Algorithms
            How I convert my Programs to Algos: 

Comments in square brackets 

eg:  [End of If Structure]

Variables in Upper Case.

eg: I, J, ITEM, LOC

Equality Operator: 

== written as =

Assignment Operator: 

= written as :=

Assignment Expression: 

eg: Set I:=0

Looping Structures:

(While Loop) eg: Repeat Steps # to # while I>=0 and ptr!=NULL

(For Loop) eg: Repeat Steps from I=N to 0 by -1

Input/Output Commands

eg: Write: LOC is the location of the Item

eg: Read: POS

Control Structures:

eg: If I>LOC then:
                           [process]
                    Else if I<LOC then:
                            [process]
                     Else:
                            [process]

Many Steps can be combined using commas & and

eg: Set K:=1, LOC :=1 and MAX:=99

Starting Algos with following format:

INSERT( LIST, N, ITEM, POS )

where LIST is the array list of elements
                N stores the no of elements in List
                ITEM is the new element to Insert
                POS is the position to insert new element

Step 1:

Step 2:

Step 3:
.
.

Step 9: Exit.

    
                Complexity Of Algorithms

                The Complexity of an Algo is a function which gives the running time and storage space requirement of the algorithm in terms of n being the size of input data. There are two cases, one being the Worst Case and the second being the Average Case.

F(n) = n

                The expectation value or Average Value can be found by following where n1, n2.. are the input numbers occurring with respective probabilities p1,p2...

E= n1p1 + n2p2 + n3p3.... 

1. Linear Search

The Complexity is given by the number of comparisons.

(Worst Case: C(n) = n )

(Average Case: ) C(n)= (n+1)/2

2. Binary Search 

            The Complexity is given by the number of comparisons.

 C(n) = log 2 n

3.  Bubble Sort

The Complexity is given by the number of comparisons.

C(n) = n(n-1)/2 = n2/2 + O(n) = O (n2)

In other words, time taken is proportional to 
n2
.

 4. Selection Sort

The Complexity is given by the number of comparisons.

C(n) = n(n+1)/2