lecture 14-16 - sharif university of...

Sharif University of TechnologyDepartment of Computer Engineering 1

Lecture 14-16Arrays

Input and Output – Lecture 4


Introduction

• Suppose, you need to store years of 100 cars. Will you define 100 variables? int y1, y2,…, y100;



IntroductionAlgorithms usually work on large data sets Sort a set of numbers

Search a specific number in a set of numbers

How to read and store a set of data?

To read Repeat the scanf statement

Use the loop statements

To store the data Save each data in a single variable??

3000 int variables! ! ! !



ArrayAn ordered collection of same type variables

A vector of

Integers, chars, floats, …

Example

An array of 8 integer

An array of 5 chars

20 1 3 4 5 6 7

3 1 5 11 10 19 012



ArrayArrays and structures are “static” entities in

that they remain the same size throughout

program execution.



Arrays in CArray declaration in C

<Elements’ Type> <identifier>[<size>]

<Elements’ Type>: int, char, float, …

<size>

Old compilers (standard): it should be constant

New compilers (standard): it can be variable

Elements in array

From 0 to (size – 1)



ArrayAn array is a group of memory locations related by the fact that they all have the same name and the same type.

To refer to a particular location or element in the array, we specify the name of the array and the position number of the particular element in the array.



Exampleint num[20];

num is array of 20 integers

num[0] is the first integer variable

num[19] is the last integer

float farr[100];

farr is array of 100 floats

farr[0] is the first float

farr[49] is the 50th float

farr[99] is the last float


Sharif University of TechnologyDepartment of Computer Engineering 9 9

One-Dimensional Arrays

• Suppose, you need to store years of 100 cars. Will you define 100 variables? int y1, y2,…, y100;

• An array is an indexed data structure to represent several variables having the same data type: int y[100];

y[0] y[1] y[2] … y[k-1] y[k] y[k+1] … y[98] y[99]



One-Dimensional Arrays (cont’d)

• An element of an array is accessed using the array name and an index or subscript,

for example: y[5] which can be used like a variable

• In C, the subscripts always start with 0 and increment by 1, so y[5] is the sixth element

• The name of the array is the address of the first element

y[0] y[1] y[2] … y[k-1] y[k] y[k+1] … y[98] y[99]



Example

int number[10];

int i, j = 3;

i = 5; //-1 < i < 10

number[i] = 0;

number[i + j] = 1;

j = number[i];

j = number[i + 1];

j = number[i] + 1;

//6th number is 0

//??

//?

//?

//?



Array• Generic declaration:

typename variablename[size];– typename is type– variablename is any legal variable name– For example : int a[10];– Defines an array of ints with subscripts ranging from 0 to 9– There are 10*sizeof(int) bytes of memory reserved for this array.

– You can use a[0]=10; x=a[2]; a[3]=a[2]; etc.– You can use scanf("%d",&a[3]);

9876543210

10a



Array Representationint A[3];

A[2]0x1008

A[1]0x1004

A[0]0x1000

A[-1]

All elements of same type – homogenous

First element (index 0)

Last element (index size - 1)

array[0] = 3;

array[2] = 4;

array[10] = 5;

array[-1] = 6;

sizeof(A)?

sizeof(A[0]) = sizeof(A[1]) = sizeof(A[2])?

No bounds checking!

3 * 4 = 12

4



Array-Bounds Checking• C, unlike many languages, does NOT check

array bounds subscripts during:

– Compilation (some C compilers will check literals)

– Runtime (bounds are never checked)

• It is the programmer’s responsibility to ensurethat their programs are correctly written anddebugged!



No Index Out of bound Checking:

There is no index out of bound checking in C, for example the followingprogram compiles fine but may produce unexpected output whenrun.

int main(){

int arr[2];

printf("%d ", arr[3]);printf("%d ", arr[-2]);

return 0;}



Using Constants to Define Arrays

• It is useful to define arrays using constants:

#define MONTHS 12

float a [MONTHS];



Initializing Arrays• Initialization of arrays can be done by a comma

separated list following its definition• For example:

int array [4] = { 100, 200, 300, 400 };

– This is equivalent to:int array [4];array[0] = 100;array[1] = 200;array[2] = 300;array[3] = 400;

• You can also let the compiler figure out the array sizefor you:

int array[] = { 100, 200, 300, 400};



