This document provides an overview of algorithms and data structures. It begins with mathematical notation and complexity analysis. It then discusses control structures like sequence, selection, and iteration. Specific algorithms are described, including finding the largest element in an array, linear search, and the sieve method for finding prime numbers. Floor, ceiling, integer, absolute value, exponent, and logarithm functions are also covered. Overall, the document serves as a lecture outline on fundamental algorithmic concepts.

1. PRELIMINARIES
NURJAHAN NIPA
LECTURER, DEPT OF ICT, BDU

2. Lecture Outlines
■ Mathematical Notation
■ Algorithm Complexity ofAlgorithms
■ Control Structures
■ Sieve Method (Cross Out Algorithm)
■ Largest Element Algorithm.
■ Linear SearchAlgorithm.

3. Floor & Ceiling Functions
■ The floor of x denotes the greatest integer that does not exceed x.
■ The ceiling of x denotes the least integer that is not less than x.
x Floor Ceiling
3.14 3 4
√5 2 3
-8.5 -9 -8
7 7 7
-18 -18 -18
π 3 4
3
30 3 4
log2 100 6 7

4. Integer & Absolute value Function
Value Integer Function AbsoluteValue
Function
3.14 INT(3.14)=3 |3.14|=3.14
-15 INT(-15)=-15 |-15|=15
7 INT(7)=7 |7|=7
-8.5 INT(-8.5)=-8 |-8.5|=8.5
√5 INT(√5)=2 |√5|=2.236

5. Exponent & Logarithms
■ How many 2s do we multiply to get 8?
Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2 s to get 8
So, log2 8=3 since 23
.
So these two things are the same:

6. Exponent & Logarithms
■ Exponents and Logarithms are related, let's find out how ...

8. Control Structures
Algorithms and their equivalent computer programs are more easily understood if they
mainly use self contained modules and three types of logic or flow of control-
 Sequence Logic or Sequential Flow
 Selection Logic or Conditional Flow
 Iteration Logic or Repetitive Flow

9. Sequence Logic or Sequential Flow
■ Sequential logic as the name suggests follows a serial or sequential flow in which the
flow depends on the series of instructions given to the computer. Unless new
instructions are given, the modules are executed in the obvious sequence.
■ Sequential execution of code statements (one line after another) -- like following a
recipe

10. Selection Logic or Conditional Flow
Selection Logic simply involves a number of conditions or parameters which decides one out of several
written modules.The structures which use these type of logic are known as Conditional Structures.
This logic is used for decisions, branching -- choosing between 2 or more alternative paths. In C, these
are the types of selection statements:
 if
 if/else
 Switch
These structures can be of three types:
 Single Alternative
 Double Alternative
 Multiple Alternative

11. Single Alternative:
This structure has the form----
If (condition) then:
[Module A]
[End of If structure]
if(condition)
{
// Statements to execute if condition is
true
}
// C program to illustrate If statement
#include <stdio.h>
int main()
{
int i = 10;
if (i > 15) {
printf("10 is greater than 15 n");
}
printf("I am Not in if");
}
// C program to illustrate If statement
#include <stdio.h>
int main()
{
int i = 10;
if (i < 15) {
printf("10 is less than 15 n");
}
printf("I am Not in if");
}

12. Double Alternative:
This structure has the form----
If (Condition), then:
[Module A]
Else:
[Module B]
[End if structure]
if (condition){
// Executes this block if condition is true
}
else{
// Executes this block if condition is false
}
// C program to illustrate If else statement
#include <stdio.h>
int main() {
int i = 25;
if (i > 15)
printf("i is greater than 15");
else
printf("i is smaller than 15");
}
// C program to illustrate If else statement
#include <stdio.h>
int main()
{
int i = 20;
if (i == 10)
printf("i is 10");
else
printf("i is 20");
printf("Outside if-else block");
}

13. If (condition A), then:
[Module A]
Else if (condition B), then:
[Module B]
..
..
Else if (condition N), then:
[Module N]
[End If structure]]
if (condition)
statement 1;
else if (condition)
statement 2;
.
.
else
statement;
■ This structure has the form----
Multiple Alternative:

14. #include<stdio.h>
int main()
{
char ch;
printf("Enter any character: ");
scanf("%c",&ch);
switch(ch)
{
case 'A' ... 'Z':
printf("%c is alphabetn", ch);
break;
case 'a' ... 'z':
printf("%c is alphabetn",ch);
break;
case '0' ... '9':
printf("%c is digitn",ch);
break;
default:
printf("%c is special charactern",ch);
}
}
#include <stdio.h>
int main()
{
char ch;
printf("Enter any character: ");
scanf("%c", &ch);
if((ch >= 'a' && ch <= 'z') || (ch >= 'A' && ch <= 'Z'))
{
printf("%c is alphabetn", ch);
}
else if(ch >= '0' && ch <= '9')
{
printf("%c is digitn", ch);
}
else
{
printf("%c is special charactern", ch);
}
}

