1. Lecture 10
Arrays

2. Introduction
Suppose, you need to store years of 100 cars. Will you define 100 variables?

3. Introduction Algorithms 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! ! ! !

4. Example
Write a program that get 10 number from user, then sort them. Finally write sorted numbers.

5. Array An ordered collection of same type variables A vector of
Integers, chars, floats, …
Example
An array of 8 integer
0 1 2
3 4 5 6 7 3 1 5 11 10 19 12
An array of 5 chars

6. Arrays in C Array 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)
Usage  <identifier>[index]

7. 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]

8. One-Dimensional Arrays (cont’d)
An element of an array is accessed using the array name and an index or subscript,
for example: y[2] 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]

9. Example int 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

10. Example

11. Array
Arrays and structures are “static” entities in that they remain the same size throughout program execution.

12. Example int number[10]; int i, j = 3; i = 5; //-1 < i < 10
number[i + j] = 1;
j = number[i];
j = number[i + 1];
j = number[i] + 1;
//6th number is 0
//??
//?

13. Array in memory 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]); 9 8 7 6 5 4 3 2 1 10 a

14. Array Representation int A[3]; A[2] 0x1008 A[1] 0x1004 A[0] 0x1000
All elements of same type – homogenous
Last element (index size - 1)
First element (index 0)
array[0] = 3;
array[2] = 4;
array[10] = 5;
array[-1] = 6;
No bounds checking!

15. 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 ensure that their programs are correctly written and debugged!

16. No Index Out of bound Checking:
There is no index out of bound checking in C, for example the following program compiles fine but may produce unexpected output when run.

17. Using Constants to Define Arrays
It is useful to define arrays using constants:
#define MONTHS 12
float a [MONTHS];
What is #define advantages?
We can use const instead of #define.

20. 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 size for you:
int array[] = { 100, 200, 300, 400};

21. Array Initialization When the size if known in compile time
If defined as a local variable (automatic storage class)
It is not initialized to any value
If defined as a global variable (external storage class)
All elements are initialized to 0

22. Array Initialization (cont’d)
Remember that objects with static storage duration will initialize to 0 if no initializer is specified:

23. Assigning values to an array
Give a for loop to assign the below values to list
list[0]
list[3]
list[4]
list[1]
list[2] 4 3 2 1

24. Accessing Array Elements
Array elements are accessed by using an integer index. Array index starts with 0 and goes till size of array minus 1.

25. Array Elements
An Example to show that array elements are stored at contiguous locations

26. Find Maximum
Find maximum value in data array

27. Find average
Find average of values in data array

28. Number of elements greater than average
After finding the average as shown in previous slide, use the following code

29. } } } Find pair sum data[0]=5 pair[0]=12 data[1]=7 pair[1]=20
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 } . }

30. solution

31. 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 .

32. solution

33. Reverse an array 1 2 3 4 5 6 3 1 9 7 2 2 7 9 1 3 6

34. Reverse an Array

35. Print sum of top-bottom pairs…
A[49]=5
A[50]=3
A[98]=4
A[99]=5 + + + ….

36. } } } Group avg Suppose we have a sorted array of hundred grades.….
Grade[9]
Grade[10] …
Grade[19]
Grade[20]
Grade[90]
Grade[99]
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. }

37. Initializing Variable Length arrays

38. ﻭ ﺩﺮﻴﮕﺑ ﺍﺭ ﺩﺪﻋ 20 ﻪﻛ ﻱﺍﻪﻣﺎﻧﺮﺑ ﺯﺍ ﺮﺘﻜﭼﻮﻛ ﻭ ﺮﺘﮔﺭﺰﺑ ﺩﺍﺪﻋﺍ ﺩﺍﺪﻌﺗ 9
#include <stdio.h>
#define SIZE 20 void main(void){
int number[SIZE]; double average;
int sum, large_size, small_size, i;
ﻭ ﺩﺮﻴﮕﺑ ﺍﺭ ﺩﺪﻋ 20 ﻪﻛ ﻱﺍﻪﻣﺎﻧﺮﺑ
ﺯﺍ ﺮﺘﻜﭼﻮﻛ ﻭ ﺮﺘﮔﺭﺰﺑ ﺩﺍﺪﻋﺍ ﺩﺍﺪﻌﺗ
.ﺪﻨﻛ ﺏﺎﺴﺣ ﺍﺭ ﻦﻴﮕﻧﺎﻴﻣ
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++)
C99 also has support for variable length arrays on the stack
Also, note that the stack is usually much more limited; it's not certain you can allocate very large arrays there
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); }

