1. Quiz 2

2. 1 2 3

3. Lecture 9
Function

4. Outline What is Function Function Definition
Standard (Predefined) Functions
User-Defined Functions
Flow of Execution

5. Functions - Mathematical ViewX
Function
Returned value

6. Function Input and Output

7. Example

8. Call power
Call power
power
Call power

9. Function Syntax Function define syntax:
<return type> <function name> (param …) {
<statements> }
param …  <data type> <variable name> , …

10. Example

11. Why we use function Provides a layer of ‘abstraction’
Reduce code line
Use one block of code several time.
Building Programs from Existing Programs
Standard library
For example : stdio, math, rand …
Provides a layer of ‘abstraction’
Helps manage complexity
Smaller blocks of code
Easier to read

12. Why we use function Divide and conquer
Construct a program from smaller pieces or components
Smaller pieces sometimes called function
Each piece more manageable than the original program
Divide and Conquer

13. Functions Every C program starts with main() function
Functions could be
Pre-defined library functions
e.g., printf, sin, tan
Programmer-defined functions
e.g., my_printf, area

14. Pre-defined library functions
<math.h>
Defines common mathematical functions
e.g. sin, cos. sqrt, pow
<stdio.h>
Defines core input and output functions
e.g. printf, scanf
<time.h>
Defines date and time handling functions
e.g. time, clock
<stdlib.h>
Defines pseudo-random numbers generation functions
e.g. rand, srand

15. C mathematical functions
double      pow( double base, double exp);
Computes the value of base raised to the power exp
double      sin( double arg );
Computes sine of arg (representing angle in radians)
double      cos( double arg );
Computes cosine of arg (representing angle in radians)
double      tan( double arg );
Computes tangent of arg (representing angle in radians)
...

16. An example

17. An example

18. Random numbers generation functions
int rand();
Returns a uniformly distributed pseudo-random integral value between ​0​ and RAND_MAX (0 and RAND_MAX included)
RAND_MAX : Expands to an integer constant expression equal to the maximum value returned by the function rand(). This value is implementation dependent.
#define RAND_MAX /*implementation defined*/
srand() should be called before any calls to rand() to initialize the random number generator
void srand( unsigned seed );
Initializes the built-in random number generator used to generate values for rand() with the seed value seed

19. An Example
#include <stdio.h> #include <stdlib.h> int main(void) { unsigned int seed; /* Declare variables. */ int k; /* Get seed value from the user. */ printf("Enter a positive integer seed value: \n"); scanf("%u",&seed); srand(seed); /* Generate and print ten random numbers. */ printf("Random Numbers: \n"); for (k=1; k<=10; k++) printf("%i ", rand()); printf("\n"); return 0; /* Exit program. */ }

20. An Example
#include <stdio.h> #include <stdlib.h> #include <time.h> int main(void) { srand(time(0)); //use current time as seed for random generator /* Generate and print ten random numbers. */ printf("Random Numbers: \n"); for (k=1; k<=10; k++) printf("%i ", rand()); printf("\n"); return 0; /* Exit program. */ }

21. Random Numbers in [a b] Generate a random number [0 .. 7]
x = rand() % 8;
Generate a random number [ ]
x = 10 + rand() % 8;
rand() % (b-a+1) + a;

22. User- defined function

23. Functions in C Queries: Return a value
sin(), fabs()
Commands: do some tasks, do not return any value or we don’t use the value
printf(...)
scanf(...)

24. Functions in C Three steps to use functions in C Function declaration
Introduce the function to compiler
Function definition
What the function does
Function call
Use the function

25. Function Definitions Function definition format
return-value-type function-name( parameter-list ) { declarations and statements }
Function-name: any valid identifier
Return-value-type: data type of the result
void – indicates that the function returns nothing
Parameter-list: comma separated list, declares parameters
A type must be listed explicitly for each parameter
No input: empty parameter list () or void

26. Functions - Definition Structure
Function 'header'
Return data type (if any)
Name
Descriptive
Arguments (or parameter list)
Notice: data type and name
Statements
Variable declaration
Operations
Return value (if any)
type function_name (type arg1, type arg2 ) {
statements; }
A function that calculates the product of two numbers
double product(double x, double y) {
double result;
result = x * y;
return result; }
The function definition declares the return data type, its name, and the data types of its parameters. Any parameter names included in the list are actually ignored by the compiler. The names are included to help document the function. Contrast this with the function prototype.

