1. Functions—Part I

2. 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

3. Slide 3 Review: Problem Solving Process * Define and analyze the problem n What is the input & output? n What constraints must be satisfied? n What information is essential? * Design an algorithm n What steps must be done? n 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. Problem solving phase Implementation phase

4. 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!

5. Slide 5 Example: Diamond Pattern * Input: nothing * Output: print out a diamond pattern * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

6. Slide 6 Example: top-down analysis * Output: print out a diamond pattern n print out the upper half  upper triangular form n print out the lower half  lower triangular form

7. Slide 7 Example: upper triangular pattern * Upper triangular pattern: n row 1: print 4 spaces, 1 star; n row 2: print 3 spaces, 3 stars; n row 3: print 2 spaces, 5 stars; n row 4: print 1 space, 7 stars; n row 5: print 0 spaces, 9 stars; * * * * * * * * * * * * * * * * * * * * * * * * *

8. Slide 8 Example: top-down refinement * Refinement: n row 1: print (5-row) spaces, (2*row - 1) stars; n row 2: print (5-row) spaces, (2*row - 1) stars; n row 3: print (5-row) spaces, (2*row - 1) stars; n row 4: print (5-row) spaces, (2*row - 1) stars; n row 5: print (5-row) spaces, (2*row - 1) stars; * For each ‘row’ (more exactly from row 1 to 5), always do n Print 5-row spaces n 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; }

9. Slide 9 Example: algorithm int 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; }

10. 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.

11. 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.

12. Slide 12 Function Input and Output Function Result Input parameters

13. 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.)

14. Slide 14 Mathematical Functions * #include * 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...

15. 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!

16. Slide 16 How to use a pre-defined function: Distance Between Two Points #include #include // 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!

17. Slide 17 How to define a function? * A function definition has following syntax: ( ){ }

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

19. Slide 19 Example: Absolute Value (1 st version) #include 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; }

20. 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: ( );

21. 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

22. Slide 22 Absolute Value (2 nd version) #include 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; }

23. Slide 23 How to use or call a function? * A function call has the following syntax: ( ) n There is a one-to-one correspondence between the parameters in a function call and the parameters in the function definition.

24. Slide 24 Summary with Absolute Value Example #include 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

25. 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 )

26. Slide 26 Example (void): Printing Cards  The main() program which calls printcard() #include using namespace std; void printcard(int);// function prototype int main(){ int c1, c2, c3, c4, c5; // pick cards... // print cards printcard(c1); printcard(c2); printcard(c3); printcard(c4); printcard(c5); // find score // print score }

27. 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)

28. 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);

29. Slide 29 Example: Total length of a triangle #include 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;

30. 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!

31. Pass by value

32. 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.

33. 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?

34. 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.

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

36. 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; }

37. Slide 37

38. 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 using namespace std; void PrintSumAve ( double, double ); int main ( ) { double x, y; cout << "Enter two numbers: "; cin >> x >> y; PrintSumAve ( x, y ); }

39. 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; }

40. Slide 40  Data areas after call to PrintSumAve() :

41. 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 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. */

42. 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; }

43. 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); }

44. Slide 44 Summary * Function parameters (like variables) * Function type (type of the function name) * Return statement (the last statement) n Finishes the function n Return the value to the caller * Understanding the ‘flow control’ between ‘main’ and a function * Communication: pass by value * Empty ‘void’ type

45. Slide 45 Input: formal parameters * Similar to (local) variables

46. 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) n It can in fact appear any places (close friends of ‘break’ and ‘continue’ n 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

47. 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.

48. Pass by Reference

49. Slide 49 Review on Pass by Value: #include 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.

50. Slide 50 Pass by Reference: Example 1 * To show how the function affects a variable which is used as a parameter: #include 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; }

51. 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.

52. Slide 52 l &, … l int& x, double& y, char& z l 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 l A reference is an alternative name for an object.

53. Slide 53 l Pass by value: formal parameters and arguments are different variables. ideal desirable behavior (but not efficient some times) l Pass by reference: they are the same variables, but different names! should carefully handled! Pass by value vs. by reference

54. Slide 54 Example 2 * It is possible to use both pass by reference and pass by value parameters in the same function.

55. 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 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; }

56. Slide 56 * Data areas after call to SumAve:

57. Slide 57 Example 3: sort 3 integers Input: three numbers First, Second, and Third Output: three numbers in order! Sort 3 numbers, F, S, and T Sort 2 numbers, F,S Sort 2 numbers, S,T Sort 2 numbers, F,S

58. Slide 58 Input: three numbers First, Second, and Third Output: three numbers in order! Sort F, S, and T Sort F,S Sort S,T Sort F,S if (first > second) swap (first, second);

59. Slide 59 // Compare and sort three integers #include 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; }

60. Slide 60 // Function for swapping two integers void swap (int& x, int& y) { int temp; temp = x; x = y; y = temp; }

61. Slide 61 #include 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) { … }

62. Slide 62 Summary int 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 y cin >> 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()

63. Slide 63 Example 4: programme tracing // Pass-by-reference versus pass-by-value example #include 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; }

64. 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; }