Data Structures Analysis
of Algorithm
Course Code : ITC303
(SE, Sem-III)
Core Concepts
Sr. No.
Major Concepts in Data Structures Algorithm
Prerequisite Concepts
1
Linear Data Structures and Operations
C Basics,
2
Non-linear Data Structures and Operations
Arrays ,
3
Searching / sorting techniques
Pointers,
4
Hashing techniques
Functions,
Structures,
5
Applications of Data Structures
Dynamic Allocation
Arrays in C
• An array can be used to store and process a fixed number of data elements that
all have the same type.
• Array elements are stored at consecutive memory locations.
• The first element in the array is numbered 0, so the last element is 1 less than
the size of the array.
• An array is also known as a subscripted variable.
• For exampleint a=11;int b=21;int c=33;int d=40;int e=74;
could be represented asint X[5]={11,-21,33,-40,74};
• Individual elements in the array can be referred using subscript asint value=X[2];
• #include<stdio.h>
• i=0;
• #include<conio.h>
• while(name[i]!='\0') //we dont know length of name entered
but know how it ends
• void main()
• {
• char name[20];
• {
• putch(name[i]);
• int i, x[]={ 22,44,77,55,99}; //initialized
• printf("\t%d its ascii value\t",name[i]);// corresponding ascii
value numerical observe
• clrscr();
• i++;
• for(i=0;i<5;i++)
• }
• printf("\t%d",x[i]);
• getch();
• printf("Observe garbage value after fifth element\n") ;
• }
• for(i=0;i<15;i++) // fifthe onwards garbage values no error
• printf("\t%d",x[i]);
• printf("Please enter your name\n");
• gets(name);
• puts(name);
output
output
#include<stdio.h>
#include<conio.h>
void main()
{
static int var=5;
printf("%d",var--);
if(var)
main();
}
Output#include<stdio.h>
• #include<conio.h>
• #include<string.h>
• int main()
•{
• char*c="GATECSIT2017";
• char*p=c;
• printf("%d",(int)strlen(c+2[p]-6[p]1));
• return 0;
•}
output
#include<stdio.h>
#include<conio.h>
void main()
{
int i=-1,j=-1,k=0,l=2,m;
clrscr();
m=i++&&j++&&k++||l++;
printf("%d%d%d%d%d",i,j,k,l,m);
getch();
}
•
•
•
•
•
•
•
•
•
•
•
#include<stdio.h>
#include<conio.h>
void main()
{
int i,j,k,n=4;
for(i=0;i<=n;i++)
for(j=0;j<=n;j++)
for(k=0;k<=n;k++)
printf("bye");
}
How many times ?
What will be output?
#include<conio.h>
int main()
{
int a[]={2,4,6,8,10};
int i,sum=0, *b=a+4;
clrscr();
printf("%d",*b);
for(i=0;i<5;i++)
sum=sum+(*b-i)-*(b-i);
printf("%d\n",sum);
return 0;
}
#include<stdio.h>
#include<conio.h>
void main()
{
int var[3]={5,10,15,20,25};
printf("%d",var[4]);
}
• Error
Operations that can be performed on arrays
Sr. No.
Operation
Description
1
Traversing
to access each data item exactly once so that it can be processed
2
Searching
to find out the location of the data item if it exists in the given
collection of data items
3
Insertion
to add a new data item in the given collection of data items
4
Deletion
to delete an existing data item from the given collection of data items
5
Sorting
to arrange the data items in some order i.e. in ascending or
descending order in case of numerical data and in dictionary order in
case of alphanumeric data
6
Merging
to combine the data items of two sorted files into single file in the
sorted form
Traversing an array
• Let X be an 1D array initialized as,
Index
X
Accessing an element
0
11
1
-21
2
33
3
-40
4
74
X[0]
X[1]
X[2]
X[3]
X[4]
• Here we will start from beginning and will go till last element and during
this process we will access value of each element exactly once asX[0]=11, X[1]=-21, X[2]=33, X[3]=-40, X[4]=74
Searching in an array
• Let X be an 1D array initialized as,
Index
X
Accessing an element
0
11
1
-21
2
33
3
-40
4
74
X[0]
X[1]
X[2]
X[3]
X[4]
• Suppose item to be searched is 20, then comparison will start from
0th index until the element is found or array is finished.
Insertion in an array
• Let X be an 1D array initialized as,
Index
X
Accessing an element
0
11
1
-21
2
33
3
-40
4
74
X[0]
X[1]
X[2]
X[3]
X[4]
• New element to be inserted is 100 and location for insertion is 2. So
shift the elements from 4th location to 2nd location downwards by 1
place. And then insert 100 at 2nd location.
Index
0
1
2
3
4
5
X
11
-21
100
33
-40
74
Insert new
element
Shift the elements to the right by 1
position
Deletion in an array
• Let X be an 1D array initialized as,
Index
X
Accessing an element
0
11
1
-21
2
100
3
33
4
-40
X[0] X[1]
X[2]
X[3]
5
74
X[4] X[5]
• The element to be deleted is -21 which is at 1st location. So shift the
elements from 2nd to last location upwards by 1 place and decrement
the count for number of elements by 1.