27. Function Definitions Function definition format (continued)
return-value-type function-name( parameter-list ) { declarations and statements }
Declarations and statements: function body (block)
Variables can be declared inside blocks
Functions can not be defined inside other functions

28. Producing output Function definition format (continued)
return-value-type function-name( parameter-list ) { declarations and statements }
Query functions
Produce output
To produce an output
Declare output type
Generate the output by return

29. The return command To generate a result by a function
return <value>;
return <expression>;
Only one value can be returned
If noting returned
return;
Or until reaches right brace

30. The return command return finishes running the function
Function can have multiple return
Only one of them runs each time
The type of the returned value = the result type
Otherwise, cast

31. Functions that do not return a value
Use the return type of void
void functionName( DataType arg_1,…)
void functionName()
void functionName( void)

32. Function call Command function Query function
<function name> (inputs);
Query function
<variable> = <function name>(inputs);
Inputs should match by function definition
Functions are called by another function
Function call comes inside in a function

33. Example void my_info(void){
printf("My name is Ahmad Ahmadi\n"); printf("My student number: \n"); }
int main(void){ my_info();
printf(" \n");
my_info(); return 0;

34. Function Call – An Example
If the function returns a value, then the returned value need to be assigned to a variable so that it can be stored
int GetUserInput (void); /* function prototype*/
int main(void) {
int input;
input = GetUserInput( );
return(0); /* return 0; */ }
However, it is perfectly okay (syntax wise) to just call the function without assigning it to any variable if we want to ignore the returned value
We can also call a function inside another function
printf("User input is: %d", GetUserInput( ));

35. N = f(pi*pow(r,2), b+c) + d;
Using Functions
Let int f(double x, int a) be (the beginning of) a declaration of a function.
Then f(expr1, expr2) can be used,
N = f(pi*pow(r,2), b+c) + d;

36. Using Functions (continued)
This is a parameter
Let int f(double x, int a) be (the beginning of) a declaration of a function.
Then f(expr1, expr2) can be used ,
N = f(pi*pow(r,2), b+c) + d;
This is an argument
This is also an argument

37. Quick review Define a function:
<return type> <function name>(<param> …) {
<Statement> … }
<param>  <data type> <value name> , …

38. Quick review
If in function execute return, function will be terminate.
Function data type and return type must be same.
If function type be void, can be use return; to terminate function.

39. Quick review In order to call a function:
<function name>(<param> …);

40. Example

41. Example Enter a number: 5 Enter a number: 4 Sum is 9
Press any key to continue

42. Example

43. Example

44. Example

45. Example

46. Example

47. Example

48. Definitions
Parameter:– a declaration of an identifier within the '()' of a function declaration
Used within the body of the function as a variable of that function
Argument:– an expression passed when a function is called; becomes the initial value of the corresponding parameter

49. Scope of variables

50. Scope of Variables Until now, Variables Scope of variable
Are declared in the start of functions
Are used any where in the function after declaration
Can we used them outside of function?
Can we used them in other functions?
Scope of variable
A range of code that the variable can be used
 Variable cannot be used outside of its scope
Compile error

51. Scopes vs. Blocks Scopes are determined by Blocks Variables
Start with { and finished by }
Example: statements of a function, statement of a
if or while, …
Variables
Can be declared in a block
Can be used in the declared block
Cannot be used outside the declared block
The Declared block is the scope of the variable

52. Example

53. Nested Scopes/Blocks Scopes can be nested
Example: Nested if, nested for, …

54. Variables in Nested Blocks
All variables from outer block can be used inner blocks
Scope of outer block contains the inner block
Variables in inner block cannot be used in outer block
Scope of the inner block does not contains the outer block

