Functions—Part I

Slide 2

Where are we now?

Simple types of variables

3 program structures

cin(>>)/cout(<<)

Array

Functions (subprograms)

(File I/O)

Midterm: structured

programming

now

Slide 3 Review: Problem Solving Process

Define and analyze the problem What is the input & output? What constraints must be satisfied? What information is essential?

Design an algorithm What steps must be done? Wirte down the solution steps in detail

Implement a program - programming or coding. Compile, test, and debug the program - testing.

Document and maintain the program.

Pro

ble

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ing

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ase

Imp

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tati

on

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ase

Slide 4

Top-down analysis A complex problem is often easier to solve

by dividing it into several smaller parts (subproblems), each of which can be solved by itself.

This is called top-down programming.

Let’s take the example of Diamand drawing!

Slide 5

Example: Diamond Pattern Input: nothing Output: print out a diamond pattern

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Slide 6

Example: top-down analysis Output: print out a diamond pattern

print out the upper half upper triangular form print out the lower half lower triangular form

Slide 7

Example: upper triangular pattern Upper triangular pattern:

row 1: print 4 spaces, 1 star; row 2: print 3 spaces, 3 stars; row 3: print 2 spaces, 5 stars; row 4: print 1 space, 7 stars; row 5: print 0 spaces, 9 stars;

* * * *

* * * * *

* * * * * * *

* * * * * * * * *

Slide 8

Example: top-down refinement Refinement:

row 1: print (5-row) spaces, (2*row - 1) stars; row 2: print (5-row) spaces, (2*row - 1) stars; row 3: print (5-row) spaces, (2*row - 1) stars; row 4: print (5-row) spaces, (2*row - 1) stars; row 5: print (5-row) spaces, (2*row - 1) stars;

For each ‘row’ (more exactly from row 1 to 5), always do Print 5-row spaces Print 2*row-1 stars

It’s a loop: pseudo-code

* * * *

* * * * *

* * * * * * *

* * * * * * * * *

int row;

row=1;

while(row<=5){

print 5-row spaces;

print 2*row-1 stars;

row=row+1;

}

Slide 9

Example: algorithmint row, space, star;

row=1;

while(row<=5){

space=1;

while(space<=5-row) {

cout << " ";

space=space+1;

}

star=1;

while(star<=2*row-1) {

cout << "*";

star=star+1;

}

cout << endl ;

row=row+1;

}

int row;

row=1;

while(row<=5){

5-row spaces;

2*row-1 stars;

row=row+1;

}

Slide 10

Introduction to Functions The subproblems are solved by

subprograms, called functions in C++. main() then executes these functions so

that the original problem is solved.

Slide 11

Advantages of Functions

separate the concept (what is done) from the implementation (how it is done).

make programs easier to understand. make programs easier to modify. can be called several times in the same

program, allowing the code to be reused.

Slide 12

Function Input and Output

Function ResultInput parameters

Slide 13

C++ Functions

C++ allows the use of both pre-defined and user-defined functions.

Predefined functions (e.g., cin, cout, rand, etc.) are usually grouped into specialized libraries (e.g., iostream, cstdlib, cmath, etc.)

Slide 14

Mathematical Functions #include <cmath>

double log(double x) natural logarithm double log10(double x) base 10 logarithm double exp(double x) e to the power x double pow(double x, double y) x to the power y double sqrt(double x) positive square root of x double ceil(double x) smallest integer not less than x double floor(double x) largest integer not greater than

x double sin(double x), cos(double x), tan(double x), etc...

Slide 15

How to use a pre-defined function: Distance Between Two Points

Output:distance

Input: two points: (x1,y1), and (x2,y2)

Distance = sqrt((x2-x1)*(x2-x1) + (y2-y1)*(y2-y1))

x1,y1, x2, y2 are input data, so we are done!

Slide 16

How to use a pre-defined function: Distance Between Two Points

#include <iostream>

#include <cmath> // contains sqrt()

using namespace std;

int main(){

double x1, y1, x2, y2; // coordinates for point 1 & 2

double dist; // distance between points

cout << "Enter x & y coordinates of the 1st point: ";

cin >> x1 >> y1;

cout << "Enter x & y coordinates of the 2nd point: ";

cin >> x2 >> y2;

dist = sqrt((x2-x1)*(x2-x1) + (y2-y1)*(y2-y1));

cout << "The distance is " << dist << endl; return 0;

}

They are also function calls!

Slide 17

How to define a function? A function definition has following syntax:

<type> <function name>(<parameter list>){

<local declarations>

<sequence of statements>

}

Slide 18

A function returns a single result

(that’s the type of the function) One of the statements in the function body should have the form:

return <expression>;

(it’s good to use ONLY one at last!) The value passed back by return should have the same type as the function.

