Sudoku modelling through JAVA

Concepts: Arrays, Loops, Functions, If-else

Sudoku

Sudoku (数独 sūdoku?, Digit-single) i/suːˈdoʊkuː/, originally called Number Place,[1] is a logic-based,[2][3] combinatorial[4] number- placementpuzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the

grid (also called "boxes", "blocks", "regions", or "sub-squares") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which typically has a unique solution.

Completed puzzles are always a type of Latin square with an additional constraint on the contents of individual regions. For example, the same single integer may not appear twice in the same 9×9 playing board row or column or in any of the nine 3×3 subregions of the 9×9 playing board.[5]

The puzzle was popularized in 1986 by the Japanese puzzle company Nikoli, under the name

Sudoku, meaning single number.[6] It became an international hit in 2005.[7]

Task:

Write a java program to model the Sodoku game.

 Create a 9 X 9 matrix inside main. Write a function or functions to check whether the solution is as per the rule.

 After that we can think of developing the Game for playing the sudoku.

Yotaphone devices to drop Android for Sailfish OS

Out of the box? Out of the droid!

Find out your device's worth with Swappa Android app

Na biwi na bachha, na baap bada na mayia, the whole thing is that ki bhaiya sabse bada Rupaya!

A Casio smartwatch is coming up next year

Shit just got serious!

First-look at the Android-running BlackBerry 'Venice'

Am I seeing a hypersport class Rolls Royace?

13 tips for shooting low light photos on your phone like a pro.

1) Get the exposure right
2) Go manual
3) Keep your shutter open as long as reasonable
4) Stabilize your shot
5) Get the white balance right
6) Use environmental light to your advantage
7) Use flash sparingly
8) Don't zoom
9) Use your native aspect ratio and resolution
10) Shoot Raw on Android
11) Use filters and edit wisely
12) Convert to black and white
13) Know thy camera

Solar Impulse 2 lands in Hawaii, setting record for longest solo flight

It's beautiful, isn't it?

Blocks in JAVA

BLOCK IN JAVA

JAVA supports 2 types of blocks.
1. Static block
2. Non static block

If the block is declared within the static keyword then the block is known as static block.
The static block always executes before the main method, which is executed by the JVM.

If the block is declared without any static keyword then it is a Non Static block.
Non static block always executes before the constructor called by the user.
Static block is executed only for a single time for the whole life cycle of the program. Whereas non static block may execute "n" number of times, as it depends on the user
The existence of the main method will be checked by the JVM before the execution of the Static block.

Static block execution depends on the JVM. Non static block execution depends on the User.

You can write more than 1 static or non static blocks within a single class, as it is accessed top to bottom manner.

Google apologizes for calling black people as gorillas in photos app

Good boy google! *pats pats*

OnePlus Two's image leaks out!

The new flagship is pegged for a July 27 announcement.

Looks gorgeous, doesn't it?
So does its features.

This is what happens when a Google robot gets annoyed with a human

As the Wall Street Journal reports, Google performed a series of experiments in which a human conversed with a computer program. The program had been fed a whole database of movie scripts. You might think, then, that this robot was something of a warmhearted romantic who believed in happy endings.

You might also think that yogurt is made from broccoli.

The conversations were recorded and presented in a paper pleasantly titled "A Neural Conversational Model." (PDF)

One conversation stood out. This was because if the computer program had had arms and legs, I suspect it would have gone MMA on its fellow human conversationalist.

They were chatting about morality. The human kept pressing his robot friend about morality. What was it? What did it mean?

"I need to know how I should behave morally," says the human. The robot understands but replies: "I don't know how to tell you."

The human wonders if morality and ethics are the same. They are, says the robot. But when the human asks for examples of moral behavior, the robot suggests "integrity."

When pressed on the definition of integrity, the robot makes like an unfaithful lover trying to explain herself to her ex: "I don't know what else to say."

It gets worse. When the human exclaims: "Be moral!" the robot shrieks back: "Be a man!"

Below the belt, somewhat?

What followed was surely an exchange that most people reading this have experienced at least 1,412 times in their lives.

The human says: "I really like our discussion on morality and ethics." Yes, the human is a true resident of California, accentuating the positive. I bet he salutes the sun and makes his dog go downward.

However, the robot answers: "And how I'm not in the mood for a philosophical debate."

Oh.

The exchange ends with both parties going to opposite sides of the bed to sulk. Metaphorically, that is.

"What do you like to talk about?" says the human.

"Nothing," replies the robot.

I understand that the human bought the robot flowers, suggested a visit to the symphony followed by a nice dinner out. The robot has yet to reply.