39. ﻪﺘﺷﺭ ﻚﻳ ﻭ ﺩﺍﺪﻋﺍ ﺩﺍﺪﻌﺗ ﻪﻛ ﻱﺍﻪﻣﺎﻧﺮﺑ ﻭ ﺮﺘﮔﺭﺰﺑ ﺩﺍﺪﻋﺍ ﺩﺍﺪﻌﺗ ﻭ ﺩﺮﻴﮕﺑ ﺍﺭ ﺩﺪﻋ
#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; 10
ﻪﺘﺷﺭ ﻚﻳ ﻭ ﺩﺍﺪﻋﺍ ﺩﺍﺪﻌﺗ ﻪﻛ ﻱﺍﻪﻣﺎﻧﺮﺑ
ﻭ ﺮﺘﮔﺭﺰﺑ ﺩﺍﺪﻋﺍ ﺩﺍﺪﻌﺗ ﻭ ﺩﺮﻴﮕﺑ ﺍﺭ ﺩﺪﻋ
.ﺪﻨﻛ ﺏﺎﺴﺣ ﺍﺭ ﻦﻴﮕﻧﺎﻴﻣ ﺯﺍ ﺮﺘﻜﭼﻮﻛ
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); }

40. Arrays and Functions

41. Array Elements in Functions
int 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

42. 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

43. Arrays in Functions (version 1)

44. Exercise
a[0]=3
a[1]=5
c=? 8 b=
n=2 i=
sum=

45. Exercise
a[0]=3 20
a[1]=5
c=? 8 b=
n=2 i=
sum=

46. تابعی که یک ارایه به طول 10 را می گیرد و اعضای آن را با اعداد 0 تا 9 مقداردهی میکند. 

47. Array Size in Functions
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

48. 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

49. ﻞﺤﻣ ﻭ ﺩﺮﻴﮕﺑ ﺍﺭ ﻪﻳﺍﺭﺁ ﻚﻳ ﻪﻛ ﻲﻌﺑﺎﺗ
.ﺪﻧﺍﺩﺮﮔﺮﺑ ﺍﺮﻧﺁ ﻮﻀﻋ ﻦﻳﺮﺘﮔﺭﺰﺑ

50. Search function
Liner search
Binary search

51. Unordered list – linear search

52. Ordered list – linear search

53. Binary Search
Key = 76

54. Binary Search

55. Sort function
Selection Sort
Bubble Sort

56. Selection Sort

57. Implementation

58. 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

59. Bubble Sort

60. Bubble Sort

61. Bubble Sort

62. Bubble Sort

63. Bubble Sort

64. Bubble Sort

65. Bubble Sort

66. Bubble Sort

67. Bubble Sort

68. Bubble Sort

69. Bubble Sort

70. Bubble Sort

71. Bubble Sort

72. Bubble Sort

73. Bubble Sort

74. Bubble Sort

75. Bubble Sort

76. Bubble Sort

77. Bubble Sort

78. Bubble Sort

79. Bubble Sort

80. Bubble Sort

81. Bubble Sort

82. Implementation

83. 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}

84. Solution

85. 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 4 5 8

86. Use arrays to represent A and B Hand example6 3 1 9 7 2 4 2 5 6 1 8 B
i=0
i=1
j=0
j=3
i=2
i=3
i=4
i=5
i=6
j=1
j=2
j=6
j=1
j=2
j=3
j=4
j=5
j=0
j=1
j=2
j=3
j=4
j=0
k=0
k=1
k=2
k=3 6 1 2 C

87. Solution 6 3 1 9 7 2 4 5 8

88. 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)

89. Multidimensional Arrays Representation
Row 0
Row 1
Row 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

90. 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 } }; 2 1 4 3 1 4 3

91. 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 to
a[0][0] = 1;
a[0][1] = 2;
a[0][2] = 3;
a[1][0] = 4;
...
a[3][2] = 12;