Slide 19

Example: Absolute Value (1st version)

#include <iostream> using namespace std;int absolute(int fx){

int abs; if (fx >= 0) abs=fx else abs = -fx;

return abs; } int main(){ int x, y, diff,adiff; cout << "Enter two integers (separated by a blank): "; cin >> x >> y; diff = x – y; adiff=absolute(diff); cout << "The absolute difference between " << x << " and " << y << " is: " << adiff << endl;

return 0;}

Slide 20

Function Prototype

The function prototype declares the interface, or input and output parameters of the function, leaving the implementation for the function definition.

(It therefore separates the concept from the implementation!)

The function prototype has the following syntax: <type> <function name>(<type list>);

Slide 21

You can place a function definition in front of main(). In this case there is no need to provide a function prototype for the function, since the function is already defined before its use.

The function definition can be placed anywhere in the program after the function prototypes.

C++ programs usually have the following form:

// include statements // function prototypes // main() function // user-defined functions

Slide 22

Absolute Value (2nd version)#include <iostream> using namespace std;int absolute (int); // function prototype for absolute()int main(){ int x, y, diff; cout << "Enter two integers (separated by a blank): "; cin >> x >> y; diff = absolute( x - y); cout << "The absolute difference between " << x << " and " << y << " is: " << diff << endl;

return 0;}

int absolute(int fx){ int abs;

if (fx >= 0) abs=fx else abs=-fx; return abs; }

Slide 23

How to use or call a function?

A function call has the following syntax:

<function name>(<parameter list>)

There is a one-to-one correspondence between the parameters in a function call and the parameters in the function definition.

Slide 24

Summary with Absolute Value Example#include <iostream> using namespace std;

int absolute (int); // function prototype for absolute()// int absolute (int fx);int main(){ int x, y, diff; cout << "Enter two integers (separated by a blank): "; cin >> x >> y;

diff = x-y; diff = absolute(diff); cout << "The absolute difference between " << x << " and " << y << " is: " << diff << endl;

return 0;} // Define a function to take absolute value of an integer int absolute(int fx){

int abs; if (fx >= 0) abs=fx; else abs= -fx; return (abs);}

formal parameter

final result of the function

function call, argument

Slide 25

A function returns a single result, but a void type function does not return anything (but does something, a sub-program)!

‘Void’ type functions

(‘main’ is just a function that has no formal parameters for the moment )

Slide 26

Example (void): Printing Cards The main() program which calls printcard()

#include <iostream>using namespace std;void printcard(int); // function prototypeint main(){

int c1, c2, c3, c4, c5;// pick cards. . . // print cardsprintcard(c1);printcard(c2);printcard(c3);printcard(c4);printcard(c5);// find score// print score

}

Slide 27

A function that prints the card (J) given the card number (11) as input:

void printcard(int cardnum){ if(cardnum==1)

cout << "A"; else if(cardnum>=2 && cardnum<=10)

cout << cardnum; else if(cardnum==11)

cout << "J"; else if(cardnum==12)

cout << "Q"; else if(cardnum==13)

cout << "K";}

(This is a void function - a function that does not return a value)

Slide 28

Example: Total length of a triangle

Output: total-length

Input: three points: A=(x1,y1), B=(x2,y2), and C=(x3,y3)

Total-length = length(AB) + length(AC) + length(AB)

Length(AB) = dist(A,B);

Length(AC) = dist(A,C);

Length(BC) = dist(B,C);

Slide 29

Example: Total length of a triangle

#include <iostream> #include <cmath> using namespace std;double dist(double, double, double, double); int main(){

double x1, y1, // coordinates for point 1 x2, y2, // coordinates for point 2 x3, y3, // coordinates for point 3

l12,l23,l13,length; cout << "Enter x & y coordinates of the 1st point: "; cin >> x1 >> y1; cout << "Enter x & y coordinates of the 2nd point: "; cin >> x2 >> y2; cout << "Enter x & y coordinates of the 3rd point: "; cin >> x3 >> y3;

Slide 30

l12 = dist(x1,y1,x2,y2);

l23 = dist(x2,y2,x3,y3);

l13 = dist(x1,y1,x3,y3);

length = l12 + l23 + l13;

return 0;

}

// Function for computing the distance between 2 pts

double dist(double fx1, double fy1, double fx2, double fy2) {

double dist;

dist = sqrt( (fx2-fx1)*(fx2-fx1) + (fy2-fy1)*(fy2-fy1) );

return dist;

}

// Function for computing the distance between 2 pts

double dist(double x1, double y1, double x2, double y2) {

double dist;

dist = sqrt( (x2-x1)*(x2-x1) + (y2-y1)*(y2-y1) );

return dist;

}

exactly the same!