Array InitializationWhen the size if known in compile time

If defined as a local variable (automatic storage class) It is not initialized to any value

i = arr[6]; // i = ?

void func(void){

int arr[50];

int

}

If defined as a global variable (external storage class) All elements are initialized to 0int arr[50];

void func(void){

int i = arr[6]; // i = 0

}



Array Initialization (cont’d)int num[3]={10, 20, 60};

num is the array of 3 integers, num[0] is 10, …

int num[]={40, 50, 60, 70, 70, 80};

num is the array of 6 integers

int num[10]={40, 50, 60};

num is the array of 10 integers

num[0] is 40, num[1] is 50, num[2] is 60

num[3], num[4], ..., num[9]are 0



Array Initialization (cont’d)70};

Compile

int num[2]={40, 50, 60,

/* warning */

3, [4] = 6};int num[5]={[0] =

/* num[5] = {3, 0, 0, 0, 6} */



Array Initialization (cont’d)• this will initialize all

elements to 0:

int myArray[10] = { 0 };

// all elements 0



Array Initialization (cont’d)• Remember that objects with static

storage duration will initialize to

0 if no initializer is specified:

• static int myArray[10];

// all elements 0

Array Examples (Cont.)

• Also, In C, it is not compiler error to initialize an array with more elements than specified size.

• For example the below program compiles fine.

int main()

{

// Array declaration by initializing it with more

// elements than specified size.

int arr[2] = {10, 20, 30, 40, 50};

return 0;

}

28

Assigning values to an array

For loops are often used to assign values to an array

Example:

int list[5], i;

for(i=0; i<5; i++){

list[i] = i;

} list[0]

list[3]

list[4]

list[1]

list[2]

0

1

23

4

list[0]

list[1]

list[2]

list[3]

list[4]

OR

for(i=0; i<=4; i++){

list[i] = i;

}

29

Assigning values to an array

Give a for loop to assign the below values to list

int list[5], i;

for(i=0; i<5; i++){

list[i] = 4-i;

}

list[0]

list[3]

list[4]

list[1]

list[2]

4

3

21

0



Accessing Array ElementsArray elements are accessed by using an integer index. Array index starts with0 and goes till size of array minus 1.

int main(){int arr[5];arr[0] = 5;arr[2] = -10;arr[3/2] = 2; // this is same as arr[1] = 2arr[3] = arr[0];

printf("%d %d %d %d", arr[0], arr[1], arr[2], arr[3]); // 5 2 -10 5

return 0;}



Array Elements• An Example to show that array elements are stored

at contiguous locations

int main(){// an array of 5 integers. If arr[0] is stored at address x,then arr[1] is// stored at x + sizeof(int), arr[2] is stored at x + sizeof(int) + sizeof(int) and so on.

int arr[5], i;printf("Size of integer in this compiler is %u\n", sizeof(int));

for (i=0; i<5; i++)// The use of '&' before a variable name, yields address of variable.printf("Address arr[%d] is %u\n", i, &arr[i]);

return 0;}



Find Maximum• Find maximum value in data array

int data[100], max, i;

for (i=0; i<100; i++)

data[i] = (rand() % 100) + 10;

max = data[0];

for (i=1; i<100; i++){

if (data[i] > max)

max = data[i];

}

printf("Max = %d\n",max);

33

Find average

Find average of values in data array

int data[100], sum, i, avg;

for (i=0; i<100; i++)

data[i] =(rand() % 100) + 10;

sum = 0;

for (i=0; i<100; i++){

sum = sum + data[i];

}

avg = (double)sum/100;

printf(“Avg = %lf\n", avg);



Number of elements greater than average

• After finding the average as shown in previous slide, use the following code

count = 0;

for (i=0; i<100; i++){

if (data[i] > avg)

count++;

}

printf(“%d elements are “

“greater than avg”, count);

35

Find pair sum

Find sum of every pair in data and write into pair array

data[0]=5

data[1]=7

data[2]=15

data[3]=5

…

…

data[98]=3

data[99]=12

pair[0]=12

pair[1]=20

…

pair[49]=15

}

}

}

.

.

