1. ARRAYS IN
ARRAYS IN
DATASTRUCTURES USING ‘C’
DATASTRUCTURES USING ‘C’
Dr. C. Saritha
Dr. C. Saritha
Lecturer in Electronics
Lecturer in Electronics
SSBN Degree & PG College
SSBN Degree & PG College
ANANTAPUR
ANANTAPUR
2. Overview
Overview
What is Array?
What is Array?
Types of Arrays.
Types of Arrays.
Array operations.
Array operations.
Merging of arrays.
Merging of arrays.
Arrays of pointers.
Arrays of pointers.
Arrays and Polynomials.
Arrays and Polynomials.
3. ARRAY
ARRAY
An array is a linear data structure. Which
An array is a linear data structure. Which
is a finite collection of similar data items
is a finite collection of similar data items
stored in successive or consecutive
stored in successive or consecutive
memory locations.
memory locations.
For example an array may contains all
For example an array may contains all
integer or character elements, but not
integer or character elements, but not
both.
both.
4. Each array can be accessed by using array
Each array can be accessed by using array
index and it is must be positive integer value
index and it is must be positive integer value
enclosed in square braces.
enclosed in square braces.
This is starts from the numerical value 0 and
This is starts from the numerical value 0 and
ends at 1 less than of the array index value.
ends at 1 less than of the array index value.
For example an array[n] containing n
For example an array[n] containing n
number of elements are denoted by
number of elements are denoted by
array[0],array[1],…..array[n-1]. where ‘0’ is
array[0],array[1],…..array[n-1]. where ‘0’ is
called lower bound and the ‘n-1’ is called
called lower bound and the ‘n-1’ is called
higher bound of the array.
higher bound of the array.
5. Types of Arrays
Types of Arrays
Array can be categorized into different
Array can be categorized into different
types. They are
types. They are
One dimensional array
One dimensional array
Two dimensional array
Two dimensional array
Multi dimensional array
Multi dimensional array
6. One dimensional array:-
One dimensional array:-
One dimensional array is also called as
One dimensional array is also called as
linear array. It is also represents 1-D
linear array. It is also represents 1-D
array.
array.
the one dimensional array stores the data
the one dimensional array stores the data
elements in a single row or column.
elements in a single row or column.
The syntax to declare a linear array is as
The syntax to declare a linear array is as
fallows
fallows
Syntax:
Syntax: <data type> <array name>
<data type> <array name>
[size];
[size];
7. Syntax for the initialization of the linear array
Syntax for the initialization of the linear array
is as fallows
is as fallows
Syntax:
Syntax:
<data type><array name>[size]={values};
<data type><array name>[size]={values};
Example:
Example:
int arr[6]={2,4,6,7,5,8};
int arr[6]={2,4,6,7,5,8};
Values
Values
array name
array name
8. Memory representation of the one
Memory representation of the one
dimensional array:-
dimensional array:-
a[0] a[1] a[2] a[3] a[4] a[5]
a[0] a[1] a[2] a[3] a[4] a[5]
100 102 104 106 108 110
100 102 104 106 108 110
The memory blocks a[0],a[1],a[2],a[3 ],a[4] ,
The memory blocks a[0],a[1],a[2],a[3 ],a[4] ,
a[5] with base addresses 1,102,104,106,108,
a[5] with base addresses 1,102,104,106,108,
110 store the values 2,4,6,7,5,8 respectively.
110 store the values 2,4,6,7,5,8 respectively.
2
2 4
4 6
6 7
7 5
5 8
8
9. Here need not to keep the track of the
Here need not to keep the track of the
address of the data elements of an array to
address of the data elements of an array to
perform any operation on data element.
perform any operation on data element.
We can track the memory location of any
We can track the memory location of any
element of the linear array by using the
element of the linear array by using the
base address of the array.
base address of the array.
To calculate the memory location of an
To calculate the memory location of an
element in an array by using formulae.
element in an array by using formulae.
