "One string";

st.find("in", 0) is 7 st.find("in", 5) is 7

st.find(' ', 0) is 3

st.find(' ', 5) is string::npos Returns string::npos if no find

(Constant defined in the string library)

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C++ Strings

Digit Value

Characters are represented by integers

The code is defined by the hardware Several code standards are used

Each character has a different code

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C++ Strings

ASCII Digit Value

ASCII: American Standard Code for

Information Interchange Most common character code

Uses first 32 values for control characters

e.g. Tab, Backspace, Return Digits begin at 48, NOT 0

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C++ Strings

ASCII Digit Value Digit values range from 48 to 57

Never need to use numeric values'0' = 48 '5' = 53

'1' = 49 '6' = 54

'2' = 50 '7' = 55

'3' = 51 '8' = 56

'4' = 52 '9' = 57

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C++ Strings

ASCII Digit Value

Subtract digit 0 value from digit character

char digit = '3'; int number;

number = digit - '0';

Numerical value ofdigit is 51

Numerical value ofnumber is 3

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Functions

Programmer-Defined Functions

Custom functions for specific uses

Can be used to provide needed capability Can be used to modularize programs

Limit size of each module

Organize in hierarchy of modules

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Functions

Programmer-Defined Functions

Three required items

Function prototype (declaration) Function definition (code)

Function call (use)

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Functions

Function Return Value None if void

Any valid type if typed int float

double

bool char

string

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Functions

Function Name

Valid C++ identifier

Uniquely identifies function Should indicate the action of the function

Used to call the function

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Functions

Function Parameters

Called parameters or formal parameters

Are placeholders for arguments of calls Specify the type & number of parameters

Specify the name of each parameter

Name not required in prototype

Should be included for completeness

Are required in the function header

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Functions

Prototype Example

void aFunction(int p1, float p2, char p3);

Return type (None) Name (aFunction)

Parameters p1 (Integer)

p2 (Float) p3 (Character)

Note required semicolon at end!

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Functions

Prototype Example

int anotherFunction(double value);

Return type (Integer) Name (anotherFunction)

Parameter value (Double)

Note required semicolon at end!

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Functions

Function Call

Same as for predefined functions

Function nameArguments

Must match the number of prototype parameters

Must match the types prototype parameters

Must be in the correct order

Exception: Automatic upconversion

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Functions

Function Definition Not required for predefined functions

Provided by #include statement Consists of two separate parts

Function header

Function body

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Functions

Function Header Same format as prototype

Specifies type, name, and parameters Does not have terminating semicolon

Must have names for parameters

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Functions

Function Body Defines the action of the function

Can include declarations Must include statements

No return statement if void

Must return value if not void Value must match type of function Value is returned with a return statement

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Functions

Function Definition Example#include

using namespace std;void aFunction(int p1, float p2, char p3){

cout

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Functions

Function Definition Exampleint anotherFunction(double value){

int result;if (value >= 0)

result = 0;else

result = 1;return result;

}

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Functions

Function Return Void functions

Return statement is optional

If used, return cannot return any value

Will return at final close brace if no return

Typed functions

Return statement is required

Must return value of function type

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Functions

Functions Calling Functions Statements in function definitions can be

any valid C++ statements A function call from within a function is valid

Every C++ program is a function (main)

Therefore all C++ function calls are actuallyinside other functions

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Functions

Preconditions Specify conditions which must be true

when a function is called Guarantee correct results if all true

Result not guaranteed if not all true

Provide limits for arguments Use assert() to check (in cassert library)

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Functions

Postconditions Describes the value returned by a function

Valid only if all preconditions are true

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Functions

Pre/postcondition Example For square root function

PreconditionArgument is a real number >= 0

Postcondition

Result will be the square root of the argument

F i

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Functions

Pre/postcondition Example For sin function (in cmath)

PreconditionArgument is a real number in radians

Postcondition

Result will be the sine of the angle Result will be be in the range -1.0 to +1.0

F ti

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Functions

Scope Rules Define the valid range of a variable

Minimize variable name conflicts Provide for global variables

Provide for local variables

F ti

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Functions

Local Variables Define within a function

Exist between opening and closing braces Do not exist outside the function except

Static variables are preserved call to call

Cannot conflict with local variables in otherfunctions, even if the name is the same

F ti

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Functions

Global Variables Exist for an entire program

Defined before the first function Good use is for global constants

Use of global variables should be limited

Use function parameters to pass data

Use function returns to return data

F ti

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Functions

Blocks Define scopes for variables

Delimited by open and close brace Variables defined in block are local to the

block in which they are defined

Block may be an entire function

F ti

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Functions

Nested Blocks Blocks defined inside other blocks

Resolves variables names Based on static structure

Variable name redefined

New instance valid within new block

Old instance revived when the new block ends

F ti

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Functions

For Loop Variables for (int index = 0; index < 10; index++)

Variable can be declared in forstatement Better practice to declare at beginning

Defined in scope offorstatement only

Some older compilers may not follow rule May allow variable to exist after loop ends

M th ti l I d ti

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Mathematical Induction

Concept Mathematical induction is a method that

can be used to prove numerical formulas. A proof requires two parts:

Show the formula is true for an initial value;

Show that if the formula is true for somevalue, then it is also true for the next value.

M th ti l I d ti

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ExampleThe formula for the sum of the positive

integers from 1 to n is as follows:

Si= n * (n + 1) / 2i = 1

n

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ProofStep 1: Show that the sum of the integers

from 1 to 1 is 1: Si = 1.Proof: S i = 1 * (1 + 1) / 2

= 1 * 2 / 2

= 1 which is true.

i = 1

1

i = 1

1

M th ti l I d ti

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ProofStep 2: Show that if the sum of the integers from 1 to m

is m * (m + 1) / 2 then the sum of the integers

from m to m+1 is (m + 1) * (m + 2) / 2.

Proof: Si= 1 * (1 + 1) / 2= S i + (m + 1)= m * (m + 1) / 2 + (m + 1)= (m2 + m) / 2 + 2m / 2 + 2 / 2

= (m2 + 3m + 2)/2 = (m+1)*(m+2)

i = 1

m+1

i = 1

m

Rec rsion

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Recursion

Concept Recursion is a method where an algorithm

is defined in terms of itself. There must be two cases in the algorithm:

A base case that does not use the algorithm;

A recursive case that uses the algorithm.

Recursion

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Recursion

ExampleThe formula for the product of the positive

integers from 1 to n is as follows:

pi = 1 for n = 0;= n *

pfor n > 0

i = 1

n

i = 1

n-1

Recursion

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Recursion

Recursive Factorial Functiondouble factor(double num)

{ if (num == 0)

return 1;

elsereturn factor (n 1);

}

Recursion

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Recursion

Recursion vs.Iteration Recursion

Function calls itself Must have base case

Must be supported by the language used

Iteration

Function does not call itself

Computation is based on a loop

Does not require any special language support

Recursion

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Recursion

Recursion vs.Iteration Recursion

More elegant Less efficient

Not practical for production use

Iteration

More common

More efficient

Usually used instead of recursion

Recursion

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Recursion

Iterative Factorial Functiondouble factor(double num)

{ double fact;

for (fact = 1.0; num > 0.0; num -= 1.0)

fact *= num;return fact;

}

UPDATES

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UPDATES

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