Its By Me . . .

1. Sunawar Khan Ahsan
MS(CS)
IIUI
ARRAYS

2. ARRAYS & Matrices
SK Ahsan
WHAT IS ARRAYS?
 An array is a group of consecutive memory locations
with same name and data type.
 Simple variable is a single memory location with
unique name and a type. But an Array is collection of
different adjacent memory locations. All these
memory locations have one collective name and type.
 The memory locations in the array are known as
elements of array. The total number of elements in the
array is called length.
 The elements of array is accessed with reference to
its position in array, that is call index or subscript.

3. ARRAYS & Matrices
SK Ahsan
WHAT IS AN ARRAY?
■ We refer to all stored values in an array by its
name
■ If we would like to access a particular value
stored in an array, we specify its index (i.e. its
position relative to the first array value)
– The first array index is always 0
– The second value is stored in index 1
– Etc.

4. ARRAYS & Matrices
SK Ahsan
WHAT IS AN ARRAYS?
■ Arrays
– Structures of related data items
– Static entity (same size throughout
program)
■ A few types
– Pointer-based arrays (C-like)
– Arrays as objects (C++)

5. ARRAYS & Matrices
SK Ahsan
What is an Array
■ We are interested in one-dimensional arrays
■ An array has a fixed number of elements and all
elements are of the same type
■ Each box has an index which in java and C++ starts
with 0
■ Here is an array which holds the ages of 10 people
0 1 2 3 4 5 6 7 8 9
32 34 56 32 12 67 21 34 21 45

6. ARRAYS & Matrices
SK Ahsan
Examples of Arrays
■ Draw an array of 20 elements which contains
student marks – what type will it be ?
■ Draw an array of 15 elements which contains
student grades ranging form A-E – what type
will it be?

7. ARRAYS & Matrices
SK Ahsan
Advantages / Uses of Arrays
■ Arrays can store a large number of value with single name.
■ Arrays are used to process many value easily and quickly.
■ The values stored in an array can be sorted easily.
■ The search process can be applied on arrays easily.

8. ARRAYS & Matrices
SK Ahsan
Types of Arrays:
–One-Dimensional Array
–Two-Dimensional Array
–N-Dimensional Array

9. ARRAYS & Matrices
SK Ahsan
One-D Array
A type of array in which all elements are arranged in the form of a list is known as 1-D array or
single dimensional array or linear list.
Declaring 1-D Array:
data_type identifier[length]; e.g: int marks[5];
o Data _type: Data type of values to be stored in the array.
o Identifier: Name of the array.
o Length: Number of elements.

10. ARRAYS & Matrices
SK Ahsan
ARRAY INITIALIZATION
■ Initializing arrays
– For loop
■ Set each element
– Initializer list
■ Specify each element when array declared
int n[ 5 ] = { 1, 2, 3, 4, 5 };
■ If not enough initializers, rightmost elements 0
■ If too many syntax error
– To set every element to same value
int n[ 5 ] = { 0 };
– If array size omitted, initializers determine size
int n[] = { 1, 2, 3, 4, 5 };
■ 5 initializers, therefore 5 element array

11. ARRAYS & Matrices
SK Ahsan
One-D array Intialization
The process of assigning values to array elements at the time of array declaration is called array
initialization.
Syntax:
data_type identifier[length]={ List of values }; e.g: int marks[5]={70,54,82,96,49};
o Data _type: Data type of values to be stored in the array.
o Identifier: Name of the array.
o Length: Number of elements
o List of values: Values to initialize the array. Initializing values must be constant
70 54 82 96 49

12. ARRAYS & Matrices
SK Ahsan
Accessing element of array
■ Individual Element:
Array_name[index];
■ Using Loop:
int marks[5];
for(int i=0;i<=4;i++)
marks[i]=i;

13. ARRAYS & Matrices
SK Ahsan
INITIALIZE AND ACCESS INDIVIDUAL INDEX
// This program displays the number of days in each month.
// It uses a 12-element int array.
#include <iostream.h>
void main(void)
{
int days[12];
days[0] = 31; // January
days[1] = 28; // February
days[2] = 31; // March
days[3] = 30; // April
days[4] = 31; // May
days[5] = 30; // June
days[6] = 31; // July

14. ARRAYS & Matrices
SK Ahsan
Cont…
days[7] = 31; // August
days[8] = 30; // September
days[9] = 31; // October
days[10] = 30; // November
days[11] = 31; // December
for (int count = 0; count < 12; count++)
{
cout << "Month " << (count + 1) << " has ";
cout << days[count] << " days.n";
}
}

15. ARRAYS & Matrices
SK Ahsan
Output
Month 1 has 31 days.
Month 2 has 28 days.
Month 3 has 31 days.
Month 4 has 30 days.
Month 5 has 31 days.
Month 6 has 30 days.
Month 7 has 31 days.
Month 8 has 31 days.
Month 9 has 30 days.
Month 10 has 31 days.
Month 11 has 30 days.
Month 12 has 31 days.