.



solution

int data[100], pair[50], i;

for (i=0; i<100; i++)

data[i] = (rand() % 100) + 10;

for (i=0; i<50; i++){

pair[i]= data[2*i] + data[2*i+1];

}

37

Randomly re-shuffle numbers 30 times

data[0]=5

data[1]=7

data[2]=15

data[3]=5

…

…

data[98]=3

data[99]=12

.

.

.

data[0]=12

data[1]=7

data[2]=5

data[3]=15

…

…

data[98]=3

data[99]=5



solution

int data[100], i, j, k, tmp;

for (i=0; i<100; i++)

data[i] = (rand() % 100) + 10;

for (n=0; n<30; n++){

i= rand() % 100;

j= rand() % 100;

tmp = data[i];

data[i] = data[j];

data[j] = tmp;

}

15

#include <stdio.h>

void main(void){

int count[4] = {0};

do{

int num;

scanf("%d", &num);

if(num < 0 ) break;

if(num > 5)

if(num > 7.5)

count[3]++;

else

count[2]++;

else

if(num < 2.5)

count[0]++;

else

count[1]++;

}while(1);

printf("[%d] = %d, [%d] = %d, [%d] = %d, [%d] = %d\n", 0, count[0], 1,count[1], 2, count[2], 3, count[3]);

}

با كه اعداد مجموعهاياز كه برنامهايتعداد بگيردو را ميشود تمام منفي عدد

[0, 2.5), [2.5, 5), [5, 7.5] بازههاي اعداددرآورد. بدست را [7.5, …)



Reverse an array

6 3 1 9 7 2

0 21 3 4 5

2 7 9 1 3 6



Reverse an Array

void reverse(double x[], int n)

{

int i=0, j=n-1;

while (i<j) {

swap(x,i,j);

i = i + 1;

j = j - 1;}

return;

}



int main(){int a[]= {1,2,3,4,5,6};int i;reverse(a,6);for(i=0;i<6;i++)printf("%d",a[i]);

}

void reverse(double x[], int n){

int i=0, j=n-1;while (i<j) {

swap(x,i,j);i = i + 1;j = j - 1;

}return;

}

void swap(int a[],int i, int j){int tmp;

tmp = a[i];a[i] = a[j];

a[j] = tmp;}

43

Print sum of top-bottom pairs

A[0]=3

A[1]=6

…

A[49]=5

A[50]=3

A[98]=4

A[99]=5

+ + +….



Group avg

• Suppose we have a sorted array of hundred grades.

• We want to find the average of top ten, second top ten students etc.

Grade[0]

Grade[1]

….

Grade[9]

Grade[10]

…

Grade[19]

Grade[20]

…

Grade[90]

….

Grade[99]

}}

}



median()

/* values in x must be sorted ! */

double median(double x[], int n)

{

/* Declare variables. */

int k;

double median_x;

/* Determine median of

values in the array. */

k = floor(n/2);

if( n % 2 != 0)

median_x = x[k];

else

median_x = (x[k-1]+x[k])/2;

/* Return median value. */

return median_x;

}

Example:

x[]={7, 9, 15, 27, 29};n=5;median_x=15

x[]={3, 6, 7, 9};

n=4;

median_x=(6+7)/2

median_x=6.5



Initializing Variable Length arraysint n;

scanf("%d", &n);

int num[n]={0}; /* Compile error */

• Variable length arrays cannot be initialized!

• Solution

for(i = 0; i < n; i++)

num[i] = 0;

9

#include <stdio.h>

#define SIZE 20

void main(void){

int number[SIZE];

double average;

int sum, large_size, small_size, i;

}

sum = large_size = small_size = 0;

for(i = 0; i < SIZE; i++){

int tmp;

scanf("%d", &tmp);

number[i] = tmp;

sum += number[i];

}

average

for(i =

= (1.0 * sum) / SIZE;

0; i < SIZE; i++)

if(number[i] >= average)

large_size++;

else

small_size++;

printf("average = %f\n", average);

printf("Small Size = %d, Large Size = %d\n", small_size, large_size);

و بگيرد را عدد برنامهايكه20از كوچكتر و بزرگتر تعداداعداد

كند. حساب ميانگينرا

10

#include <stdio.h>

void main(void){

int n;

printf("Enter n: ", n);

scanf("%d", &n);

int number[n];

double average;

int sum, large_size, small_size, i;

