1. Functions Programming Applications

2. Functions every C program must have a function called main program execution always begins with function main any other functions are subprograms and must be called

3. Functions Functions are subprograms that can be called from another function(s) (such as the Main function). printf and scanf are examples of functions.

4. Every C function has 2 parts int main ( )heading { body block return 0; }

5. Program with Several Functions main function Square function Cube function

6. 6 Writing Functions Need to specify: the name of the function its parameters what it returns The block of statements is called the “function body”

7. 7 Example1: hello.c Function definition Function call #include /* * Print a simple greeting. */ void sayHello ( void ) { printf(“Hello World!\n”); } /* * Call a function which prints a * simple greeting. */ int main() { sayHello(); return 0; }

8. 8 Example1: hello.c Function name Function body #include /* * Print a simple greeting. */ void sayHello ( void ) { printf(“Hello World!\n”); } /* * Call a function which prints a * simple greeting. */ int main() { sayHello(); return 0; }

9. 9 Example1: hello.c Return type Formal Parameter List #include /* * Print a simple greeting. */ void sayHello ( void ) { printf(“Hello World!\n”); } /* * Call a function which prints a * simple greeting. */ int main() { sayHello(); return 0; }

10. 10 Example2: sort.c /* Print two numbers in order. */ void Sort ( int a, int b ) { int temp; if ( a > b ) { printf("%d %d\n", b, a); } else { printf("%d %d\n", a, b); } Parameters

11. 11 int main() { int x = 3, y = 5; Sort ( 10, 9 ); Sort ( y, x + 4 ); return 0; } Example2: sort.c /* Print two numbers in order. */ void Sort ( int a, int b ) { int temp; if ( a > b ) { printf("%d %d\n", b, a); } else { printf("%d %d\n", a, b); } Formal parameters Actual parameters

12. 12 Example3: Average.c Function definition Function call #include float Average ( int X, int Y, int Z ) { float AVG; AVG = (X+Y+Z)/ 3.0; return AVG; } void main(void) { int a,b,c; float AVG; a = 5; b = 6; c = 2; AVG = Average (a, b, c); printf (“Average = %6.3f \n”, AVG); }

13. Two Kinds of Functions Always returns a single value to its caller and is called from within an expression. Never returns a value to its caller, and is called as a separate statement. Value-Returning Void

14. Trace void main() { int a = 2; int b = 2; int c = 3; b = mult( a, c ) ; printf(“ a = %d b = %d c = %d \n “, a, b, c ) ; c = squares( a, b ) ; printf(“ a = %d b = %d c = %d \n “, a, b, c ) ; } int mult (int x, int y ) { return x * y; } int squares ( int p, int q ) { int r = p * p + q * q ; return r ; }

15. Example4 Write a C program to read two integer numbers and Use function to find the maximum of them

16. Example5 Write a complete program that asks for radius of a circle and calculates its area using a function with return value of float type.

17. Call by Value & Call by Reference

18. Call by Value: The Formal Parameters are not the Actual Parameters. Only Values from the Actual Parameters are passed to the Formal Parameters. Call by Reference: The Formal Parameters are referring to the Actual Parameters.

19. Call by Value & Call by Reference Call by Value: Changes in the Formal Parameters Will not affect the Actual Parameters. Call by Reference: Changes in the Formal Parameters Will affect the Actual Parameters.

20. Call By Value

21. 21 int main() { int a = 3, b = 5; printf("%d %d\n", a, b); badSwap ( a, b ); printf("%d %d\n", a, b); return 0; } Example6: bad_swap.c /* Swap the values of two variables. */ void badSwap ( int a, int b ) { int temp; temp = a; a = b; b = temp; printf("%d %d\n", a, b); } Output: 3 5

22. 22 int main() { int a = 3, b = 5; printf("%d %d\n", a, b); badSwap ( a, b ); printf("%d %d\n", a, b); return 0; } Example6: bad_swap.c /* Swap the values of two variables. */ void badSwap ( int a, int b ) { int temp; temp = a; a = b; b = temp; printf("%d %d\n", a, b); } Output: 3 5 5 3

