fundamental of programming (c)

Lecturer: Omid Jafarinezhad

Sharif University of TechnologyDepartment of Computer Engineering 1

Fundamental of Programming (C)

Lecture 7Modular programming

Modular programming – Lecture 7


Outline• Introduction to pointer• Introduction to function• User define function

– Function prototype (declaration)– Function definition– Function call and return

• Formal and Actual Parameters• Scope of Identifiers• Storage classes• Recursion



Pointer Fundamentals• When a variable is defined the

compiler (linker/loader actually) allocates a real memory address for the variable– int x;

• When a value is assigned to a variable, the value is actually placed to the memory that was allocated– x=3;

00000000000000000000000000000011

x



Pointers• When the value of a variable is used, the contents in the

memory are used– y=x; will read the contents in the 4 bytes of memory, and

then assign it to variable y• &x can get the address of x (referencing operator &)• The address can be passed to a function:

– scanf("%d", &x);• The address can also be stored in a variable ……



Pointers• To declare a pointer variable

type * pointername;

• For example:– int x, k;– int * p1; //(or p1 is a int pointer)– char *p2; – p1 = &x; /* Store the address in p1 */



Using Pointers• You can use pointers to access the values of other variables, i.e.

the contents of the memory for other variables

• To do this, use the * operator (dereferencing operator)– Depending on different context, * has different meanings

• For example:int n, m=3, *p;p=&m;n=*p;printf("%d\n", n); // 3printf("%d\n",*p); // 3



Using Pointersint i1;int i2;int *ptr1;int *ptr2;

i1 = 1;i2 = 2;

ptr1 = &i1;ptr2 = ptr1;

*ptr1 = 3;i2 = *ptr2;

i1:

i2:0x1000

0x1004

0x1008ptr1:

ptr2:

0x100C

0x1010

0x1014

1

2

0x1000

0x1000

3

3



An Exampleint m=3, n=100, *p, *q;p=&m;printf("m is %d\n",*p); // 3m++;printf("now m is %d\n",*p); // 4

p=&n;printf("n is %d\n",*p); // 100*p=500; printf("now n is %d\n", n); // 500

q=&m;*q = *p;printf("now m is %d\n", m); // 500

q p n m

.... ? ? 100 3q p n m

.... ? 100 3

q p n m

.... ? 100 4*pq p n m

.... ? 100 4*p

q p n m

.... 500 4



Modular Programming• Break a large problem into smaller pieces

– Smaller pieces sometimes called functions

• Why?– Helps manage complexity

• Smaller blocks of code• Easier to read

– Encourages re-use of code• Within a particular program or across different programs

– Allows independent development of code– Provides a layer of ‘abstraction’

Divide and Conquer



Functions - Mathematical View

32)( 2

xxxf

11 is )2(113443)2(2)2()2( 2

ff

f(2)? isWhat

)(xf2 11X Function

Returnedvalue



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

int main(){ …}



Pre-defined library functions • The C standard library is a standardized

collection of header files and library functions, which are used to implement common operations



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, puts, gets

• <time.h>– Defines date and time handling functions– e.g. time, clock

• <stdlib.h>– Defines pseudo-random numbers generation functions– e.g. rand, srand

http://en.wikipedia.org/wiki/C_mathematical_functions

http://en.wikipedia.org/wiki/C_file_input/output

http://en.wikipedia.org/wiki/C_date_and_time_functions

http://en.wikipedia.org/wiki/C_mathematical_functions#stdlib.h



C mathematical functions• double fmod( double x, double y );

– Computes the remainder of the division operation x/y

• double exp( double arg );– Computes the e (Euler's number, 2.7182818) raised to the given power arg