16. ARRAYS & Matrices
SK Ahsan
PARTIAL ARRAY INITIALIZATION
// This program displays the number of days in each month.
// It uses a 12-element int array.
#include <iostream.h>
void main(void)
{
int days[12] = {31, 28, 31, 30,
31, 30, 31, 31,
30, 31, 30, 31};
for (int count = 0; count < 12; count++)
{
cout << "Month " << (count + 1) << " has ";
cout << days[count] << " days.n";
}
}

17. ARRAYS & Matrices
SK Ahsan
OUTPUT
Month 1 has 31 days.
Month 2 has 28 days.
Month 3 has 31 days.
Month 4 has 30 days.
Month 5 has 31 days.
Month 6 has 30 days.
Month 7 has 31 days.
Month 8 has 31 days.
Month 9 has 30 days.
Month 10 has 31 days.
Month 11 has 30 days.
Month 12 has 31 days.

18. ARRAYS & Matrices
SK Ahsan
Print ASCII Values
// This program uses an array of ten characters to store the
// first ten letters of the alphabet. The ASCII codes of the
// characters are displayed.
#include <iostream.h>
void main(void)
{
char letters[10] = {'A', 'B', 'C', 'D', 'E',
'F', 'G', 'H', 'I', 'J'};
cout << "Character" << "t" << "ASCII Coden";
cout << "--------" << "t" << "----------n";
for (int count = 0; count < 10; count++)
{
cout << letters[count] << "tt";
cout << int(letters[count]) << endl;
}
}

19. ARRAYS & Matrices
SK Ahsan
Output
Character ASCII Code
--------- ----------
A 65
B 66
C 67
D 68
E 69
F 70
G 71
H 72
I 73
J 74

20. ARRAYS & Matrices
SK Ahsan
// Histogram printing program.
#include <iostream>
#include <iomanip>
using std::setw;
int main() {
const int arraySize = 10;
int n[ arraySize ] = { 19, 3, 15, 7, 11, 9, 13, 5, 17, 1 };
cout << "Element" << setw( 13 ) << "Value"<< setw( 17 ) << "Histogram"<< endl;
// for each element of array n, output a bar in histogram
for ( int i = 0; i < arraySize; i++ ) {
cout << setw( 7 ) << i << setw( 13 )<< n[ i ] << setw( 9 );
for ( int j = 0; j < n[ i ]; j++ ) // print one bar
cout << '*';
cout << endl; // start next line of output
} // end outer for structure
return 0; // indicates successful termination
} // end main
PRINT HISTOGRAM
Element Value Histogram
0 19 *******************
1 3 ***
2 15 ***************
3 7 *******
4 11 ***********
5 9 *********
6 13 *************
7 5 *****
8 17 *****************
9 1 *

21. ARRAYS & Matrices
SK Ahsan
#include <iostream>
#include <stdlib.h>
using namespace std;
int main(){
float a[] = { 22.2,44.4, 66.6 };
float x=11.1;
cout << "I m going to Crash " << endl;
cin >> x;
a[3333] = 88.8; // ERROR: index is out of bounds!
system("PAUSE"); return 0;
}
ARRAY OUT OF BOUND

22. ARRAYS & Matrices
SK Ahsan
Accumulating the elements of array
■ You may need to sum the elements of an
array
■ Initialise the sum variable which contains the
total to zero
■ The instruction Sum = Sum + A(R ) tells the
computer to add the valve of element A(R ) to
the old valve of the sum (Sum) and to store
the result into sum memory location (Sum)
■ Algorithm
■ Loop : R = 1 to 10
■ sum = Sum + A( R)
■ Loop end
■ The number of elements in array is 10
■ The counter of loop (R ) allows the computer
to increase the element number by 1 each
time a piece of data is entered into a memory
location
■ Sum = Sum of the elements of A
■ A(R ) = element R in the A array
R
1 5
1
Sum = Sum +
A(R )
R
B
Calc

23. ARRAYS & Matrices
SK Ahsan
Searching In Array
Searching is a process of finding the required
data in the array. Searching becomes more
important when the length of the array is very
large.
There are two techniques to searching
elements in array as follows:
■ Sequential search
■ Binary search