VARIABLES IN JAVA

VARIABLES IN JAVA

JAVA supports 6 types of variables
1. Local variable
2. Static variable
3. Instance variable
4. Final variable
5. Transient variable
6. Volatile variable

LOCAL VARIABLE:
If the variable is declared within a block (block of method, block of constructor, Block of loop, block of if or else, block of switch or case, or any general block)   it is known as local variable.

class Test{
-------block-------
}

We cannot make the local variable as public
We cannot make the local variable as public , private or protected because the local variable can only be accessed within the same block , but the public access specifier makes the variable global. Thus it is not possible.
In short, no access specifier is used for a local variable.
Private makes it accessible within the same class.
Local variable is only able to access within the same block in which it is declared.

Local variable is not a member of the class or object, so it can't be called by class name or object name. It only accesses directly within the same block. Before using the local variable, that variable should be initialised.

Static variable
If the variable is declared within the class and not within the block, with a static keyword, then it is known as static variable. Static variable is known as class level variable. This type of variable can be called by class_name or object_name, within the same class as well as outside , it's possible to call a static variable within the same class directly.
Static variable creates a single copy for the whole program.

Instance variable.
This is known as object level variable, because Instance Variable only allocates memory at the time of the object creation.
If the variable is within the class and not within the block without any static keyword, it is known as non static or instance variable. Instance variable only can be called by the object name.

Final variable.
If the variable is declared with a "final" keyword, then it is known as final variable.
JAVA never supports any "const" keyword to declare a constant. If the variable is declared with a "final" keyword, then it is constant in JAVA.
Final variable may or may not be static in JAVA, by its better for programmer to declare the Final variable as Static.

Lifehack: Make an Air Conditioner Out of a Cooler for Less Than $50BGR

The fan in the video was connected to a battery pack that lasted seven hours, but you can use other power sources including solar panels. Meanwhile, the ice in the cooler melted after five hours.

desertsun02 recommends using big jugs of frozen water inside the cooler so that when they melt, you won’t have to clean it all up. Instead, simply put them back in the freezer when you’re done, and reuse them once the water freezes up again.

OPERATORS IN JAVA

OPERATORS IN JAVA

JAVA supports 44 number of operators and like C and C++, it's divided into 3 categories ,
1. Unary operator.
2. Binary operator
3. Conditional operator.

UNARY: + , - , ++ , -- , !

BINARY:
Arithmatic: + , - , * , / , ÷
Logical: && , ||
Bitwise: & , | , ^
Relational: > , < , >= , <= , != , ==
Assignment: = , += , -= , *= , ÷= , /=
Shift: << , >> , >>> ( unsigned right shift)

Ternary: ?!
Special: ( ), [ ] , , , . , type , instanceof

Modulus operator never works for float and double value in C or C++, but works in JAVA. I.e System.out.println(10.0℅3.0); o/p = 1.0

TYPE OPERATOR OR TYPE CASTING OPERATOR
Typecasting in JAVA is divided into 3 types-
1. Implicit casting
2. Explicit casting
3. Boolean casting.

Instanceof operator: it's am object comparison operator.
This operator always checks the object existence and returns Boolean value.
Object if the child class can be the object of the parent class.

DOT OPERATOR: It access the variable or the constant, accesses the method , accesses the object, accesses the class and accesses the package.

FLOAT AND DOUBLE

Float and Double : these two datatypes always stores the real Constant.
Real Constant is always by default double in nature.( example, 4.2 is double in nature and thus, it is a real Constant.)
Thus, float x = 4.2; is an error.
Rather you have to typecast it as : float x = (float)4.2; or float x = 4.2f.

CHARACTER DATATYPE:
Character in JAVA supports Unicode. 65536 number of characters are supported by the JAVA language, since the maximum value of 16bits is 216 which is 65536.
Boolean in JAVA only supports true or false values.

DATATYPE AND WRAPPER CLASS

JAVA supports 8 primitive datatypes, then the language is not purely object oriented.
For each datatype. JAVA provides a predefined class ( known as wrapper class in JAVA).
Wrapper class is used to make JAVA pure object oriented.

All the wrapper class present in java.lang package and the default package in JAVA.

PRIMITIVE DATATYPE

Datatype.    Size.    default value.    Wrapper class
Byte.             8 Bits.           0.                    Byte
Short.            16 Bits.        0.                    Short      
Int.                 32 Bits.         0                    Integer
Long.             64 Bits.          0L.                Long
Float.             32 Bits.          0.0f.             Float
Double.          64 Bits.         0.0.                Double
Boolean.         1 Bit.             False.           Boolean
Char.               16 Bits.        /u0000.         Character

Wrapper class makes JAVA pure object oriented but still it's not purely object oriented ad it supports primitive datatypes.