}

sum = large_size = small_size = 0;

for(i = 0; i < n; i++)

scanf("%d", &(number[i]));

for(i =

sum

average

for(i =

0; i < n; i++)

+= number[i];

= (1.0 * sum) / n;

0; i < n; i++)

if(number[i] >= average)

large_size++;

else

small_size++;

printf("average = %f\n", average);

printf("Small Size = %d, Larg Size = %d\n", small_size, large_size);

رشته يك اعدادو تعداد برنامهايكهبزرگترو اعداد تعداد و بگيرد عددراكند. حساب ميانگينرا كوچكتراز



Array Elements in Functionsint number[20];

number[i] is an integer variable

Array element can be used for call by value input

Array element can be use for output

int f(int x);

void h(void){

int arr[50];

in call by value//Array element

arr[30] = f(arr[5]);

}



Arrays in Functions (cont’d)Array cannot be used as output type of

function

int [] f(int x, int y); //compile error

Arrays can be used in input list of functions

Arrays are not passed by Call By Value

Arrays are passed by Call By Reference

If we change array elements in a function

The element is changed in the caller function



Arrays in Functions (version 1)Function arr_func takes an array of integers

int arr_func(int num[90]){

}

or

int arr_func(int num[]){

}

Array a is passed to function arr_func

int a[90];

i = arr_func(a);



main()

{

int a[2]={3, 5};

int c;

c = sum_arr(a, 2)

}

int sum_arr(int b[], int n)

{

int i, sum=0;

for(i=0; i < n; i++)

sum = sum + b[i];

return(sum);

}

a[0]=3

a[1]=5

c=? 8

b=

n=2

i=0 1 2

sum=0 3 8

Exercise



main()

{

int a[2]={3, 5};

int c;

c = sum_arr(a, 2)

}

int sum_arr(int b[], int n)

{

int i, sum=0;

for(i=0; i < n; i++)

sum = sum + b[i];

b[0] = 20;

return(sum);

}

a[0]=3 20

a[1]=5

c=? 8

b=

n=2

i=0 1 2

sum=0 3 8

Exercise

21

#include <stdio.h>

void init_array(int arr[10]){

int i;

for(i = 0; i < 10; i++)

arr[i] = i;

}

void main(void){

int a[10];

init_array(a);

int j;

for(j = 0; j < 10;

printf("a[%d] =

j++)

%d\n", j, a[j]);

}

10طولبهارايهيككهتابعيباراآناعضايوگيردميرا

.ميكندمقداردهي9تا0اعداد



Array Size in Functions

55

If array is an input parameter of a function It cannot find out the size of the array

Array size should be passed from caller function to called function Using definitions

#define SIZE 20

for(int i = 0; i < SIZE; i++)void func(int a[]){

…

Using input variablevoid read(int a[], int size){ for(int i = 0; i < size; i++)

or

void read(int size, int a[size]){

for(int i = 0; i < size; i++)



Array Size in Functions (cont’d) If array is declared in a function It knows the size of the array

It can find out the size of the array using sizeof

void func(void){

int i, a[200];

for(i = 0; i < 200; i++)

a[i] = 0;

or

for(i = 0; i < sizeof(a)/sizeof(a[0]); i++)

a[i] = 0;

}



27

#include <stdio.h>

int max_index(int a[], int size){

int i;

int index = 0;

for(i = 1; i < size; i++)

if(a[i] > a[index])

index = i;

return index;

}

void main(void){

int arr[] = {1, 4, 12, 93,

printf("max index = %d\n",

23};

max_index(arr, 5));

}

محل بگيردو آرايهرا ك ي كه تابعي

برگرداند. آنرا بزرگترينعضو

28

#include <stdio.h>

}

a[], int i, int j){void array_swap(int

int tmp;

tmp = a[i];

a[i] = a[j];

a[j] = tmp;

}

void main(void){

int num[10] = {1, 2, 5, 6};

int x = 2, y = 6;

printf("num[%d] = %d, num[%d] = %d\n", x, num[x], y,

num[y]);

array_swap(num, x, y);

printf("num[%d] = %d, num[%d] = %d\n", x, num[x], y,

num[y]);

آنرا محل دو آرايهو ك ي تابعيكه

كند. جابجا باهم آنهارا بگيردو



#include <stdio.h>

a[], int i, int j){void array_swap(int

int tmp;

tmp = a[i];

a[i] = a[j];

a[j] = tmp;