• double log( double arg );– Computes the natural (base e) logarithm of arg

• double log10( double arg );– Computes the common (base 10) logarithm of arg

• double sqrt( double arg );– Computes square root of arg

• double pow( double base, double exp);– Computes the value of base raised to the power exp

http://en.cppreference.com/w/c/numeric/math/fmod

http://en.cppreference.com/w/c/numeric/math/exp

http://en.cppreference.com/w/c/numeric/math/log

http://en.cppreference.com/w/c/numeric/math/log10

http://en.cppreference.com/w/c/numeric/math/sqrt

http://en.cppreference.com/w/c/numeric/math/pow



C mathematical functions• 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)

• overview of math functions in http://en.wikipedia.org/wiki/C_mathematical_functions#stdlib.h

http://en.cppreference.com/w/c/numeric/math/sin

http://en.cppreference.com/w/c/numeric/math/cos

http://en.cppreference.com/w/c/numeric/math/tan





An example#include <stdio.h>#include <math.h>int main(void){ double angle; printf("Input angle in radians: \n"); scanf("%lf", &angle); printf("The sine of the angle is %f\n", sin(angle) ); return 0;}



An example#include <stdio.h>#include <math.h>

int main(void){ double x1,y1,x2,y2, dist; printf("Enter x1 y1 x2 y2 :"); scanf("%lf %lf %lf %lf", &x1, &y1, &x2, &y2);

dist = sqrt(pow((x2-x1),2) + pow((y2-y1),2)); //

printf("Distance is %lf\n", dist); return 0;}



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 32767 /*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

http://en.cppreference.com/w/c/numeric/random/rand

http://en.cppreference.com/w/c/numeric/random/RAND_MAX

http://en.cppreference.com/w/c/numeric/random/srand



http://en.cppreference.com/w/c/numeric/random/rand



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. */}



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. */}


Sharif University of TechnologyDepartment of Computer Engineering 21 21

Random Numbers in [a b]• Generate a random number [0 .. 7]

– x = rand() % 8;

• Generate a random number [10 ..17]– x = 10 + rand() % 8;

• rand() % (b-a+1) + a;



User- definedOR

Programmer-defined function



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;}

double product(double x, double y)

{ double result;

result = x * y; return result; }

A function that calculates the product of two numbers



An Example• Function prototype

– Like a variable declaration• Tells compiler that the function will be defined later• Helps detect program errors• Note semicolon!!

• Function definition– See previous slide– Note, NO semicolon

• Function return– return statement terminates execution of the

current function– Control returns to the calling function– if return expression;

• then value of expression is returned as the value of the function call

• Only one value can be returned this way• Function call

– main() is the 'calling function'– product() is the 'called function'– Control transferred to the function code– Code in function definition is executed

#include <stdio.h>/* function prototype */double product(double x, double y);int main(){ double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); printf("var1 = %.2f\n" "var2 = %.2f\n",var1,var2); printf("var1*var2 = %g\n", ans); return 0;}/* function definition */ double product(double x, double y){ double result; result = x * y; return result;}



Function – An Example• Write a function named 'sum'

– sums two integers– returns the sum

Steps1. Function header

• return data type• function name• argument list with data types

2. Statements in function definition• variable declaration• operations• return value

int sum_int(int x, int y)

{ int result;

result = x + y; return result; }



Formal and Actual Parameters• Formal parameter– Variables declared in the formal list of the function header (written in function prototype &

function definition)

• Actual parameter– Constants, variables, or expression in a function call that correspond to its formal parameter

• The number of actual parameters in a function call must be the same as the number of formal parameters in the function definition

• A one-to-one correspondence must occur among the actual and formal parameters. The first actual parameter must correspond to the first formal parameter and the second to the second formal parameter, an so on

• The type of each actual parameter must be the same as that of the corresponding formal parameter



An Example#include <stdio.h>int calSum(int,int); /*function prototype*/int main(void){

…..…..sum = calSum(num1,num2); /* function call */…..