Loc (a[k])=base address +w(k-lower
Loc (a[k])=base address +w(k-lower
bound)
bound)
10. Here k specifies the element whose
Here k specifies the element whose
location to find.
location to find.
W means word length.
W means word length.
Ex
Ex: We can find the location of the
: We can find the location of the
element 5, present at a[3],base address is
element 5, present at a[3],base address is
100, then
100, then
loc(a[3])=100+2(3-0)
loc(a[3])=100+2(3-0)
=100+6
=100+6
=106.
=106.
11. Two dimensional array:-
Two dimensional array:-
A two dimensional array is a collection of
A two dimensional array is a collection of
elements placed in rows and columns.
elements placed in rows and columns.
The syntax used to declare two
The syntax used to declare two
dimensional array includes two
dimensional array includes two
subscripts, of which one specifies the
subscripts, of which one specifies the
number of rows and the other specifies
number of rows and the other specifies
the number of columns.
the number of columns.
These two subscripts are used to
These two subscripts are used to
reference an element in an array.
reference an element in an array.
12. Syntax to declare the two dimensional
Syntax to declare the two dimensional
array is as fallows
array is as fallows
Syntax:
Syntax:
<data type> <array name> [row size]
<data type> <array name> [row size]
[column size];
[column size];
Syntax to initialize the two dimensional
Syntax to initialize the two dimensional
array is as fallows
array is as fallows
Syntax:
Syntax:
<data type> <array name> [row size]
<data type> <array name> [row size]
[column size]={values};
[column size]={values};
13. Example
Example:
:
int num[3][2]={4,3,5,6,,8,9};
int num[3][2]={4,3,5,6,,8,9};
or
or
int num[3][2]={{4,3},{5,6},{8,9}};
int num[3][2]={{4,3},{5,6},{8,9}};
values
values
column size
column size
row size
row size
array name
array name
data type
data type
15. Memory representation of a 2-D array is
Memory representation of a 2-D array is
different from the linear array.
different from the linear array.
in 2-D array possible two types of memory
in 2-D array possible two types of memory
arrangements. They are
arrangements. They are
Row major arrangement
Row major arrangement
Memory representation of 2-D
Memory representation of 2-D
array:-
array:-
17. We can access any element of the array
We can access any element of the array
once we know the base address of the array
once we know the base address of the array
and number of row and columns present in
and number of row and columns present in
the array.
the array.
In general for an array a[m][n] the address
In general for an array a[m][n] the address
of element a[i][j] would be,
of element a[i][j] would be,
In row major arrangement
In row major arrangement
Base address+2(i*n+j)
Base address+2(i*n+j)
In column major arrangement
In column major arrangement
Base adress+2(j*m+i)
Base adress+2(j*m+i)
18. Ex:
we can find the location of the element 8
then an array a[3][2] , the address of
element would be a[2][0] would be
In row major arrangement
loc(a[2][0])=502+2(2*2+0)
=502+8
=510
In column major arrangement
loc(a[2][0])=502+2(0*3+2)
=502+4
=506
19. Multi dimensional arrays:-
An array haves 2 or more subscripts, that
An array haves 2 or more subscripts, that
type of array is called multi dimensional
type of array is called multi dimensional
array.
array.
The 3 –D array is called as
The 3 –D array is called as
multidimensional array this can be thought
multidimensional array this can be thought
of as an array of two dimensional arrays.
of as an array of two dimensional arrays.
Each element of a 3-D array is accessed
Each element of a 3-D array is accessed
using subscripts, one for each dimension.
using subscripts, one for each dimension.
20. Syntax for the declaration and
Syntax for the declaration and
initialization as fallows Syntax
initialization as fallows Syntax
<data type><array name>[s1][s2][s3]
<data type><array name>[s1][s2][s3]
={values};
={values};
Ex:
Ex:
int a[2][3][2]={
{ {2,1},{3,6},{5,3} },
{ {0,9},{2,3},{5,8} }
};
21. Memory representation of 3-D
array:-
In multi dimensional arrays permits only
In multi dimensional arrays permits only
a row major arrangement.
a row major arrangement.