}

void selection _sort(int a[], int size){

int i, j;

for(i = 0; i < size - 1; i++)

for(j = i + 1; j < size; j++)

if(a[i] < a[j])

array_swap(a, i, j);

}

اعدادصحيح مجموعه مرتبسازي تابع

30

void

}

print(int a[], int size){

int i;

for(i = 0; i < size; i++)

printf("%d ", a[i]);

11, 0};

sizeof(arr[0]);

printf("\n");

}

int main(void){

int arr[] = {1, 7, 3, 7,

int size = sizeof(arr) /

printf("Before sort: ");

print(arr, size);

selection_sort(arr, size);

printf("After sort: ");

print(arr, size);

return 0;



Unordered list – linear search

int search1(int x[], int n, int value)

{

int i;

for(i=0; i < n; i++) {

if (x[i]== value)

return i;

}

return(-1);

}



Ordered list – linear search

int search2(int x[], int n, int value)

{

int i;

for(i=0; i < n; i++) {

if (x[i]== value)

return i;

else if (x[i] > value)

break;

}

return(-1);

}



Binary Searchint end, int a[], intint bsearch(int start,

value){

int mid =

if(a[mid]

return

(start + end) / 2;

== value)

mid;

>= end)else if(start

return -1;

else if(value > a[mid])

bsearch(mid + 1, end, a, value);return

else

return bsearch(start, mid - 1 , a, value);

}



64

Bubble sort • Bubble sort Several passes through the array

– Successive pairs of elements are compared • If increasing order (or identical ), no change• If decreasing order, elements exchanged

– Repeat

• Example:– original: 3 4 2 6 7– pass 1: 3 2 4 6 7– pass 2: 2 3 4 6 7 –



/* Bubble sort code */

#include <stdio.h>

int main()

{

int array[100], n, c, d, swap;

printf("Enter number of

elements\n");

scanf("%d", &n);

printf("Enter %d integers\n", n);

for (c = 0; c < n; c++)

scanf("%d", &array[c]);

for (c = 0 ; c < ( n - 1 ); c++)

{

for (d = 0 ; d < n - c - 1; d++)

{

if (array[d] > array[d+1]) /* For decreasing order use < */

{

swap = array[d];

array[d] = array[d+1];

array[d+1] = swap;

}

}

}

printf("Sorted list in ascending order:\n");

for ( c = 0 ; c < n ; c++ )

printf("%d\n", array[c]);

return 0;

}



Merge two sorted array• Assume we have A and B arrays containing

sorted numbers

• For example– A = { 3, 5, 7, 9, 12}

– B = {4, 5, 10}

• Merge these two arrays as a single sorted array C, for example– C = {3, 4, 5, 5, 7, 9, 10, 12}



Intersection Set

• Suppose we have two sets (groups) represented by A and B

• E.g., A is the set of students taking Math,

B is the set of students taking Science.

• Find set C, the intersection of A and B, i.e., students taking both Math and Science

For each element ID in A

Search that ID in B

if found, put ID into C

3 6 9 17 2

458

Use arrays to represent A and B Hand example

68

6 3 1 9 7 2A 4 2 5 6 1 8B

6 1 2C

i=0 j=0

k=0

j=1 j=3

k=1

i=1j=2

k=2

i=2

i=3

k=3

j=0 j=1 j=2 j=3 j=4 j=5 j=6

j=0 j=1 j=2 j=3 j=4i=4 i=5 i=6



int intersection(int A[],int B[],

int C[], int n)

{

int i=0, j=0, k=0;

for(i=0; i < n; i++) {

for(j=0; j < n; j++) {

if (A[i]==B[j]){

C[k]=A[i];

k++;

break;

}

}

}

return(k);

}

Solution

6 3 1 9 7 2

4 2 5 6 1 8

6 1 2



Multidimensional Arrays• Arrays in C can have virtually as many dimensions as you

want• Definition is accomplished by adding additional subscripts

when it is defined• If element of an array is array itself, it will be

Multidimensional array• For example:

– int a [4] [3] ;• 2-dimensional array• 4 * 3 * sizeof(int)

– int a[4][3][2]• 3-dimention array• 4 * 3 * 2 * sizeof(int)



