This document discusses algorithms and their notations. It defines an algorithm as a well-defined computational procedure that takes inputs and produces outputs. Algorithms use three main types of logic: sequential flow, conditional flow, and repetitive flow. Conditional flow uses if structures like single alternative (if/then), double alternative (if/then else), and multiple alternative (if/else if/else). Repetitive flow uses repeat structures like repeat-for (with an index from start to end) and repeat-while (with a condition). Proper comments, variable names, assignments, inputs/outputs, and procedures are also discussed for writing clear algorithms.

1. Chapter-2
INTRODUCTION TO ALGORITHMS
Preliminaries
MRS.SOWMYA JYOTHI, SDMCBM, MANGALORE
Reference: Data Structures with C by Seymour
Lipschutz, Schaum’s Outlines Series.

2. INTRODUCTION
• Study of data structures includes development of algorithms for
creation and processing of data structures.
• An algorithm may be complex.
• The computer programs implementing the more complex data
structures can be easily understood if the programs are organized into
hierarchies of modules.
• In such an organization, each program contains first, a main module
which in turn refers to one or more sub-modules.

4. ALGORITHMIC NOTATIONS
A well-defined computational procedure is the one that takes some
value, or a set of values, as input and produces some value, or a set of
values, as output.
It can also be defined as sequence of computational steps that transform
the input into the output.

5. Identifying number: Each algorithm is assigned an identifying number.
For example, Algorithm 1.3
• Steps, Control Exit: The steps of the algorithm are executed one after
the other, beginning with step 1. Control may be transferred to step n
of the algorithm by the statement “go step n”. The algorithm is
completed when the statement “Exit” is encountered.
• Comments: Each step may contain a comment in brackets which
indicates the main purpose of the step. The comment will usually
appear at the beginning or the end of the step.
• Variable Names: Variable names will use capital letters, as in MAX
and DATA. Single letter names of variables used as counters or
subscripts will also be capitalized in the algorithms (K and N for
example). Lowercase may be used for these same variables.

6. • Assignment Statements: assignment statements will use the dots-equal
notation :=
For example,
K := 5
MAX :=DATA[1]
• Input and Output: data may be input and assigned to variables by means
of a Read statement with the following form:
Read: variables names.
• Similarly, messages placed in quotation marks, and data in variables may
be output by means of a Write or Print statement with the following
form:
Write: Messages and/or variable names.
• Procedures: Procedures will be used for an independent algorithmic
module which solves a particular problem. It is used to write sub
algorithms.

7. Example:
Algorithm 1.3
• (Largest Element in Array) A nonempty array DATA with N numerical values
is given. This 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 and 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

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, called
1. Sequence logic, or sequential flow
2. Selection logic, or conditional flow
3. Iteration logic, or repetitive flow.

9. 1. Sequence logic (Sequential Flow):
• The modules are executed in the sequence i.e. by the order in which the
modules are written.

10. 2. Selection logic (Conditional Flow):
• It employs a number of conditions which lead to a selection
of one out of several alternative modules. The structures
which implement this logic are called conditional structures
or If structures. For clarity, the end of such a structure will be
indicated by the statement [End of If structure].
These conditional structures fall into three types:
a) Single alternative: This structure has the form
If condition, then:
[module A]
[End of If structure]

11. 1. Single Alternative:
The logic of this structure is pictured here.
● If the condition holds, then Module A,
which may consist of one or more
statements, is executed;
● Otherwise Module A is skipped and
control transfers to the next step of
the algorithm

12. 2. Double Alternative:
The logic of this structure is:
This structure has the form:
If (Condition), then:
[Module A]
Else:
[Module B]
[End if structure]
As indicated by the flowchart, if the condition holds, then Module A is executed; otherwise Module B is executed.

13. 3. Multiple Alternatives:
● The logic of this structure
allows only one of the modules will
be executed.
● If condition 1 is true then module A1
will be executed. Otherwise condition
2 will be checked. If condition 2 is true
then module A2 will be executed. And
so on. If none of the conditions is true
then module B will be executed.

14. 3) Multiple Alternative: This structure has the form
If condition(1), then:
[module A]
Else if condition(2), then:
[module B]
.....
Else if condition(M), then:
[module M]
Else:
[module N]
[End of If structure]

18. Iteration Logic (Repetitive Flow):
• The third kind of logic refers to either of two types of structures involving
loops.
• Each type begins with a repeat statement and is followed by a module,
called the body of the loop.
• For clarity, we will indicate the end of the structure by the statement
[End of loop]

19. Iteration Logic (Repetitive Flow)
The Iteration logic employs
a loop which involves a
repeat statement followed
by a module known as the
body of a loop.
The two types of these structures are:
1. Repeat- For structure
2. Repeat-While structure
Repeat-For Structure
This structure has the form:
Repeat for i = A to N by I:
[Module]
[End of loop]
Here, A is the initial value, N is the end value
and I is the increment. The loop ends when
A>B. K increases or decreases according to
the positive and negative value of I
respectively.

20. • The repeat-for-loop uses an index variable such as, K to control the
loop.
The loop will usually have the form:
Repeat for K=R to S by T:
[Module]
[End of loop]
The cycling begins with K=R , then with K=R+T and so on and ends
when K>S.
If T is negative, K decreases in value, then the cycling ends when K<S.

22. • The repeat-while-loop uses condition to control the loop. The loop
will usually have the form:
Repeat while condition:
[Module]
[End of loop]
• The cycling continues until the condition is false.
• We emphasize that there must be a statement before the structure
that initializes the condition controlling the loop, and in order that the
looping may eventually cease, there must be a statement in the body
of the loop that changes the condition.

23. Repeat-While Structure
It also uses a condition to control the
loop. This structure has the form:
Repeat while condition:
[Module]
[End of Loop]