23. 23 int main() { int a = 3, b = 5; printf("%d %d\n", a, b); badSwap ( a, b ); printf("%d %d\n", a, b); return 0; } Example6: bad_swap.c /* Swap the values of two variables. */ void badSwap ( int a, int b ) { int temp; temp = a; a = b; b = temp; printf("%d %d\n", a, b); } Output: 3 5 5 3 3 5

24. 24 int main() { int a = 3, b = 5; printf("%d %d\n", a, b); badSwap ( a, b ); printf("%d %d\n", a, b); return 0; } Example6: bad_swap.c /* Swap the values of two variables. */ void badSwap ( int a, int b ) { int temp; temp = a; a = b; b = temp; printf("%d %d\n", a, b); } Output: 3 5 5 3 3 5

25. Call By Reference

26. 26 int main() { int a = 3, b = 5; printf("%d %d\n", a, b); Swap ( &a, &b ); printf("%d %d\n", a, b); return 0; } Example7: swap.c /* Swap the values of two variables. */ void Swap ( int *a, int *b ) { int temp; temp = *a; *a = *b; *b = temp; printf("%d %d\n", *a, *b); } Output: 3 5

27. 27 int main() { int a = 3, b = 5; printf("%d %d\n", a, b); Swap ( &a, &b ); printf("%d %d\n", a, b); return 0; } Example7: swap.c /* Swap the values of two variables. */ void Swap ( int *a, int *b ) { int temp; temp = *a; *a = *b; *b = temp; printf("%d %d\n", *a, *b); } Output: 3 5 5 3

28. 28 int main() { int a = 3, b = 5; printf("%d %d\n", a, b); Swap ( &a, &b ); printf("%d %d\n", a, b); return 0; } Example7: swap.c /* Swap the values of two variables. */ void Swap ( int *a, int *b ) { int temp; temp = *a; *a = *b; *b = temp; printf("%d %d\n", *a, *b); } Output: 3 5 5 3

29. 29 int main() { int a = 3, b = 5; printf("%d %d\n", a, b); Swap ( &a, &b ); printf("%d %d\n", a, b); return 0; } Example7: swap.c /* Swap the values of two variables. */ void Swap ( int *a, int *b ) { int temp; temp = *a; *a = *b; *b = temp; printf("%d %d\n", *a, *b); } Output: 3 5 5 3

30. Remember !! void Average ( int x, y, z)  Wrong void Average (int x, int y, int z)  Correct

31. 31 void main(void) { int x = 5, y = 3, z = 7; int Max, Min; MaxMin(x,y,z,&Max, &Min); printf("%d %d\n", Max, Min); } Example8: Max_Min.c void MaxMin ( int a,int b,int c, int *MX, int *MN) { if ((a>b)&&(a>c)) *MX = a; else if (b>c) *MX = b; else *MX = c; if ((a<b)&&(a<c)) *MN = a; else if (b<c) *MN = b; else *MN = c; } Output:

32. 32 void main(void) { int x = 5, y = 3, z = 7; int Max, Min; MaxMin(x,y,z,&Max, &Min); printf("%d %d\n", Max, Min); } Example8: Max_Min.c void MaxMin ( int a,int b,int c, int *MX, int *MN) { if ((a>b)&&(a>c)) *MX = a; else if (b>c) *MX = b; else *MX = c; if ((a<b)&&(a<c)) *MN = a; else if (b<c) *MN = b; else *MN = c; } Output: 7 3

33. What is in a prototype? A prototype looks like the function heading but must end with a semicolon”;” It has no body. Usually located at the beginning of the program to declare all the functions to be used. int Cube( int n); /* prototype */

34. Program with Three Functions #include int Square( int n); /* declares these functions */ int Cube( int n); int main( ) { int num = 3 ; int sq, cb ; sq = Square(num); printf(“ The square of 3 is %d \n “, sq ); cb = Cube(num); printf(“ The cube of 3 is %d \n “, cb ); return 0; }