0
0th
th
2-D array 1
2-D array 1st
st
2-D array
2-D array
10 12 14 16 18 20 22 24 26 28 30 32
10 12 14 16 18 20 22 24 26 28 30 32
2 1
1 3
3 6
6 5
5 3
3 0
0 9
9 2
2 3
3 5
5 8
8
22. For any 3-D array a [x][y][z], the element
For any 3-D array a [x][y][z], the element
a[i][j][k] can be accessed as
a[i][j][k] can be accessed as
Base address+2(i*y*z +j*z+ k)
Base address+2(i*y*z +j*z+ k)
Array a can be defined as int a [2][3][2] ,
Array a can be defined as int a [2][3][2] ,
element 9 is present at a[1][0][1]
element 9 is present at a[1][0][1]
Hence address of 9 can be obtained as
Hence address of 9 can be obtained as
=10+2(1*3*2+0*2+1)
=10+2(1*3*2+0*2+1)
=10+14
=10+14
=24
=24
23. ARRAY OPERATIONS
ARRAY OPERATIONS
There are several operations that can be
There are several operations that can be
performed on an array. They are
performed on an array. They are
Insertion
Insertion
Deletion
Deletion
Traversal
Traversal
Reversing
Reversing
Sorting
Sorting
Searching
Searching
24. Insertion:
Insertion:
Insertion is nothing but adding a new
Insertion is nothing but adding a new
element to an array.
element to an array.
Here through a loop, we have shifted the
Here through a loop, we have shifted the
numbers, from the specified position, one
numbers, from the specified position, one
place to the right of their existing
place to the right of their existing
position.
position.
Then we have placed the new number at
Then we have placed the new number at
the vacant place.
the vacant place.
25. Ex:
Ex:
for (i=4;i>= 2;i++)
for (i=4;i>= 2;i++)
{
{
a[i]=a[i-1];
a[i]=a[i-1];
}
}
a[i]=num;
a[i]=num;
26. Before insertion :
Before insertion :
0 1 2 3 4
0 1 2 3 4
After insertion:
After insertion:
0 1 2 3 4
0 1 2 3 4
Fig:
Fig: shifting the elements to the right while
shifting the elements to the right while
Insuring an element at 2
Insuring an element at 2nd
nd
position
position
11
11 13
13 14
14 4
4 0
0
11
11 12
12 13
13 14
14 4
4
27. Deletion:
Deletion:
Deletion is nothing but process of remove
Deletion is nothing but process of remove
an element from the array.
an element from the array.
Here we have shifted the numbers of
Here we have shifted the numbers of
placed after the position from where
placed after the position from where
the number is to be deleted, one place to
the number is to be deleted, one place to
the left of their existing positions.
the left of their existing positions.
The place that is vacant after deletion of
The place that is vacant after deletion of
an element is filled with ‘0’.
an element is filled with ‘0’.
29. Before deletion:
Before deletion:
0 1 2 3 4
0 1 2 3 4
After deletion:
After deletion:
0 1 2 3 4
0 1 2 3 4
Fig:
Fig: shifting the elements to the left while
shifting the elements to the left while
deleting 3
deleting 3rd
rd
element in an array.
element in an array.
11
11 12
12 13
13 14
14 4
4
11
11 13
13 14
14 4
4 0
0
30. Traversal:
Traversal:
Traversal is nothing but display the
Traversal is nothing but display the
elements in the array.
elements in the array.
Ex:
Ex:
for (i=0;i<5;i++)
for (i=0;i<5;i++)
{
{
Printf (“%dt”, a[i]);
Printf (“%dt”, a[i]);
}
}
11
11 12
12 14
14 4
4 0
0
31. Reversing:
Reversing:
This is the process of reversing the elements
This is the process of reversing the elements
in the array by swapping the elements.
in the array by swapping the elements.