55. Example

56. Same Variables in Nested Block
If a variable in inner block has the same identifier of a variable in outer block
The inner variable hides the outer variable
Changing inner variables does not change outer variable

57. Local Variables
All defined variables in a function are the local variable of the function
Can ONLY be used in the function, not other functions

58. Global Variables Global variables are defined outside of all functions
Global variables are initialized to zero
Global variables are available to all subsequent functions

59. Example

60. Example

61. Argument Passing

62. Argument Passing In C language we study two type of argument passing.
Pass by value
Pass by reference

63. Call by value In call by value mechanism
The values are copied to the function
Only the copy of variable’s value (copy of actual parameter’s value) is passed to the function.
If we change values in the function
The copied version is changed
The original value does not affected
Any modification to the passed value inside the function will not affect the actual value

64. Example
Enter two numbers to calculate its sum: 4 9
4 + 9 = 13
Press any key to continue
#include <stdio.h> int calSum(int,int); /*function protototype*/ int main(void) { int sum, num1, num2; printf("Enter two numbers to calculate its sum:\n"); scanf("%d%d",&num1,&num2); sum = calSum(num1,num2); /* function call */ printf("\n %d + %d = %d", num1, num2, sum); return(0); } int calSum(int val1, int val2) /*function definition*/ int sum; sum = val1 + val2; val2 = 100; return sum; 4
num2 9
num1 13
sum 4
num2 9
num1 ?
sum ?
num2
num1
sum
100
val2 9
val1 13
sum 4
val2 9
val1 13
sum 4
val2 9
val1 ?
sum

65. Call by reference Call by reference
In this method, the reference (memory address) of the variable is passed to the function. Any modification passed done to the variable inside the function will affect the actual value

66. Call by reference 10 b a 5 b 1 a b a main -5 b a main 5 b 1 a CalByVal
#include <stdio.h> void CalByVal(a, b) { a = 0; b = 10; } void CalByRef(int *a, int *b) // CalByRef(int *p, int *q) *a = 0; *b = -5; int main(void) int a = 1, b = 5; printf("Before cal CalByVal: a = %d, b = %d\n", a, b); CalByVal(a, b); printf("After cal CalByVal: a = %d, b = %d\n", a, b); printf("Before cal CalByRef: a = %d, b = %d\n", a, b); CalByRef(&a, &b); printf("After cal CalByRef: a = %d, b = %d\n", a, b); return 0; /* Exit program. */
CalByVal 10 b a
CalByVal 5 b 1 a
CalByRef b a
main -5 b a
main 5 b 1 a

67. Recursive function

68. Recursion
Recursion is a technique that solves a problem by solving a smaller problem of the same type
A recursive function is a function invoking itself, either directly or indirectly
Recursion: A → B → C → D → A
Concept of recursive function (generally):
A recursive function is called to solve a problem
The function only knows how to solve the simplest case of the problem. When the simplest case is given as an input, the function will immediately return with an answer
if (stopping case)
solve it
else
reduce the problem using recursion

69. Recursion Recursive Algorithm
An algorithm uses itself to solve the problem
There is a basic problem with known solution
Recursive Algorithms are implemented by recursive functions
Recursive function
A function which calls itself
There is a condition that it does not call itself

70. Recursion
Any problem that can be solved recursively can also be solved iteratively (using loop)
Recursive functions are slow and takes a lot of memory space compared to iterative functions
So why bother with recursion? There are 2 reasons:
Recursion approach more naturally resembles the problem and therefore the program is easier to understand and debug
Iterative solution might not be apparent

71. An Example: xy
In this example, we want to calculate x to the power of y
i.e. xy
If we analyze the formula for xy, we could see that xy could be written as (x being multiplied to itself, y times)
An example is 24, which can be written as
24 = 2 x 2 x 2 x 2 (in this case, x = 2, y = 4)
24 could also be rewritten as
24 = 21 x where 21 = 2 (i.e the number itself)
Therefore, we could divide the problem into two stage:
Simplest case: when y = 1, the answer is x
Recursive case, we need to solve for x * x(y-1)