}int calSum(int val1, int val2) /*function header*/{

………………

}

Formal Parameters

Formal Parameters

Actual Parameters



An Example• If the function requires some arguments to be passed along, then the arguments

need to be listed in the bracket ( ) according to the specified order

void Calc(int, double, char, int);

int main(void) { int a, b; double c; char d; … Calc(a, c, d, b);return (0);}

Function Call



Functions that do not return a value• Use the return type of void

– void functionName( DataType arg_1,…)– void functionName()– void functionName( void)



Function Call – An Example#include <stdio.h>

//function prototype//global variable declaration

int main(void){

local variable declaration;statements;fn1( );fn2( );

return (0);}

void fn1(void){

local variable declaration;statements;

}

void fn2(void){

local variable declaration;statements;return;

}

1

2

3

4



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 functionprintf("User input is: %d", GetUserInput( ));



Receive nothing and return nothing#include <stdio.h>void greeting(void); /* function prototype */

int main(void){

greeting( );greeting( );return(0); // return 0;

}

void greeting(void){

printf("Have fun!! \n");}

Have fun!!Have fun!!Press any key to continue



Receive nothing and return nothing#include <stdio.h>int getInput(void) /* ignore function prototype */{

int number;printf("Enter a number:");scanf("%d",&number);return number;

}int main(void){

int num1, num2, sum;num1 = getInput( );num2 = getInput( );sum = num1 + num2;printf("Sum is %d\n",sum);return(0);

}

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



Receive parameter(s) and return nothing#include <stdio.h>int getInput(void);void displayOutput(int); int main(void){

int num1, num2, sum;num1 = getInput();num2 = getInput();sum = num1 + num2;displayOutput(sum);return(0);

}int getInput(void){

int number;printf("Enter a number:");scanf("%d",&number);return number;

}void displayOutput(int sum){

printf("Sum is %d \n",sum);}

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



Call by value And Call by reference• Call by value

– In this method, only the copy of variable’s value (copy of actual parameter’s value) is passed to the function. Any modification to the passed value inside the function will not affect the actual value

– In all the examples that we have seen so far, this is the method that has been used

• 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

– To do this, we need to have knowledge about pointers and arrays



Call by value – An Example• How are the arguments passed

into functions?– 'Pass by value'– function arguments are

expressions

– In the function call:• Expressions are evaluated and

copies of their values are put into temporary memory locations

• The names of the corresponding parameters in the function definition are made to be the names of the copies

– The values of the expressions in the function call are not changed

#include <stdio.h>double product(double x, double y);

int main(){ int a = 10; double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); printf("var1 = %.2f\n" "var2 = %.2f\n",var1,var2); printf("var1*var2 = %g\n", ans);}/* function definition */ double product(double A, double B) { double result; result = A * B; return result; }



Call by value – An Example#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;

}

Enter two numbers to calculate its sum: 494 + 9 = 13Press any key to continue

? num2

? num1

? sum

4 num2

9 num1

? sum

4 val2

9 val1

? sum

4 val2

9 val1

13 sum

100 val2

9 val1

13 sum

4 num2

9 num1

13 sum

Array and String – Lecture 6


Call by reference#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; // a = 0; !!!!}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); getch(); return 0; /* Exit program. */}

main 5 b

1 a

CalByVal 5 b

1 a

CalByVal 10 b

0 aCalByRef b

a

main -5 b

0 a



Call by reference• Instead of product()

– prod_sum()– How can I get the

function to give both product and sum?

• put * in front of variable name in prototype and function definition

• put & in front of variable names in function call

#include <stdio.h>void prod_sum(double x, double y, double *ptr1, double *ptr2);int main(){ double var1 = 3.0, var2 = 5.0; double prod, sum; prod_sum(var1, var2, &prod, &sum);

printf("var1= %g\n" "var2= %g\n",var1, var2); printf("prod= %g\n" "sum= %g\n", prod, sum);}/* function definition */ void prod_sum(double A, double B, double *rslt_prod, double *rslt_sum) { *rslt_prod = A * B; *rslt_sum = A + B; }



Pointers and Arrays • Recall that the value of an array name is also an address

void main(){

int x[10];ReOrder(x); // ReOrder(&x);