Here swapping should be done only half
Here swapping should be done only half
times of the array size.
times of the array size.
Ex:
Ex:
for (i=0;i<5/2;i++)
for (i=0;i<5/2;i++)
{
{
int temp=a[i];
int temp=a[i];
a[i]=a[5-1-1];
a[i]=a[5-1-1];
a[5-1-i]=temp;
a[5-1-i]=temp;
}
}
32. Before swapping:
Before swapping:
0 1 2 3 4
0 1 2 3 4
After swapping:
After swapping:
0 1 2 3 4
0 1 2 3 4
Fig:
Fig: swapping of elements while reversing an
swapping of elements while reversing an
array.
array.
11
11 12
12 13
13 14
14 0
0
0
0 14
14 13
13 12
12 11
11
33. Sorting:
Sorting:
Sorting means arranging a set of data
Sorting means arranging a set of data
in some order like ascending or
in some order like ascending or
descending order.
descending order.
34. Ex:
Ex: for (i=0;i<5;i++)
for (i=0;i<5;i++)
{
{
for (j=i+1;j<5;j++)
for (j=i+1;j<5;j++)
{
{
if (a[i]>a[j])
if (a[i]>a[j])
{
{
temp=a[i];
temp=a[i];
a[i]=a[j];
a[i]=a[j];
a[j]=temp;
a[j]=temp;
} } }
} } }
36. Searching:
Searching:
Searching is the process of finding the
Searching is the process of finding the
location of an element with a given
location of an element with a given
element in a list..
element in a list..
Here searching is starts from 0
Here searching is starts from 0th
th
element
element
and continue the process until the given
and continue the process until the given
specified number is found or end of list is
specified number is found or end of list is
reached.
reached.
37. Ex:
Ex:
for (i=0;i<5;i++)
for (i=0;i<5;i++)
{
{
if (a[i]==num)
if (a[i]==num)
{
{
Printf(“n element %d is present at %d
Printf(“n element %d is present at %dth
th
position”,num,i+1);
position”,num,i+1);
return;
return;
}}if (i==5)
}}if (i==5)
Printf (“the element %d is not present in the
Printf (“the element %d is not present in the
array ”,num);
array ”,num);
39. Merging of arrays
Merging of arrays
Merging means combining two sorted list
Merging means combining two sorted list
into one sorted list.
into one sorted list.
Merging of arrays involves two steps:
Merging of arrays involves two steps:
They are
They are
sorting the arrays that are to be
sorting the arrays that are to be
merged.
merged.
Adding the sorted elements of both
Adding the sorted elements of both
the arrays a to a new array in sorted
the arrays a to a new array in sorted
order.
order.
40. Ex:
Ex:
Before merging:
Before merging:
1
1st
st
array 2
array 2nd
nd
array
array
After merging:
After merging:
2
2 8
8 11
11
1
1 2
2 3
3 8
8 11
11 13
13
1
1 3
3 13
13
41. Arrays of pointers
Arrays of pointers
A pointer variable always contains an
A pointer variable always contains an
address.
address.
An array of pointer would be nothing but
An array of pointer would be nothing but
a collection of addresses.
a collection of addresses.
The address present in an array of pointer
The address present in an array of pointer
can be address of isolated variables or
can be address of isolated variables or
even the address of other variables.
even the address of other variables.
42. An array of pointers widely used for
An array of pointers widely used for
stoning several strings in the array.
stoning several strings in the array.
The rules that apply to an ordinary array
The rules that apply to an ordinary array
also apply to an array of pointer as well.
also apply to an array of pointer as well.
The elements of an array of pointer are
The elements of an array of pointer are
stored in the memory just like the elements
stored in the memory just like the elements
of any other kind of array.
of any other kind of array.
Memory representation of the array of
Memory representation of the array of
integers and an array of pointers
integers and an array of pointers
respectively.
respectively.