72. Introduction Factorial GCD n! = n x n-1 x … x 2 x 1
GCD(a, b) = Euclidean Algorithm
GCD(a, b) = GCD(b, a mod b)
There is a simple (basic) problem which we can solve it directly (without recursion)
Factorial: 1! = 1
GCD: b == 0

73. Fibonacci solution

74. Fibonacci x = 5; temp = 1; temp = 1 + Fib(1); return temp;
temp = Fib(2) + Fib(1);
return temp;
x = 5; temp = 1;
temp = ;
return temp;
x = 5; temp = 1;
temp = 1 + Fib(1);
return temp;
x = 1; temp = 1;
return temp;
x = 5; temp = 1;
temp = 1 + Fib(1);
return temp;
x = 5; temp = 1;
temp = Fib(2) + Fib(1);
return temp;
x = 5; temp = 1;
temp = ;
return temp;
int Fib (int x) {
/* handles base cases of */
/* Fib(1) and Fib(2) */
int temp = 1;
if (x > 2) /* other cases */
temp = Fib(x-1) + Fib(x-2);
return temp; }
x = 4; temp = 1;
temp = 2 + 1;
return temp;
x = 4; temp = 1;
temp = 2 + Fib(2);
return temp;
x = 4; temp = 1;
temp = Fib(3) + Fib(2);
return temp;
x = 5; temp = 1;
temp = 3 + 2;
return temp;
x = 5; temp = 1;
temp = Fib(4) + Fib(3);
return temp;
x = 5; temp = 1;
temp = 3 + Fib(3);
return temp;

75. Fibonacci 5 fib(5) fib(3) fib(4) fib(3) fib(2) fib(2) fib(1) fib(2)
int Fib (int n) {
/* handles base cases of */
/* Fib(1) and Fib(2) */
int temp = 1;
if (n > 2) /* other cases */
temp = Fib(n-1) + Fib(n-2);
return temp; }
fib(5) 3 2
fib(3)
fib(4) 1 1 2 1
fib(3)
fib(2)
fib(2)
fib(1) 1 1
fib(2)
fib(1)

76. Print Right to Left Example

77. Print Left to Right Example

78. Recursion solution of xy

79. Factorial solution

80. GCD solution

81. Indirect recursion What we have seen are direct recursion
A function calls itself directly
Indirect recursion
A function calls itself using another function
Example:
Function A calls function B
Function B calls function A

82. Example

83. Storage Class

84. Storage Classes Storage class(Refers to the lifetime of a variable)
How memory is allocated for the variable
Until when the variable exists
How it is initialized
Storage classes in C
 Automatic
External
 Static
Register

85. Storage Classes Refers to the lifetime of a variable
Local variables only exist within a function by default. When calling a function repeatedly, we might want to
Start from scratch – reinitialize the variables
The storage class is ‘auto’
Continue where we left off – remember the last value
The storage class is ‘static’
Another two storage classes (seldomly used)
register (ask to use hardware registers if available)
extern (global variables are external)

86. Syntax storage_classes variable_type variable_name Example: int auto
float
double
char
auto
register
static
extern
Example:

87. Storage Classes: Automatic
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

88. Example
Auto example: 1
Press any key to continue

89. Storage Classes: External
All global variables are external by default
Are generated when program starts
Are destroyed when program finishes
Usage of keyword “extern”
To use global variables in other files
To emphasize that variable is global
This usage is optional

90. Storage Classes: Static
Keyword “static” comes before them
For local variables:
1) Generated in the first run of the block
2) Destroyed when program finishes
3) Initialized
If no value  initialized by 0
Only initialized in the first run of the block

91. Static storage class
However the static keyword can be applied to a local variable so that the variable still exist even though the program has gone out of the function. As a result, whenever the program enters the function again, the value in the static variable still holds

92. Example
Static example: 1 3 5
Press any key to continue

93. Storage Classes: Register
Keyword “register” comes before them
Can be used for local variables
Compiler tries to allocated the variable in registers of CPU
But does not guaranteed
Registers are very fast and small memories
Improve performance