Multidimensional Arrays Representation

Row 0Row 1Row 2

Column 0 Column 1 Column 2 Column 3

a[ 0 ][ 0 ]

a[ 1 ][ 0 ]

a[ 2 ][ 0 ]

a[ 0 ][ 1 ]

a[ 1 ][ 1 ]

a[ 2 ][ 1 ]

a[ 0 ][ 2 ]

a[ 1 ][ 2 ]

a[ 2 ][ 2 ]

a[ 0 ][ 3 ]

a[ 1 ][ 3 ]

a[ 2 ][ 3 ]

Row subscript

Array name

Column subscript

a[0][0]

a[0][1]

a[0][2]

a[0][3]

a[1][0]

a[1][1]

a[1][2]

a[1][3]

a[2][0]

a[2][1]

a[2][2]

a[2][3]



Examples• Initialization

– Example:

• short b[ 2 ][ 2 ] = { { 1, 2 }, { 3, 4 } };

– If not enough, unspecified elements set to zero

• short b[ 2 ][ 2 ] = { { 1 }, { 3, 4 } };

21

43

01

43



Initializing Multidimensional Arrays• The following initializes a[4][3]:

int a[4] [3] = { {1, 2, 3} , {4, 5, 6} , {7, 8, 9} ,{10, 11, 12} };

• Also can be done by:int a[4] [3] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 };

– is equivalent toa[0][0] = 1;a[0][1] = 2;a[0][2] = 3;a[1][0] = 4;...a[3][2] = 12;



Multidimensional Arraysint t[10][20];

10x20 matrix of integers

t[1][1]; //t[1,1] compile error

Integer variable in location (1,1)



Initializing Multidimensional Arraysint num[2][3]

int num[2][3]

= {1, 2, 0, 3, 4

= {{1, 2, 0},{3,

, 7};

4, 7}};

num[0][2] is ?, num[1][0] is ?

int num[2][3][2] = {{{1,2},{3,4},{5,6}},{{1},{2},{3}}};

num[0][2][1] is ?, num[1][0][1] is ?

int num[5][3] = {{1, 2,0},{3, 4, 7}};

num[0][2] is 0, num[1][0] is 3

num[2][2] is 0, num[1][2] is 7 num[2][2] is ?, num[1][2] is ?

num[1][1] is 2, num[2][0] is 3

num[0][2][1] is 6, num[1][0][1] is 0

int num[][2] = {{1,1},{2,2},{3,3}};

num[1][1] is ?, num[2][0] is ?

Array In Memory

76



Initialization

int i, j, matrix[3][4];

for (i=0; i<3; i++)

for (j=0; j<4; j++)

matrix[i][j] = i;j

0 1 2 3

0

1

2

i

0 0 0 0

1 1 1 1

2 2 2 2

j

0 1 2 3

0

1

2

i

0 1 2 3

0 1 2 3

0 1 2 3

matrix[i][j] = j;



Exercise

0 1 2

1 2 3

2 3 4

3 4 5

• Write the nested loop to initialize a 2D array as follow

int i, j, x[4][3];

for(i=0; i<4; i++)

for(j=0; j<3; j++)

x[i][j] = i+j;



An Example#include <stdio.h>#include <stdlib.h>int main () {

int random1[10][8];int a, b;for (a = 0; a < 10; a++)

for (b = 0; b < 8; b++)random1[a][b] = rand() % 2;

for (a = 0; a < 10; a++){

for (b = 0; b < 8; b++)printf ("%c ", random1[a][b] ? 'x' : 'o');

printf("\n");}

return 0; }



Multidimensional Arrays in FunctionsCan be used as input of functions

All dimensions except the first one must be given

void func(int a[10][20][5]);

Input is a 10x20x5 integer matrix

void func(int a[][20][30], int size);

void func(int size1, int size2, int

a[size1][size2]);

Input is a matrix of integers that both rows and columns are variable



Multidimensional Arrays in FunctionsThe first subscript therefore only indicates the amount of storage that is needed when the array is declared

Others are required because the computer needs to know how far along to increment the pointer for each "row"



37

#include <stdio.h>

}

void displayMatrix (int nRows, int nCols, int matrix[nRows][nCols]){

int row, column;

for ( row = 0; row < nRows; ++row) {

0; column < nCols; ++column )

matrix[row][column]);

for ( column =

printf ("%5i",

printf ("\n");