43. Fig1
Fig1:Memory representation of an array of
:Memory representation of an array of
integers and integer variables I and j.
integers and integer variables I and j.
a[0] a[1] a[2] a[3] i j
a[0] a[1] a[2] a[3] i j
100 102 104 106 200 312
100 102 104 106 200 312
Fig2:
Fig2:Memory representation of an array of
Memory representation of an array of
pointers.
pointers.
b[0] b[1] b[2] b[3] b[4] b[5]
b[0] b[1] b[2] b[3] b[4] b[5]
8112 8114 8116 8118 8120 8122
8112 8114 8116 8118 8120 8122
3
3 4
4 5
5 6
6
100
100 102
102 104
104 106
106 200
200 312
312
1
1 9
9
44. Arrays and polynomials
Arrays and polynomials
Polynomials like 5x
Polynomials like 5x4
4
+2 x
+2 x3
3
+7x
+7x2
2
+10x-8
+10x-8
can be maintained using an array.
can be maintained using an array.
To achieve each element of the array
To achieve each element of the array
should have two values coefficient and
should have two values coefficient and
exponent.
exponent.
45. While maintaining the polynomial it is
While maintaining the polynomial it is
assumes that the exponent of each
assumes that the exponent of each
successive term is less than that of the
successive term is less than that of the
previous term.
previous term.
Once we build an array to represent
Once we build an array to represent
polynomial we can use such an array to
polynomial we can use such an array to
perform common polynomial operations
perform common polynomial operations
like addition and multiplication.
like addition and multiplication.
46. Addition of two polynomials
Addition of two polynomials:
:
Here if the exponents of the 2 terms
Here if the exponents of the 2 terms
beinf compared are equal then their
beinf compared are equal then their
coefficients are added and the result is
coefficients are added and the result is
stored in 3
stored in 3rd
rd
polynomial.
polynomial.
If the exponents of the 2 terms are not
If the exponents of the 2 terms are not
equal then the term with the bigger
equal then the term with the bigger
exponent is added to the 3 rd
exponent is added to the 3 rd
polynomial.
polynomial.
47. If the term with an exponent is present in
If the term with an exponent is present in
only 1 of the 2 polynomials then that
only 1 of the 2 polynomials then that
term is added as it is to the 3
term is added as it is to the 3rd
rd
polynomial.
polynomial.
Ex:
Ex:
1
1st
st
polynomial is 2x
polynomial is 2x6
6
+3x
+3x5
5
+5x
+5x2
2
2
2nd
nd
polynomial is 1x
polynomial is 1x6
6
+5x
+5x2
2
+1x+2
+1x+2
Resultant polynomial is
Resultant polynomial is
3x
3x6
6
+3x
+3x5
5
+10x
+10x2
2
+1x+2
+1x+2
48. Multiplication of 2 polynomials:
Multiplication of 2 polynomials:
Here each term of the coefficient of the 2
Here each term of the coefficient of the 2nd
nd
polynomial is multiplied with each term of the
polynomial is multiplied with each term of the
coefficient of the 1
coefficient of the 1st
st
polynomial.
polynomial.
Each term exponent of the 2
Each term exponent of the 2nd
nd
polynomial is
polynomial is
added to the each tem of the 1
added to the each tem of the 1st
st
polynomial.
polynomial.
Adding the all terms and this equations placed
Adding the all terms and this equations placed
to the resultant polynomial.
to the resultant polynomial.
49. Ex:
Ex:
1
1st
st
polynomial is
polynomial is
1x
1x4
4
+2x
+2x3
3
+2x
+2x2
2
+2x
+2x
2
2nd
nd
polynomial is
polynomial is
2x
2x3
3
+3x
+3x2
2
+4x
+4x
Resultant polynomial is
Resultant polynomial is
2x
2x7
7
+7x
+7x6
6
+14x
+14x5
5
+18x
+18x4
4
+14x
+14x3
3
+8x
+8x2
2