35. Rest of Program int Square( int n ) { int s = n * n ; return s; } int Cube( int n ) { int c = n * n * n ; return c; }

36. int main() { int a, b=1, c=2, d=3, e; a=d; e=c; a=1; printf(" %d \t %d \t %d \n", e, c, d); b=SomeFunction(&c); printf(" %d \t %d \t %d \n", b, c, e); return 0; } int SomeFunction(int *m) { *m= (*m)+1; return (*m); }

37. #include void duplicate (int a, int *b, int *c) { *b=a; a=1; *c=2; } int Star(int a, int b) { int c=0; int i; for(i=0 ; i<2 ; i++) {

38. duplicate ( c, &a, &b); a++; b++; c++; printf(“%d %d %d\n”, a, b, c); } return a; } void main (void) { int x=1, y=3, z=7; x = Star(y, z); printf("x=%d\t y=%d\n z=%d", x, y, z); }

39. Recursive Function The recursive function is function calls itself The function repeat to call itself with different parameter values.

40. Trace #include int f(int x) { if (x==0) return 0; else if (x>=1) return x+f(x-1); } void main() { int y=f(0); int z = f(4); printf (“ %d \t %d \n “, y, z); }

41. Example what are the value of fun(7, 1) and fun(6, 3) int fun (int m, int n) { if(n==1) return m; else return (m+fun(m, n-1)); }

42. Trace #include int f(int x){ if (x==0) return 0; else if (x>=1) return x+f(x-1); } void main() { int y=f(0); int z = f(4); printf (“ %d \t %d \n “, y, z); }

43. Trace #include int g(int a) {if (a==0) return 1; Else if(a==1) return 2; Else if (x>=2) return g(a-1)*g(a-2);} void main() {Int y=g(0); Int z = g(1); Int x = g(5) Printf (“ %d \t %d \t %d \n “, y, z, x);}

44. Example What are the values of gcd(7,21) and gcd(5,3) int gcd(int m, int n) { int r; if (m < n) return gcd(n,m); r = m%n; if (r = = 0) return(n); else return(gcd(n,r));

45. Example Write a recursive function MULT to perform integer multiplication m n using addition operator where n>0.

46. Example int MULT (int m, int n) { int ans; if( n==1 ) ans= m; else ans = m + MULT (m, n-1); return ans; }

47. Sheet The value of x y can be calculated as recursive function Write recursive function called power() that accept real number and integer number as arguments and return the value of x y

48. Sheet Write recursive function called Fact() that applies the factorial of integer N as

49. Organizing a Parade P(1) = 2 P(2) = 3 P(n) = P(n-1) + P(n-2) for n > 2

50. Example Implements the bisection method for approximation a root of a function in interval [Xl, Xu]. Approximation the root within epsilon of a root.

51. Bisection algorithm Compute x_mid = (xl + xu)/2 If f(xl)*f(x_mid) <0 Find root by Bisection (xl, x_mid) Find root by Bisection (x_mid, xu)

52. The Bisection program double Bis (double xl, double xu) { double root, x_mid; x_mid = (xl +xu)/2.0; if ((xu – xl) < epslion) || (f (x_mid)<0.0)) root = x_mid; else if ( f(xl) * f(x_mid)<0.0) root = Bis (xl, x_mid); else root = Bis(x_mid, xu); return root; }

53. Example Write a program that inputs a vector v and call function Normalize to display a corresponding unit vector W where

54. Example Write a program contains function Mystrlen() to find the length of given string

55. Example Write a program to read group of numbers from the user and then average them after stored them in an array and print the result.

56. Recursive Solutions A binary search is recursive Repeatedly halves the collection and determines which half could contain the item Uses a divide and conquer strategy

57. Example ( Hanoi Game) The object of game is to transfer the disks from the leftmost pole to rightmost pole, without ever placing a larger disk on top of a smaller disk. Only one disk may be moved at a time, and each disk must always be placed on one pole.

58. The End