}void ReOrder(int *x){

int i, j, t;for(i = 0; i < 9; i++) for(j = i + 1; i < 10; ++j) if(x[i] < x[j]) { t = x[i]; x[i] = x[j]; x[j] = t; }

}



Organizing Multi-File Programs• A large C program should be divided into multiple files

// main.c#include <stdio.h>void Test(){ // …}int main(){ // … return 0;}

// math.cdouble mathVar;double sin(){ double tempSin; // … return tempSin;}



Identifiers and Scope• Identifier

– The name of a variable, function, label, etc.• int my_var1; /* a variable */• pow_table(); /* a function */• start: /* a label */

• Question:– Does it make a difference where in a program an

identifier is declared?YES! --> concept of ‘scope’



Scope of Identifiers• Scope of a declaration of an identifier

– The region of the program that the declaration is active (i.e., can access the variable, function, label, etc.)

• Five types of scope:– Program (global scope)– File– Function prototype– Function– Block ("between the { } scope")



Scope of Identifiers - Program Scope• Program (global) scope

– if declared outside of all functions

– "Visible" to all functions from point of declaration

– Visible to functions in other source files

– Use only when necessary and then very carefully!!

– If there exist a local variable and a global variable with the same name, the compiler will refer to the local variable

#include <stdio.h>int a = 10;double product(double x, double y);

int main(){ double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); // …}/* function definition */ double product(double x, double y){ double result; a = 20; result = x * y; return result;}

a = 10

a = 20



An Example// File name: main.c#include <stdio.h>int a = 10;

/* function definition */ double product(double x, double y){ double result; // … a = 70; return result;}

int main(){ a = 80;}

// File name: ExternFile.cextern int a = 10;/* function definition */ void TestExtern(){ // … a = 90; // …}



Scope of Identifiers - File Scope• File scope

– Keyword static• Makes variable a ‘visible’

only within this source file– Use file scope to avoid

naming conflict if multiple source files are used

#include <stdio.h>static int a = 10;double product(double x, double y);

int main(){ double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); // …}/* function definition */ double product(double x, double y){ double result; result = x * y; return result;}



An Example// File name: main.c#include <stdio.h>static int a = 10;

/* function definition */ double product(double x, double y){ double result; // … a = 70; return result;}

int main(){ a = 80;}

// File name: ExternFile.cextern int a = 10;/* function definition */ void TestExtern(){ // … a = 90; // …}



• Function prototype scope– Identifiers x and y are not

visible outside the prototype

– Thus, names in the prototype do not have to match names in the function definition

• MUST match types, however!

Scope of Identifiers - Function Prototype Scope#include <stdio.h>double product(double x, double y);

int main(){ int a = 10; double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); printf("var1 = %.2f\n" "var2 = %.2f\n",var1,var2); printf("var1*var2 = %g\n", ans);}/* function definition */ double product(double A, double B) { double result; result = A * B; return result; }



• Function scope– Active from the beginning to the end of a function

Scope of Identifiers - Function Scope

#include <stdio.h>

int main(){ int a; // … return 0;}

int FunctionScopeTest(){ int b; // … return 0;}



Scope of Identifiers - Block Scope• Block (local) scope

– A block is a series of statements enclosed in braces { }

– The identifier scope is active from the point of declaration to the end of the block ( } )

– Nested blocks canboth declare the same variable name and not interfere

#include <stdio.h>double product(double x, double y);

int main(){ int a = 10; double var1 = 3.0, var2 = 5.0; double ans; ans = product(var1, var2); // … }/* function definition */ double product(double x, double y){ double result; // a = 60; Error result = x * y; return result;}



An Example#include <stdio.h>int a = 10;int f1(){ int a; a = 70; { int a;

a = 100; } return a;}

void main(){ a = 80; f1();}

a = 10

a = 80

a = ?

a = 70

a = 100

a = 70



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)



Auto storage class• Variables with automatic storage duration are created

when the block in which they are declared is entered, exist when the block is active and destroyed when the block is exited.