24. ARRAYS & Matrices
SK Ahsan
Why Search ?
■ Everyday life -We always Looking for something – builder yellow
pages, universities, hairdressers
■ Computers can search
■ World wide web –
■ Spreadsheet –
■ Databases –
■ Large records – 1000s takes time - many comparison slow
system – user wont wait long time

25. ARRAYS & Matrices
SK Ahsan
Search Algorithms
■ Different types
– Sequential Search
– Binary Search
■ Discuss - search algorithms - analyze them
■ Analysis of the algorithms enables
programmers to decide which algorithm to use
for a specific application

26. ARRAYS & Matrices
SK Ahsan
Some observations – Key
■ Each item in a data set - special member that
uniquely identifies the item in the data set
■ For e.g University - a data set which contains
student records – student ID uniquely identifies
each student
■ This unique member of the item is called Key of
the item

27. ARRAYS & Matrices
SK Ahsan
Some observations - Key
■ Where can Keys of the item in a data set be used in ?
■ When searching the data set - for a particular item,
what do we do ?
■ compare the key of the item for which we are searching -
with the keys of the items in the data set – e.g if we
looking particular student id in a list of student id exam
results

28. ARRAYS & Matrices
SK Ahsan
Analysis of Algorithms
■ In addition to describing the algorithms – analyse
them
■ What does analysis of algorithms involve ?
- key comparisons
- Moreover – the number of key comparisons refers
to - the number of times the key of the item (in
search & sort algorithms) is compared with the
keys of the items in the list

29. ARRAYS & Matrices
SK Ahsan
Sequential search
■ Problem :-
– we want to search for a given element in a list.
■ Do we know where the target element occurs?.

30. ARRAYS & Matrices
SK Ahsan
Sequential Search
Sequential search is also known as linear or serial search. It follows
the following step to search a value in array.
– Visit the first element of array and compare its value with
required value.
– If the value of array matches with the desired value, the
search is complete.
– If the value of array does not match, move to next element an
repeat same process.

31. ARRAYS & Matrices
SK Ahsan
10 20 30 40 50 60 70 80 90 100
1 2 3 4 5 6 7 8 9 10
• Visit the first element of array and compare its value with
required value.
• If the value of array matches with the desired value, the search
is complete.
• If the value of array does not match, move to next element an
repeat same process.

32. ARRAYS & Matrices
SK Ahsan
• Visit the first element of array and compare its value with
required value.
• If the value of array matches with the desired value, the search
is complete.
• If the value of array does not match, move to next element an
repeat same process.
arr[1],10 = = 50
10 20 30 40 50 60 70 80 90 100
1 2 3 4 5 6 7 8 9 10

33. ARRAYS & Matrices
SK Ahsan
• Visit the first element of array and compare its value with
required value.
• If the value of array matches with the desired value, the search
is complete.
• If the value of array does not match, move to next element an
repeat same process.
arr[2],20 = = 50
10 20 30 40 50 60 70 80 90 100
1 2 3 4 5 6 7 8 9 10

34. ARRAYS & Matrices
SK Ahsan
• Visit the first element of array and compare its value with
required value.
• If the value of array matches with the desired value, the search
is complete.
• If the value of array does not match, move to next element an
repeat same process.
arr[3],30 = = 50
10 20 30 40 50 60 70 80 90 100
1 2 3 4 5 6 7 8 9 10

35. ARRAYS & Matrices
SK Ahsan
• Visit the first element of array and compare its value with
required value.
• If the value of array matches with the desired value, the search
is complete.
• If the value of array does not match, move to next element an
repeat same process.
arr[4],40 = = 50
10 20 30 40 50 60 70 80 90 100
1 2 3 4 5 6 7 8 9 10

36. ARRAYS & Matrices
SK Ahsan
• Visit the first element of array and compare its value with
required value.
• If the value of array matches with the desired value, the search
is complete.
• If the value of array does not match, move to next element an
repeat same process.
loc = i
loc = 5
arr[5],50 = = 50
Example Code 1
10 20 30 40 50 60 70 80 90 100
1 2 3 4 5 6 7 8 9 10

37. ARRAYS & Matrices
SK Ahsan
Binary Search
Binary search is a quicker method of searching for value in the array. Binary search is very quick
but it can only search an sorted array. It cannot be applied on an unsorted array.
o It locates the middle element of array and compare with desired number.
o If they are equal, search is successful and the index of middle element is returned.
o If they are not equal, it reduces the search to half of the array.
o If the search number is less than the middle element, it searches the first half of array.
Otherwise it searches the second half of the array. The process continues until the required
number is found or loop completes without successful search.

