What is an Algorithm

Definition

An algorithm is a finite set of instructions that, if followed, accomplishes a particular task.

In addition, Every algorithms must satisfy the following five characteristic features

1. Input: Zero or more quantities are externally supplied.
2. Output: At least one quantity is produced.
3. Definiteness: Each instruction is clear and unambiguous.
4. Finiteness: If we trace out the instructions of an algorithm, then for all cases, the algorithm terminates after a finite number of steps.
5. Effectiveness: Every instruction must very basic so that it can be carried out, in principle using only pencil & paper. i.e tracing each step should be possible

Study of algorithm includes 4 distince areas one can identify:

1. How to devise or design an algorithm: Creating of an algorithm is an art which may never be fully automated. It includes, writing algorithms using the existing design techniques.
2. How to validate an algorithm: After the algorithm is written it is necessary to check the correctness of the algorithm. It is necessary to show that algorithm computes correct output for all possible legal inputes.
3. How to analysis an algorithm: Analysis of algorithms refers to the task of determining how much computing time and storage an algorithm requires. This helps us to judge which algorithm is better.
4. How to test a program: Testing consists of two phases: Debugging and Profiling
   • Debugging: It is detection and correction of errors (check whether program produces faulty results for valid inputs, if it is found then the program has to be corrected).
   • Profiling: It is a process of measuring the actual amount of time and space required by a corrected program to compute for valid set of inputes.

Algorithm specifications

An algorithm may be specified in any one of the following methods.
a) Natural language: Natural languages are the languages that people speak, such as English
b) Flow chart: By using a predefined geometric shapes we can describe the procedure in algorithm. Flow chart is unable to represent complex algorithms.
c) Pseudo code: It is a mixture of natural language and programming language. There are different forms of pseudo code and all these dialects are close to each other.

How to Wrtire an Algorithm (Pseudocode)

1. Comments begin with // and continue until the end of line.
2. Blocks are indicated with matching braces { and }.
3. An identifier begins with a letter. The data types of variables are not explicitly declared.
   Compound data types can be formed with records. Here is an example,
   
   Example:

   Node = Record
   {
   	datatype_1 data_1;
   	. .
   	. .
   	datatype_n data_n;
   	node *link;
   }

   
   Here link is a pointer to the record type node. Individual data items of a record can be accessed with → and period.
4. Assignment of values to variables is done using the assignment statement. <Variable> := <expression>;
5. There are two Boolean values TRUE and FALSE.
   Logical Operators AND, OR, NOT
   Relational Operators <, ≤, >, ≥, =, ≠
6. A conditional statement has the following forms.
   • if statement:
     syntax:

     if <condition> then 
         <statement>

   • if-else statement:
     syntax:

     if <condition> then 
         <statement_1> 
     else 
         <statement_2>

   • case statement:
     syntax:

     Case{ 
     	:<condition_1>: <statement_1>
     		.
     		.
     	:<condition_n>: <statement_n>
     	:else: <statement_n+1>
     }

7. The following looping statements: while, repeat-until and For.
   • While Loop:
     syntax:

     while (condition) do
     {
     	statement_1
     	.
     	.
     	statement_n
     }

   • repeat-until:
     syntax:

     repeat{
     	statement_1
     	.
     	.
     	statement_n
     }until (condition)

   • For Loop:
     syntax:

     for variable: = starting_value to target_value step step_count do
     	statement_1
     	.
     	.
     	statement_n
     }

8. Elements of multidimensional arrays are accessed using [ and ]. example: A[ i,j ]
9. Input and output are done using the instructions read & write.
10. There is only one type of procedure: Algorithm.
    syntax:

    Algorithm Algorithm_Name(<Parameter list>)

Algorithm add(a,b){
		c:= a+b
		return c;
	}

The following algorithm finds and returns the maximum of n given numbers

Algorithm Max(A, n)
// A is an array of sizen.
{
	Result:=A[1];
	for i := 2 to n do
		if A[i] > Result then 
		    Result:=A[i];
	return	Result;
}