• The keyword auto explicitly declares variables of automatic storage duration. It is rarely used because when we declare a local variable, by default it has class storage of type auto.– int a, b; // is the same as – auto int a, b;



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



Auto - Example#include <stdio.h>void auto_example(void);

int main(void){

int i;

printf("Auto example:\n");

auto_example( );auto_example( );auto_example( );

return(0);

}void auto_example(void){

auto int num = 1;

printf(" %d\n",num);num = num + 2;

}

Auto example:111Press any key to continue



Static - Example#include <stdio.h>void auto_example(void);

int main(void){

int i;

printf("Static example:\n");static_example( );static_example( );static_example( );return(0);

}void static_example(void){

static int num = 1;

printf(" %d\n",num);num = num + 2;

}

Static example:135Press any key to continue



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

– However, if a more complex input is given, a recursive function will divide the problem into 2 (or more) pieces: a part that it knows how to solve and another part that it does not know how to solve

if (stopping case) solve itelse reduce the problem using recursion



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



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 23 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)



Recursion solution of xy

#include <stdio.h>double XpowerY(double, int);int main(void){

double power, x; int y;printf("Enter the value of x and y:\n");scanf("%lf%d", &x, &y);power = XpowerY(x, y);printf("%.2f to the power of %d is %.2f\n\n", x, y, power);return(0);

}double XpowerY(double x, int y){

if (y ==1)return x;

elsereturn x * XpowerY(x, y-1);

}

Enter the value of x and y:232.00 to the power of 3 is 8.00Press any key to continue


Sharif University of TechnologyDepartment of Computer Engineering 61 10-61

How C Maintains the Recursive Steps• C keeps track of the values of variables by the

stack data structure.– Recall that stack is a data structure where the last

item added is the first item processed– There are two operations (push and pop) associated

with stack

abc

bc

dbc

pop push d



How C Maintains the Recursive Steps• Each time a function is called, the execution

state of the caller function (e.g., parameters, local variables, and memory address) are pushed onto the stack

• When the execution of the called function is finished, the execution can be restored by popping up the execution state from the stack



Recursive Steps of xy

#include <stdio.h>double XpowerY(double, int);int main(void){

double power, x; int y;printf("Enter the value of x and y:\n");scanf("%lf%d", &x, &y);power = XpowerY(x, y);printf("%.2f to the power of %d is %.2f\n\n", x, y, power);return(0);

}double XpowerY(double x, int y){

if (y ==1)return x;

elsereturn x * XpowerY(x, y-1);

}

x = 2; y = 4;x * XpowerY(2, 3)

x = 2; y = 3;x * XpowerY(2, 2)

x = 2; y = 2;x * XpowerY(2, 1)

x = 2; y = 2;return x;

2 * 8

2

2 * 2

2 * 4



Factorial• Analysis:

– n!= n * (n-1) * (n-2) * (n-3) * (n-4) ……… * 1– n! could be rewritten as n * (n-1)!– Example: 5! = 5 * 4 * 3 * 2 * 1 = 5 * (4)!, where n = 5– Fact: 0! Or 1! is equal to 1

• Therefore, we could divide this problem into two stages for n!:– Simplest case: if (n <= 1), answer is 1– Recursive case: we need to solve for n * (n-1)!



Factorial#include <stdio.h>double fact(double);int main(void){

double n, result;printf("Please enter the value of n:");scanf("%lf", &n);

result = fact(n);printf(" %.f! = %.2f\n", n, result);return(0);

}double fact(double n){

if (n <= 1)return 1;

elsereturn n * fact(n-1);

}

Enter the value of n: 33! = 6.00Press any key to continue

int fact(int n){ int factres = 1; while(n>1) { factres = factres*n; n--; } return (factres);}



Reuse of factorial function• Write a statement to compute

// Enter X, Z, K, D…y = (fact(X) + fact(Z) * 5) / (fact(K) - fact(D));

!!5!*!