38. ARRAYS & Matrices
SK Ahsan
Binary Search

39. ARRAYS & Matrices
SK Ahsan
Binary Search: middle element
left + right
2
mid =

40. ARRAYS & Matrices
SK Ahsan
Binary Searchbool BinSearch(double list[ ], int n, double item, int&index){
int left=0;
int right=n-1;
int mid;
while(left<=right){
mid=(left+right)/2;
if(item> list [mid]){
left=mid+1; }
else if(item< list [mid]){
right=mid-1;}
else{
item= list [mid];
index=mid;
return true; }
}// while
return false;
}

41. ARRAYS & Matrices
SK Ahsan
Binary Search: Example
Example Code 1

42. ARRAYS & Matrices
SK Ahsan
Sorting Arrays
Sorting is a process of arranging the value of array in a particular order. An array can be
sorted in two order.
o Ascending Order
o Descending Order
12 25 33 37 48
48 37 33 25 12

43. ARRAYS & Matrices
SK Ahsan
Techniques Of Sorting Array
There are two techniques of sorting array:
o Selection Sort
o Bubble Sort

44. ARRAYS & Matrices
SK Ahsan
Bubble Sort
Bubble Sort is also known as exchange sort. It repeatedly visits the array and compares two
items at a time. It works as follows:
o Compare adjacent element. If the first is greater than the second, swap them.
o Repeat this for each pair of adjacent element, starting with the first two and
ending with the last two. (at this point last element should be greatest).
o Repeat the step for all elements except the last one.
o Keep repeating for one fewer element each time until there are no pairs to
compare.

45. ARRAYS & Matrices
SK Ahsan
Bubble sort
 Compare each element (except the last one) with its
neighbor to the right
 If they are out of order, swap them
 This puts the largest element at the very end
 The last element is now in the correct and final place
 Compare each element (except the last two) with its
neighbor to the right
 If they are out of order, swap them
 This puts the second largest element next to last
 The last two elements are now in their correct and final places
 Compare each element (except the last three) with its
neighbor to the right
 Continue as above until you have no unsorted elements on the
left

46. ARRAYS & Matrices
SK Ahsan
Example of bubble sort
7 2 8 5 4
2 7 8 5 4
2 7 8 5 4
2 7 5 8 4
2 7 5 4 8
2 7 5 4 8
2 5 7 4 8
2 5 4 7 8
2 7 5 4 8
2 5 4 7 8
2 4 5 7 8
2 5 4 7 8
2 4 5 7 8
2 4 5 7 8
(done)

47. ARRAYS & Matrices
SK Ahsan
Analysis of bubble sort
■ Let n = a.length = size of the array
■ The outer loop is executed n-1 times (call it n, that’s close enough)
■ Each time the outer loop is executed, the inner loop is executed
– Inner loop executes n-1 times at first, linearly dropping to just
once
– On average, inner loop executes about n/2 times for each
execution of the outer loop
– In the inner loop, the comparison is always done (constant
time), the swap might be done (also constant time)
■ Result is n * n/2 * k, that is, O(n2/2 + k) = O(n2)

48. ARRAYS & Matrices
SK Ahsan
Selection sort
■ Given an array of length n,
– Search elements 0 through n-1 and select the smallest
■ Swap it with the element in location 0
– Search elements 1 through n-1 and select the smallest
■ Swap it with the element in location 1
– Search elements 2 through n-1 and select the smallest
■ Swap it with the element in location 2
– Search elements 3 through n-1 and select the smallest
■ Swap it with the element in location 3
– Continue in this fashion until there’s nothing left to search

49. ARRAYS & Matrices
SK Ahsan
Selection Sort
Selection sort is a technique that sort an array. It selects an element in the array and moves
it to its proper position. Selection sort works as follows:
1. Find the minimum value in the list.
2. Swap it with value in the first position.
3. Sort the remainder of the list excluding the first value.