Index
0
1
2
3
4
X
11
100
33
-40
74
Shift the elements to the left by 1 position
Sorting an array
• Let X be an 1D array initialized as,
Index
0
1
2
3
4
X
11
-21
33
-40
74
Accessing an element
X[0]
X[1]
X[2]
X[3]
X[4]
• After arranging the elements in increasing order by using a sorting
technique, array will look like,
Index
0
1
2
3
4
X
-40
-21
11
33
74
Accessing an element
X[0]
X[1]
X[2]
X[3]
X[4]
Merging two sorted arrays
• Let X be an 1D array initialized as,
Index
X
Accessing an element
0
-40
1
-21
2
11
3
33
4
74
X[0]
X[1]
X[2]
X[3]
X[4]
• Let Y be an 1D array initialized as,
Index
Y
Accessing an element
0
20
Y[0]
1
35
Y[1]
2
45
Y[2]
3
90
Y[3]
Merging in arrays
• After merging merged array Z is as below:
Index
0
1
2
3
4
5
6
7
8
Z
Accessing an
element
-40
-21
11
20
33
35
45
74
90
Z[0]
Z[1]
Z[2]
Z[3]
Z[4]
Z[5]
Z[6]
Z[7]
Z[8]
Pointers in C
• A pointer is a variable that contains the address of a variable.
• It is possible to goto that address and retrieve the data stored in it.
• Need to tell the compiler during declaration time, about the pointer
variable & what type of memory it points to.
• For example,
int *ptr;
Pointer Notation
• Consider the declaration,
int i=3;
• To print the address through C program:
#include<stdio.h>
main()
{
int i = 3 ;
printf("\nAddress of i = %u\n",&i);
printf("\nValue of i = %d",i);
}
Address of i = 65524
Value of i = 3
• “&” used in this statement is C’s “address of” operator.
• “*” is used for “value at address” or “indirection” operator.
• This address can be collected in a variable as, j=&i
• To make variable “j” capable of holding an address of another
variable, “j” must be declared as, int *j;
• The memory map will look like
Example
#include<stdio.h>
main( )
{
int i = 3 ;
int *j ;
j = &i ;
printf ("\n%u %u %u",&i,j,&j) ;
printf ("\n%u %d %d %d",j,i,*(&i),*j) ;
}
What will be the output of the C program?
Example1
#include<stdio.h>
int main()
{
char temp;
char arr[10] = {1, 2, 3, 4, 5, 6, 9, 8};
temp = (arr + 1)[2];
printf("%d\n", temp);
return 0;
}
Example2
#include<stdio.h>
int main()
{
int arr[2] = {1, 2, 3, 4, 5};
printf("%d", arr[3]);
return 0;
}
Example3
#include<stdio.h>
int main()
{
int rows = 3, cols = 4, i, j, k;
int a[3][4] = {1, 2, 3, 5, 7};
i = j = k = 00;
for(i=0; i<rows; i++)
for(j=0; j<cols; j++)
if(a[k][j]<k)
k = a[i][j];
printf("%d\n", k);
return 0;
}
Example4
#include<stdio.h>
int main()
{
int arr[ ]={1.2, 2.4, 3.6, 4.8, 5};
int j, *ptr = arr;
for(j = 0;j<5;j++)
{
printf("%d ", *arr);
++ptr;
}
}
Example5
#include<stdio.h>
int main()
{
void swap();
int x = 5, y = 10;
swap(&x, &y);
printf("x = %d y = %d",x,y);
return 0;
}
void swap(int *a, int *b)
{
*a ^= *b, *b ^= *a, *a ^= *b;
}
Example6
#include<stdio.h>
#include<stdio.h>
int main(){
int i = 3;
int *j;
j = &i;
j++;
printf("%d ",*j);
return 0;
}
Functions
• A function is combined of a block of code that can be called or used anywhere in
the program by calling the name.
• Any C program contains at least one function i.e. main(), with which the program
execution begins.
• Once created, a function can be called within any other function or itself.
• For example,
#include<stdio.h>
myfunc();
//function prototype
main()
{
myfunc();
}
myfunc()
//function definition
{
printf*”Hello World”);
}
Function arguments
#include<stdio.h>
myfunc(int count);
//function prototype
main()
{
myfunc(5);
}
myfunc(int count)
//function definition
{
int i;
for(i=0; i<count; i++)
printf(“\nHello World”);
}
Function return values
#include<stdio.h>
int myfunc()
//function definition
{
int i=4,j=5,k;
k=i*j;
return k;
}
main()
{
int n;
n=myfunc();
//function call
printf(“%d”, n);
}
output
• int fun2(int n)
• {
• static int i=0;
• #include<stdio.h>
•
•
•
•
•
•
•
•
•
•
#include<conio.h>
int fun1(int n)
{
static int i=0;
if(n>0)
{
++i;
fun1(n-1);
}
return(i);
• }
• if(n>0)
• {
• ++i;
• i=i+fun1(n);
• fun2(n-1);
• }
• return(i);
• }
• void main()
• {
• int x;
• x=fun2(5);
• printf("%d\t",x) ;
• }
•
•
•
•
•
•
•
•
•
•
•
•
•
#include<stdio.h>
#include<conio.h>
int r()
{
static int num=7;
return num--;
}
int main()
{
for(r();r();r())
printf("%d",r());
return 0;
}
Recursive Function
#include<stdio.h>
int rec(int);
main()
{
int a, fact ;
printf("\nEnter any number ");
scanf ("%d", &a);
fact = rec(a);
printf ("Factorial value = %d",
fact);
}
int rec (int x)
{
int f;
if (x == 1)
return (1);
else
f = x * rec (x - 1) ;
return (f) ;
}
How recursion works for calculating factorial
fact(5)
120
5*fact(4)
5*24
4*fact(3)
4*6
3*fact(2)
3*2
2*fact(1)
2*1
1