Algorithm of sorting

An algorithm to sort an elements using Insertion Sort.

Algorithm for Insertion sort:-
Step 1 : START
Step 2 : Input N
Step 3 : For I←0 to N -1
Read A [ I ]
( end of I for loop )
Step 4 : For I←1 to N -1 Do
Step 5 : J = I
Step 6 : While ( J > = 1 ) and ( A[ J ] < A [ J -1 ] )
Step 7 : TEMP = A [ J ]
Step 8 : A [ J ] = A [ J - 1 ]
Step 9 : A[ J - 1 ] = TEMP
Step 10 : J = J - 1
[ end of While loop ]
[ end of step I For loop ]
Step 11 : For I←0 to N -1
Step 12: Print A [ I ]
Step 13 : Stop

Consider the elements
A[0 ]    20
A[1]    16
A[2]    4
A [3]    3

Pass 1:
A[1],A[0]>16,20,4,3
Pass 2:
A[2],A[1]> 16,4,20,3
A[1],A[0]>4,16,20,3
Pass 3:
A[3],A[2]> 4,16,3,20
A[2],A[1]>4,3,16,20
A[1],A[0]> 3,4 16,20
Sorted order is 3,4,16,20

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Algorithm for bubble sort:-

Step 1 : START
Step 2 : Input N
Step 3 : For I←0 to N -1
Step 4 : Read ( A [ I ] )
( end of for loop )
Step 5 : For I←1 to N -1
Step 6 : For J←0 to N –I - 1
Step 7 : If (A[ J ] > A [ J +1] )
Temp←A [ J ]
A [ J ]←A [ J + 1 ]
A [ J +1 ]←Temp
[ end of if ]
[ end of J loop ]
[ end of I loop ]
Step 8 : For J←0 to N -1
Print A [ J ]
Step 9 : Stop

Consider the following elements: 50 , 20, 10 , 05
Pass 1:- 50    20    10    05
             20    50    10     05
             20    10     50    05
             20     10    05    50
Pass 2:-  20    10    05    50
               10    20    05    50
               10    05    20     50
Pass 3:- 10    05    20    50
             05    10     20    50

Sorted order is 5, 10, 20 , 50

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 Algorithm for selection sort:-

Step 1 : START
Step 2 : Input N
Step 3 : For I←0 to N -1
Step 4 : Read A [ I ]
Step 5 : For I←0 to N -2
Step 6 : S←A [ I]
Step 7 : Pos←I
Step 8 : For J←I + 1 to N -1
Step 9 : If ( A[ J] < S )
Step 10 : S←A [ J ]
Step 11 : Pos←J
[ end of if ]
[ end of J For loop ]
Step 12 : A [ Pos ]←a[ I ]
Step 14 : A[ I ]←S
[end of I For loop ]
Step 15: For I = 0 to N – 1
Step 16: Print A[ I ]
Step 17: Stop

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An algorithm to find the maximum in an array:-

Step 1 : [Assume 1st element is the largest ]large = A [ 0 ]
Step 2 : POS = 0
Step 3 : [ Find the largest element in the array and its position]For I = 1 to N – 1 Do
Step 4 : If ( A [ I ] > large ) Then
Step 5 : large = A [ I ]
Step 6 : POS = 1
[ End if ]
[ End of step 3 for loop ]
Step 7: [ Print the largest and its position]Print “ Largest = “ , large , “ position = “ , pos
Step 8: Exit

---

An algorithm to find the minimum in an array:-

Step 1 : [Assume 1st element is the smallest]small = A [ 0 ]
Step 2 : POS = 0
Step 3 : [ Find the smallest element in the array and its position]
For I = 1 to N – 1 Do
Step 4 : If ( A [ I ] < small ) Then
Step 5 : small = A [ I ]
Step 6 : POS = 1
[ End if ]
[ End of step 3 for loop ]
Step 7: [ Print the smallest and its position]
Print “ smallest = “ , small , “ position = “ , pos
Step 8: Exit

---

Linear search method with an algorithm:-

Step 1 : START
Step 2 : input N
Step 3 : for I←0 to N -1
Read A [ I ]
Step 4 : Loc = -1
Step 5 : For I = 0 to N- 1 do
Step 6 : If ( ele = A[I]) Then
Step 7: Loc = I
Step 8 : Goto step 9
[ end if ]
[ end for ]
Step 9 : If ( Loc > = 0 ) then
Step 10: Print “ ele Found in location “ , Loc
Step 11: else
Step 12: Print “ ele not found ”

Step 13 Stop

---

 Algorithm for Binary Search:


Step 1: Low = 0
Step 2 : High = N – 1
Step 3 : Loc = -1
Step 4 : While ( Low < = High ) Do
Step 5 : M = ( Low + High ) / 2
Step 6 : If (ele = A[M ] ) Then
Step 7: Loc = M goto Step 12
[ end if ]
Step 8 : If (ele < A [M ] ) Then
 Step 9: High←M – 1
Step 10 : Else
Step 11 : Low←M + 1
[ end of if ]
[ end of While loop ]
Step 12 : if ( Loc > = 0 ) Then
Step 13: Print “ element , found , search successful ” , Loc
Step 14: else
Step 15 : Print “ Item not found , search Unsuccessful ”
[ end if ]
Step 16 : Stop

Memristor

Memristor Definition:-

According to the original 1971 definition, the memristor was the fourth fundamental circuit element, forming a non-linear relationship between electric charge and magnetic flux linkage.

What is memristor?

Ans.As its name implies, the memristor can "remember" how much current has passed through it. And by alternating the amount of current that passes through it, a memristor can also become a one-element circuit component with unique properties. Most notably, it can save its electronic state even when the current is turned off, making it a great candidate to replace today's flash memory. 

The memristor definition is based solely on the fundamental circuit variables of current and voltage and their time-integrals, just like the resistor, capacitor and inductor. Unlike those three elements however, which are allowed in linear time-invariant or LTI system theory, memristors of interest have a dynamic function with memory and may be described as some function of net charge. There is no such thing as a standard memristor. Instead, each device implements a particular function, wherein the integral of voltage determines the integral of current, and vice versa. A linear time-invariant memristor, with a constant value for M, is simply a conventional resistor.Like other two-terminal components, real-world devices are never purely memristors ("ideal memristor"), but also exhibit some amount of capacitance, resistance and inductance.

Memristors will theoretically be cheaper and far faster than flash memory, and allow far greater memory densities. They could also replace RAM chips as we know them, so that, after you turn off your computer, it will remember exactly what it was doing when you turn it back on, and return to work instantly. This lowering of cost and consolidating of components may lead to affordable, solid-state computers that fit in your pocket and run many times faster than today's PCs. 

Symbol:-

Someday the memristor could spawn a whole new type of computer, thanks to its ability to remember a range of electrical states rather than the simplistic "on" and "off" states that today's digital processors recognize. By working with a dynamic range of data states in an analog mode, memristor-based computers could be capable of far more complex tasks than just shuttling ones and zeroes around. 

Beyond that, memristors will likely replace both DRAM and hard disks.

Conceptual symmetry between the resistor, capacitor, inductor, and the memristor..

The technology, called memristor, could allow computers to make decisions by understanding past patterns of data it has collected, similar to human brains collecting and understanding a series of events.

For example, a memristor circuit could be capable of telling a microwave the heating time for different food types based on the information it has collected over time, said Stanley Williams, senior fellow at HP.

A memristor circuit requires lower voltage and less time to turn on than competitive memory like DRAM and flash.