50. ARRAYS & Matrices
SK Ahsan
Example and analysis of selection sort
 The selection sort might swap an array element
with itself--this is harmless, and not worth
checking for
 Analysis:
 The outer loop executes n-1 times
 The inner loop executes about n/2 times on
average (from n to 2 times)
 Work done in the inner loop is constant
(swap two array elements)
 Time required is roughly (n-1)*(n/2)
 You should recognize this as O(n2)
7 2 8 5 4
2 7 8 5 4
2 4 8 5 7
2 4 5 8 7
2 4 5 7 8

51. SORTING
TECHNIQUES

52. ARRAYS & Matrices
SK Ahsan
Selection Sort
■ Algorithm
– Step 1 − Set MIN to location 0
– Step 2 − Search the minimum element in the list
– Step 3 − Swap with value at location MIN
– Step 4 − Increment MIN to point to next element
– Step 5 − Repeat until list is sorted

53. ARRAYS & Matrices
SK Ahsan
Selection sort
■ Pseudo code
– procedure selection sort
– list : array of items
– n : size of list
– for i = 1 to n - 1
– /* set current element as minimum*/
– min = i ;
– /* check the element to be minimum */
– for j = i+1 to n
– if list[j] < list[min] then
– min = j ;
– end if
– end for
– /* swap the minimum element with the
current element*/
– if index Min != i then
– swap list[min] and list[i]
– end if
– end for
– end procedure EXAMPLE CODE 1
EXAMPLE CODE 2

54. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 1
PASS 1
0 1 2 3 4
56 78 33 81 12

55. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 2
PASS 1
0 1 2 3 4
56 78 33 81 12

56. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 3
PASS 1
0 1 2 3 4
56 78 33 81 12

57. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 4
PASS 1
0 1 2 3 4
56 78 33 81 12
12 78 33 81 56

58. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 1
PASS 2
0 1 2 3 4
12 78 33 81 56

59. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 2
PASS 2
0 1 2 3 4
12 78 33 81 56

60. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 3
PASS 2
0 1 2 3 4
12 78 33 81 56
12 33 78 81 56

61. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 1
PASS 3
0 1 2 3 4
12 33 78 81 56

62. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 2
PASS 3
0 1 2 3 4
12 33 78 81 56
12 33 56 81 78

63. ARRAYS & Matrices
SK Ahsan
DRY RUN
■ Iteration 1
PASS 4
0 1 2 3 4
12 33 56 81 78
12 33 56 78 81

64. ARRAYS & Matrices
SK Ahsan
Bubble sort■ Algorithm
– begin BubbleSort(list)
– for all elements of list
– if list[i] > list[i+1]
– swap(list[i], list[i+1])
– end if
– end for
–
– return list
– end BubbleSort

65. ARRAYS & Matrices
SK Ahsan
Bubble sort
■ Pseudo code
– procedure bubbleSort( list : array of items )
– loop = list.count
– for i = 0 to loop-1 do:
– swapped = false
– for j = 0 to loop-1 do:
– /* compare the adjacent elements */
– if list[j] > list[j+1] then
– /* swap them */
– swap( list[j], list[j+1] )
– swapped = true
– end if
– end for
– /*if no number was swapped that means array is sorted now, break the
loop.*/
– if(not swapped) then
– break
– end if
– end for
– end procedure return list

66. ARRAYS & Matrices
SK Ahsan
Two-D Arrays
Two-D array can be considered as table that consists of rows and columns. Each element in 2-D
array is refered with the help of two indexes. One index indicates row and second indicates the
column.
Declaring 2-D Array:
Data_type Identifier[row][column]; e.g:
int arr[4][3];
o Data _type: Data type of values to be stored in the array.
o Identifier: Name of the array.
o Rows : # of Rows in the table of array.
o Column : # of Columns in the table of array.
0,0 0,1 0,2
1,0 1,1 1,2
2,0 2,1 2,2
3,0 3,1 3,2

67. ARRAYS & Matrices
SK Ahsan
Two-D array Intialization
The two-D array can also be initialized at the time of declaration. Initialization is performed by
assigning the initial values in braces seperated by commas.
Some important points :
o The elements of each row are enclosed within braces and seperated by comma.
o All rows are enclosed within braces.
o For number arrays, if all elements are not specified , the un specified elements are
initialized by zero.

68. ARRAYS & Matrices
SK Ahsan
Two-D array Intialization
Syntax:
int arr[4][3]={ {12,5,22},
{95,3,41},
{77,6,53},
{84,59,62} }
12 5 22
95 3 41
77 6 53
84 59 62
Column indexes
Row indexes
0
2
1
3
10 2

69. ARRAYS & Matrices
SK Ahsan
Case Study: Computing Mean, Median and
Mode Using Arrays
■ Mean
– Average (sum/number of elements)
■ Median
– Number in middle of sorted list
– 1, 2, 3, 4, 5 (3 is median)
– If even number of elements, take average of middle two
■ Mode
– Number that occurs most often
– 1, 1, 1, 2, 3, 3, 4, 5 (1 is mode)

70. ARRAYS & Matrices
SK Ahsan
Case Study
■Find Set Properties
–Set Union
–Set Differences