DKZXy



Reuse of factorial function• Write a select function that takes n and k and

computes "n choose k" where

int select(int n, int k){ return fact(n) / (fact(n-k) * fact(k));}

!)!(!kkn

nkn



Fibonacci• Fibonacci Sequence

1, 1, 2, 3, 5, 8, 13, 21, …1st 2nd 3rd 4th 5th 6th 7th 8th

– Fib(1) = 1 defined base case

– Fib(2) = 1 defined base case

– Fib(3) = 2 = 1 + 1– Fib(2) + Fib(1)

– Fib(7) = 13 = 8 + 5– Fib(6) + Fib(5)

• Fib(n) = Fib(n-1) + Fib(n-2)



Fibonacciint Fib (int n){ int temp = 1; /* handles base cases */ if (n > 2)

temp = Fib(n-1) + Fib(n-2); return temp;}

/* Iterative Version */int fibonacci(int k){ int a,b,c,i; if (k <= 1) return 1; else { a = 1; b = 1; i = 2; while (i <= k) {

c = a + b; a = b; b = c; i++;

} return(c); }}



Fibonacci

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 = 5; temp = 1;

temp = Fib(4) + Fib(3);return temp;

x = 1; temp = 1;

return temp;

x = 4; temp = 1;


x = 5; temp = 1;


x = 1; temp = 1;

return temp;x = 1; temp = 1;

return temp;

x = 5; temp = 1;


x = 1; temp = 1;

return temp;

x = 1; temp = 1;

return temp;

x = 5; temp = 1;

temp = 1 + Fib(1);return temp;

x = 5; temp = 1;

temp = 1 + 1;return temp;

x = 4; temp = 1;


x = 4; temp = 1;


x = 5; temp = 1;


x = 5; temp = 1;


x = 5; temp = 1;


x = 5; temp = 1;




Fibonacci

fib(5)

fib(4) fib(3)

fib(3) fib(2)

fib(2) fib(1)

fib(2) fib(1)

1

1

1

12 1

3 2

5int 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;}



Exercise• Write a function to compute logba

# include <math.h>double log_any_base(double a, double b){ return log(a) / log(b);}

baab

10

10

logloglog



Exercise#include <stdio.h>int function1(int x){ x = 2; return(x+1);}int function2(int *x){ *x = 2; return(*x+1);}int main(){ int x = 4, y1, y2; y1 = x + function1(++x); // y1? y2 = ++x + function2(&x); // y2? return 0;}



Exercise• What is the output of the following program

void function2(){ printf("In function 2\n");}void function1(){ function2(); printf("In function 1\n");}

#include <stdio.h>// function prototypes void function3(){ printf("In function 3\n"); function2();}

int main(){ function1(); function3(); return 0;}

In function 2In function 1In function 3In function 2



Exercise• Given radius and height of a cylinder. Write a

function to compute the surface area– A = 2*pi*r*(r*h)

#define PI 3.14double area(double radius, double height){

return 2 * PI * radius * (radius+height);}



Exercise• Write a function to compute the median of 3

numbers x, y and z• Possible order of numbers

– x<y<z -> median y– x<z<y -> median z– y<x<z -> median x– y<z<x -> median z– z<x<y -> median x– z<y<x -> median y

int median(int x, int y, int z){

if (((x < y) && (y < z)) || ((z < y) && (y < x))) return y;

else if (((y < x) && (x < z)) || ((z < x) && (x < y))) return x;

return z;}



Exercise• Recursive Definitions of gcd

– A: Euclid’s algorithm makes use of the fact that gcd(x,y ) = gcd(y, x mod y)

otherwiseif

),mod,gcd(0 ,

),gcd(yxy

yxyx

int gcd (unsigned int x, unsigned int y) { if (y == 0 ) return x; return gcd(y, x % y);}

fundamental of programming (c)

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