92. Multidimensional Arrays
int t[10][20];
10x20 matrix of integers
t[1][1];
//t[1,1] 
compile
error
Integer variable in location (1,1)

93. Initializing Multidimensional Arrays
int num[2][3]
= {1, 2, 0, 3, 4
= {{1, 2, 0},{3,
, 7};
4, 7}};
 num[0][2] is 0, num[1][0] is 3
 num[0][2] is ?, num[1][0] is ?
int num[5][3] = {{1, 2,0},{3, 4, 7}};
 num[2][2] is ?, num[1][2] is ?
 num[2][2] is 0, num[1][2] is 7
int num[2][3][2] = {{{1,2},{3,4},{5,6}},
{{1},{2},{3}}};
 num[0][2][1] is 6, num[1][0][1] is 0
 num[0][2][1] is ?, num[1][0][1] is ?
int num[][2] = {{1,1},{2,2},{3,3}};
 num[1][1] is ?, num[2][0] is ?
 num[1][1] is 2, num[2][0] is 3

94. Array In Memory

95. Initialization j i j i 1 2 1 2 3 matrix[i][j] = j; 0 1 2 3 1 2 0 1 2 3 1 2 i j 1 2 i 1 2 1 2 3

96. Exercise Write the nested loop to initialize a 2D array as follow 1 21 2 3 4 5

97. An Example

98. Multidimensional Arrays in Functions
Can 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

99. Multidimensional Arrays in Functions
The 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"

100. #include <stdio.h>37
#include <stdio.h>
void displayMatrix (int nRows, int nCols, int matrix[nRows][nCols]){
int row, column;
for ( row = 0; row < nRows; ++row) {
for ( column = printf ("%5i",
printf ("\n");
0; column < nCols; ++column ) matrix[row][column]); }
ﺲﻳﺮﺗﺎﻣ ﻚﻳ پﺎﭼ ﻱﺍﺮﺑ ﻲﻌﺑﺎﺗ }
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);
7 }, { -2, 1, }

101. ﺲﻳﺮﺗﺎﻣ ﻩﺩﺎﻬﻧﺍﺮﺗ ﻪﺒﺳﺎﺤﻣ
#define
SIZE 5
ﺲﻳﺮﺗﺎﻣ ﻩﺩﺎﻬﻧﺍﺮﺗ ﻪﺒﺳﺎﺤﻣ
// Matrix Transpose
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]){
int i, j;
0; i
for(i =
< SIZE;
i++)
for(j
= i; j < SIZE;
j++)
swap(a,
i, j); }

102. 2-Dim Arrays as Arguments to Functions
void print_m(int m[3][4],
int r, int c)
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"); }
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);

103. Matrix sum Compute the addition of two matrices + = 0 1 2 3 0 1 2 3 1 2 3 -1 3 1 3 3 3 + -1 2 4 3 1 4 2 = 6 6 3 1 1 1 -1 3 1 2 1 1 3 2 4 4 2 2 2

104. 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];

105. Exchange Two Rows 4 6 2 5 3 8 1 4 6 2 1 8 5 3

106. Transpose 1 5 3 4 2 6 1 4 5 2 3 6 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; a 1 5 3 4 2 6 b 1 4 5 2 3 6

107. Matrix multiplication
double a[3][2], b[2][4], c[3][4];
Find c = a * b; 3 4 5 2 1 6 22 29 45 35 18 40 47 21 26 33 43 49 2 3 7 1 4 5 6 8 = x
3*2 + 4*4=22
3*3 + 4*5=29
3*7 + 4*6=45
3*1 + 4*8=35
5*2 + 2*4=18
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

108. Matrix Multiplication cont’dj j 22 29 45 35 18 40 47 21 26 33 43 49 3 4 5 2 1 6 1 2 1 2 2 3 7 1 4 5 6 8 = x i i
j=0
c[i][j] =
a[i][k=0]*b[k=0][j] +
a[i][k=1]*b[k=1][j] 2 4 3 4 k =
i=0 x k

109. 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;

110. 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 [])
???
(int)
???
(int)
???
(int)
???
(int)
int m[4]; m