}

}

7 }, { -2, 1,

int main (void){

int sampleMatrix[3][5] =

{{ 7, 16, 55, 13, 12 }, { 12, 10, 52, 0,

2, 4, 9 }};

printf ("Original matrix:\n");

displayMatrix (3, 5, sampleMatrix);

ماتريس ك ي برايچاپ تابعي

#define

}

SIZE 5

void swap(int a[SIZE][SIZE], int i, int j){

int tmp;

tmp = a[i][j];

a[i][j]

a[j][i]

= a[j][i];

= tmp;

}

void transpose(int a[][SIZE]){

for(i =

int i, j;

0; i < SIZE; i++)

for(j = i; j < SIZE; j++)

swap(a, i, j);

ماتريس ترانهاده محاسبه// Matrix Transpose



2-Dim Arrays as Arguments to Functions

void print_m(int m[][4], int r, int c)

{

int i,j;

for (i=0; i < r; i++) {

for (j=0; j < c; j++)

printf("%.5d ",m[i][j]);

printf("\n");

}

printf("\n");

return;

}

int i, j, matrix[3][4];

for (i=0; i<3; i++)

for (j=0; j<4; j++)

matrix[i][j] = i;

print_m(matrix, 3, 4);

void print_m(int m[3][4], int r, int c)



Matrix sum

• Compute the addition of two matrices

3 0 33

0 6 6 3

2 0 4 4

0 1 2 3

0

1

2

0 1 20

-1 2 4 3

0 -1 3 1

0

1

2

0 1 2 3

+

3 -1 13

1 4 2 0

2 1 1 3

0

1

2

0 1 2 3

=



solution

int matrix1[3][4],

matrix2[3][4],

sum[3][4];

// initialize matrix1 and matrix2

for (i=0; i<3; i++)

for (j=0; j<4; j++)

sum[i][j]= matrix1[i][j]+matrix2[i][j];

Exchange Two Rows

87

4 6 2

0 5 3

0 8 1

2 1 4

4 6 2

2 1 4

0 8 1

0 5 3



Transpose

void transpose(int a[NROWS][NCOLS],

int b[NCOLS][NROWS])

{

/* Declare Variables. */

int i, j;

/* Transfer values to the

transpose matrix. */

for(i=0; i<NROWS; i++) {

for(j=0; j<NCOLS; j++) {

b[j][i] = a[i][j];

}

}

return;

}

1 5 3

4 2 6

1 4

5 2

3 6

b

a



89

Matrix multiplication

double a[3][2], b[2][4], c[3][4];

• Find c = a * b;

x =

3*2 + 4*4=22 3*3 + 4*5=29

2 3 7 1

4 5 6 8

3 4

5 2

1 6

22 29 45 35

18 40 47 21

26 33 43 49

5*2 + 2*4=18

3*7 + 4*6=45 3*1 + 4*8=35

5*3 + 2*5=40 5*7 + 2*6=47 5*1 + 2*8=21

1*2 + 6*4=26 1*3 + 6*5=33 1*7 + 6*6=43 1*1 + 6*8=49

90

Matrix Multiplication cont’d

x =2 3 7 1

4 5 6 8

3 4

5 2

1 6

22 29 45 35

18 40 47 21

26 33 43 49

i=0

i

jj

3 42

4x

j=0

k

k =

c[i][j] =

a[i][k=0]*b[k=0][j] +

a[i][k=1]*b[k=1][j]

0 1 2 3

i

0

1

2

0 1 2 3

0

1

2

91

Matrix Multiplication cont’d

#define N 3

#define M 2

#define L 4

void matrix_mul(a[N][M], int b[M][L], int c[N][L])

{

int i, j, k;

for(i=0; i < N; i++) {

for(j=0; j < L; j++) {

c[i][j] = 0;

for(k=0; k < M; k++) {

c[i][j] = c[i][j] + a[i][k] * b[k][j];

}

}

}

return;

}



Common Bugs & Avoiding them You cannot assign a value to array

int a[4], b[4]; a = b; // Error

Each array name refers to a constant

pointer.

Can’t change where the array name

refers to

But you can change the array elements,

via pointer arithmetic

(int [])

m

???(int)

???(int)

???(int)

???(int)

int m[4];

lecture 14-16 - sharif university of...

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