Two different variables

How to communicate?

Pass by value!

Pass by value

Slide 32

Passing parameters by Value

This is by default and desirable behavior!

An important fact to remember about parameter passing by value is that changes to the parameters inside the function body have no effect outside of the function.

You may think that calling parameters and formal parameters are just different variables.

Slide 33

Example 0 For example, consider the following code:

int sum(int a, int b){ a = a + b; return a; } void main(){ int x, y, z; x = 3; y = 5; z = sum(x,y); } What is the value of x, y, and z at the end of the main() program?

Slide 34

The answer: 3, 5, and 8. Even though the value of parameter a is changed, the

corresponding value in variable x does not change. This is why this is called pass by value. The value of the original variable is copied to the

parameter, but changes to the value of the parameter do not affect the original variable.

In fact, all information in (local) variables declared within the function will be lost when the function terminates.

The only information saved from a pass by value function is in the return statement.

Slide 35

Example 1 An example to show how the function does not affect a

variable which is used as a parameter:

// Test the effect of a function // on its parameter #include <iostream> using namespace std;

void Increment(int Number) { Number = Number + 1; cout << "The parameter Number is: " << Number << endl; }

Slide 36

void main() { int I = 10; //parameter is a variable Increment(I); cout << "The variable I is: " << I << endl;

//parameter is a constant Increment(35); cout << "The variable I is: " << I << endl;

//parameter is an expression Increment(I+26); cout << "The variable I is: " << I << endl; }

Slide 37

Slide 38

Example 2// Print the sum and average of two numbers // Input: two numbers x & y // Output: sum - the sum of x & y // average - the average of x & y #include <iostream> using namespace std;void PrintSumAve ( double, double ); int main ( ) { double x, y;

cout << "Enter two numbers: "; cin >> x >> y; PrintSumAve ( x , y ); }

Slide 39

void PrintSumAve (double no1, double no2) {

double sum, average;

sum = no1 + no2;

average = sum / 2;

cout << "The sum is " << sum << endl;

cout << "The average is " << average << endl;

}

Slide 40

Data areas after call to PrintSumAve() :

Slide 41

Example 3//Compute new balance at a certain interest rate //Inputs: A positive balance and // a positive interest rate //Output: The new balance after interest was posted #include <iostream> using namespace std;

double new_balance(double balance, double rate); /* Returns the balance in a bank account after adding interest. For example, if rate is 5.0, then the interest rate is 5% and so new_balance(100, 5.0) returns 105.00. */

Slide 42

int main(){ double interest, balance;

cout << "Enter balance (positive number): "; cin >> balance; if (balance <= 0.0) cout <<"Balance not positive; stopping" << endl; else { cout <<"Enter interest rate (positive number): "; cin >> interest; if (interest <= 0.0) cout << "Interest not positive; stopping" << endl; else cout <<"New balance = $" << new_balance(balance, interest)<< endl; } return 0; }

Slide 43

// New balance is computed as balance + balance * %rate double new_balance(double balance, double rate) { double interest_fraction, interest; interest_fraction = rate / 100; interest = interest_fraction * balance; return (balance + interest); }

Slide 44

Summary Function parameters (like variables) Function type (type of the function name) Return statement (the last statement)

Finishes the function Return the value to the caller

Understanding the ‘flow control’ between ‘main’ and a function

Communication: pass by value Empty ‘void’ type

Slide 45

Input: formal parameters

Similar to (local) variables

Slide 46

Output: return statement

The final result (that should be returned to the calling expression), the end of the ‘sub-programme’

Recommended to use only one ‘return’ as the last statement of the function (for good structure of the programmes) It can in fact appear any places (close friends of ‘break’ and

‘continue’ Example: int max(int a, int b) {if (a>b) return a; else return b;}

or int max(int a, int b) {int m; if (a>b) m=a; else m=b; return

m;}

The type should match that of the function

Slide 47

Function call: pass by value

Effective parameters (variables) and formal parameters (variables) are completely different

We just copy to or initialize the formal parameters from the effective parameters

‘effective parameters’ are ‘originals’, and ‘formal parameters’ are ‘photocopies’! They are different.

Pass by Reference

Slide 49

Review on Pass by Value:

#include <iostream> using namespace std;void Increment(int Number){

Number = Number + 1; cout << "The parameter Number: " << Number << endl;

}

void main(){ int I = 10; Increment(I); // parameter is a variable

cout << "The variable I is: " << I << endl;

} Note: replacing ‘I’ by ‘Number’ in the main does not change anything.