15. Iteration Logic or Repetitive Flow
Generally used for looping, i.e. repeating a piece of code multiple times in a row.The Iteration
logic employs a loop which involves a repeat statement followed by a module known as the
body of a loop.
In C, there are three types of loops:
■ while
■ do/while
■ for

16. Repeat While Loop
Repeat while condition:
[Module]
[End of Loop]
//Infinite loop
while (true) {
print("Hello,World!") }
Or
while (1) { print("Hello,World!") }
#include <stdio.h>
int main()
{
int i = 1;
while (i < 6) {
printf("HelloWorldn");
i++;
}
}

17. #include <stdio.h>
int main()
{
int i = 0;
for (i = 1; i <= 5; i++) {
printf("HelloWorldn");
}
}
Repeat for i = A to N by I:
[Module]
[End of loop]
Repeat For Loop
//Infinite loop
#include<stdio.h>
int main()
{
for( ; ; )
printf("Hello world.t");
}

18. // infinite do...while loop
int count = 1;
do {
// body of loop
}
while(count == 1);
Repeat Do/While Loop
#include <stdio.h>
int main()
{
int x;
x = 0;
do {
printf( "Hello, world!n" );
} while ( x != 0 );
}

19. Largest Element in an Array
Algorithm 2.1: (Largest element in an array) A nonempty array DATA with N numerical values is
given.The algorithm finds the location LOC and the value MAX of the largest element of DATA.
The variable K is used as a counter.
Step-1: [Initialize] SET K:=1, LOC:=1 and MAX:=DATA[1];
Step-2: [Increment Counter] Set K:=K+1
Step-3: [Test Counter] if K>N then
Write: LOC, MAX, EXIT
Step-4: [Compare and Update] If MAX<DATA[K], then:
Set LOC:=K and MAX:=DATA[K]
Step-5: [Repeat Loop]Go to step 2.

22. Largest Element in an Array(Using RepeatWhile
Loop)
■ Algorithm 2.3: (Largest element in an array using repeat while) A nonempty array DATA with N
numerical values is given. The algorithm finds the location LOC and the value MAX of the largest
element of DATA.The variable K is used as a counter.
Step-1: [Initialize] SET K:=1, LOC:=1 and MAX:=DATA[1];
Step-2: Repeat steps 3 and 4 while k<=N
Step-3: [Compare and Update] If MAX<DATA[K], then:
Set LOC:=K and MAX:=DATA[K]
[End of If structure]
Step-4: Set K:=K+1
[End of step 2 loop]
Step-5:Write: LOC, MAX
Step-6: EXIT

23. Searching
Searching is the process of finding some particular element in the list. If the element is present in
the list, then the process is called successful and the process returns the location of that element,
otherwise the search is called unsuccessful.
There are two popular search methods –
 Linear Search
 Binary Search
 Linear search is the simplest search algorithm and often called sequential search. In this type of
searching, we simply traverse the list completely and match each element of the list with the
item whose location is to be found. If the match found then location of the item is returned
otherwise the algorithm return NULL.
 Linear search is mostly used to search an unordered list in which the items are not sorted.

24. ■ Find the number 13 in the given list.
■ You just look at the list and there it is!
■ A computer cannot look at more than the value at a given instant of time. So it takes one item
from the array and checks if it is the same as what you are looking for.
■ The first item did not match. So move onto the next one.
■ And so on.This is done till a match is found or until all the items have been checked.

25. Linear Search
■ Algorithm 2.4: A linear array DATA
with N elements and a specific ITEM of
information are given.The algorithm
finds the location LOC of ITEM in an
array DATA or sets LOC=0.
1. [Initialize] Set K:=1 and LOC:=0
2. Repeat steps 3 and 4 while LOC=0 and K<=N
3. If ITEM= DATA[K], then: Set LOC:=K
4. Set K:=K+1.[Increments counter]
[End of Step 2 loop]
5. [Successful?]
If LOC=0, then
Write: Item is not in the array DATA.
Else:
Write: LOC is the location of ITEM.
[End of If structure]
6. Exit

26. Finding Prime number using Sieve
Method
1. [Initialize array A] Repeat for k=1 to N:
Set A[K]:=K
2. [Eliminate multiples of K] Repeat for K=2 to √N
Call CROSSOUT(A,N,K)
3. [Print the primes] Repeat for K=2 to N
IfA[K]≠1 then:WRITE:A[K]
4. Exit
CROSSOUT(A,N,K)
1. If A[K]=1, then Return.
2. Repeat for L=2K to N by K:
Set A[L]:=1
[End of Loop]
3. Return.

27. Explanation with Example:
Let us take an example when n = 50. So we need to print all prime numbers smaller than or equal to 50.
We create a list of all numbers from 2 to 50.
According to the algorithm we will mark all the numbers which are divisible by 2 and are greater than or equal
to the square of it.

28. Explanation with Example:
Now we move to our next unmarked number 3 and mark all the numbers which are multiples of 3 and are
greater than or equal to the square of it.
We move to our next unmarked number 5 and mark all multiples of 5 and are greater than or equal to the
square of it.

29. We continue this process and our final table will look like below:
So the prime numbers are the unmarked ones: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

30. THANKYOU!