Slide 50

Pass by Reference: Example 1 To show how the function affects a variable which is

used as a parameter:

#include <iostream> using namespace std;void Increment(int& Number){

Number = Number + 1; cout << "The parameter Number: " << Number << endl;

}

void main(){ int I = 10; Increment(I); // parameter is a variable

cout << "The variable I is: " << I << endl;

}

Slide 51 Passing Parameters by Reference

To have a function with multiple outputs, we have to use pass by reference.

Efficiency for large objects!

Reference (address) of parameter is passed to the function, instead of its value.

If the function changes the parameter value, the changes will be reflected in the program calling it.

Slide 52

<type>& <variable>, … int& x, double& y, char& z The notation T& means a reference to T

Specify the passing of a parameter by reference: T&

Very ‘interesting’ notation we will continue to see it later on …

‘reference’ does not exist in C, ramification of low-level pointer.

int y=10;

int& x = y; // x and y refer to the same int

A reference is an alternative name for an object.

Slide 53

Pass by value: formal parameters and arguments are different variables.

ideal desirable behavior

(but not efficient some times) Pass by reference: they are the same variables,

but different names!

should carefully handled!

Pass by value vs. by reference

Slide 54

Example 2

It is possible to use both pass by reference and pass by value parameters in the same function.

Slide 55

// Print the sum and average of two numbers // Input: two numbers x & y // Output: sum - the sum of x & y // average - the average of x & y #include <iostream> using namespace std;

void SumAve (double, double, double&, double&); void main ( ) { double x, y, sum, mean;

cout << "Enter two numbers: "; cin >> x >> y; SumAve (x, y, sum, mean); cout << "The sum is " << sum << endl; cout << "The average is " << mean << endl; } void SumAve(double no1, double no2, double& sum,

double& average) { sum = no1 + no2; average = sum / 2; }

Slide 56

Data areas after call to SumAve:

Slide 57

Example 3: sort 3 integersInput: three numbers First, Second, and ThirdOutput: three numbers in order!

Sort 3 numbers, F, S, and T

Sort 2 numbers, F,SSort 2 numbers, S,TSort 2 numbers, F,S

Slide 58

Input: three numbers First, Second, and ThirdOutput: three numbers in order!

Sort F, S, and T

Sort F,SSort S,TSort F,S

if (first > second) swap (first, second);

Slide 59

// Compare and sort three integers #include <iostream> using namespace std;void swap (int&, int&); void main ( ) { int first, second, third; // input integers // Read in first, second and third. cout << "Enter three integers: "; cin >> first >> second >> third;

if (first > second) swap (first, second); if (second > third) swap (second, third); if (first > second) swap (first, second); cout << "The sorted integers are " << first <<

" , " << second << " , " << third << endl; }

Slide 60

// Function for swapping two integers

void swap (int& x, int& y) {

int temp;

temp = x;

x = y;

y = temp;

}

Slide 61

#include <iostream> using namespace std;void sort (int&, int&);Void swap (int&, int&); void main ( ) { int first, second, third; // input integers // Read in first, second and third. cout << "Enter three integers: "; cin >> first >> second >> third;

sort(first,second); sort(second,third);

sort(first,third); cout << "The sorted integers are " << first << " , " << second << " , " << third << endl;

}

Also possible …

void sort(int& x, int& y) {

if(x>y) swap(x,y);

}

void swap (int& x, int& y) {

…

}

Slide 62

Summaryint max(int x, int y) {

int m;if (x>y) m=x; else m=y;return m;

}

void max(int x, int y, int& m) {if (x>y) m=x; else m=y;

}

void minmax(int x, int y, int& min, int& max) {if (x>y) {min=y; max=x;}else (min=x; max=y;}

}

int xx,yy,mm; // OK with m, x, and ycin >> xx >> yy;mm=max(xx,yy); // functional programming style

int xx,yy,mm;cin >> xx >> yy;max(xx,yy,mm);

int xx,yy,mmin,mmax;cin >> xx >> yy;minmax(xx,yy,mmin,mmax);

int main()

Slide 63

Example 4: programme tracing// Pass-by-reference versus pass-by-value example #include <iostream> using namespace std;

void One (int a, int b, int& c) {

int d;

a = 10; b = 11; c = 12; d = 13;

cout << "The values of a, b, c, and d in One: ";

cout << a << " " << b << " " << c << " " << d << endl; } void Two (int a, int b, int& d) { int c = 0; cout << "The values of a, b, c, and d in Two: "; cout << a << " " << b << " " << c << " " << d << endl; }

Slide 64

void main () {

int a = 1, b = 2, c = 3, d = 4;

One(a, b, c);

cout << "The values of a, b, c, and d after One: ";

cout << a << " " << b << " " << c << " " << d << endl;

Two(a, b, d);

cout << "The values of a, b, c, and d after Two: ";

cout << a << " " << b << " " << c << " " << d << endl;

}