Signed and unsigned are the two keywords that are not available in JAVA. So by default the datatype is signed in nature. Character datatype in JAVA is signed in nature, I.e it only holds positive value. (As ASCII value us always positive)

Negative number is always stored in the form of 2's complement. Example: 11111111 -> 00000001(2's complement) = -1.

MAX_VALUE & MIN_VALUE are the two predefined static constants which always display the maximum and the minimum value related to the datatype and present in each wrapper class.

toString ( ) is a predefined static method present in the wrapper class which converts any datatype to the string format.
parseByte( ) is a static method present in the Byte upper class which converts a string to byte datatype.

FLIR One : The thermal camera for Android and iOS now available

Just plug it into your micro USB port(for Android) or to the lightning port( for iPhone) and pheww, work's done! Some cool stuff to handle thereafter.

The FLIR thermal camera allows mobile users to see heat from the comfort of their smartphone or tablet.

Spy stuff huh? Well, to be honest, I have seen better( in James Bond and Mission Impossible of course ).

Google takes next-gen autonomous cars to the streets.

Vroom! Tech has always been something orgasmic to me.
And this is, well... NextGen tech!

Google posted pictures of the car driving ...well, itself, in the streets!

Apple removes Civil War games from App Store for showing the Confederate flag

Poor game developers, all their hard work was also shot upon.

In the wake of last week's horrific shooting at a church in Charleston, Apple assassinated all its civil war games, as a gesture of goodwill, I suppose.

Think different! That's always been Apple. Right?

Class 2

Class 2

Void: The main method never returns any value to the JVM. If the main method doesn't return any value, then the return type should be void in JAVA.
public static = static public
COMMAND LINE ARGUMENT
The arguments accepted by the main function is called command line arguments. The main function in JAVA only accepts array of strings as an argument.
String is a predefined class present in JAVA language.
String args [ ] -> name of the array of strings.

NAMING CONVENTION FOR PREDEFINED MEMBERS.
1. Class -
Example: BufferedReader , String
Each word's first letter should be capital, and there shouldn't be any space.
2. Predefined "to" Method -
Example: toString( ), toCharArray( ) ; I.e except the first word, each word's first letter should be capital.
3. Predefined Constant: SIZE , MAX_VALUE; All the letters should be inupper case.
4. Package: java.lang, javax.swing, java.applet ; here each letter should be in lower case and the packages are separated by a "." symbol.

DEFAULT LENGTH OF THE COMMAND LINE ARGUMENT IS 0.

EXAMPLE OF A COMMAND LINE ARGUMENT:
public class Test{
static public void main ( String args[  ] )
{
    System.out.println (args.length); // 2
    for(int i=0; I<args.length; I++)
    {
        System.out.println (args [ i ]); //10, 20
    }
    System.out.println( args[ 0 ] + args [ 1 ] ); // 1020
    System.out.println(10+20); // 30
    System.out.println (5+6+'A'+'B'+5+6+(4+5)); //76B569
    System.out.println("10" + (5 - 10)); // 10-5
}
}

Convert string to integer by parseInt( ). It is a static member and it is called by a class.
Similarly, string to float can be converted by the use of parseFloat.

SYSTEM.OUT.PRINTLN:
A static member is always called by a Class name and a Non Static member is always called by an object name.
The difference between System.out and System.err is that the output produced by System.err can't redirect a file but System.out can
The difference between print and println is that println just adds a new line after printing your desired line.

Masala of the Maggi

The milk that your milkman leaves at your doorstep every morning is milched from a cow drugged with Oxytocin.

The mangoes you enjoyed this summer had calcium carbide coated onto their skins.

The cauliflower you munched into last winter, was doped with Arsenic.

Yet we panic only when we realise Maggi had lead.

How did Apple manage to reduce the storage size of iOS 9 to 1GB from 5 GB in iOS 8?

This is due to a new technology called 'App Thinning'

Now this consisted of 3 parts, let's just have an bird's eye view:

App Slicing: iOS apps are developed to run on a variety of devices, so they come with code to support all them, whether or not your particular device requires it. App Slicing will allow your device to download only those files required by our device. Example: you don't need the 3x iPhone 6 Plus assets if you're running a 4-inch model.

On-Demand Resources (ODRs): It works on the idea that an app probably doesn't need its entire library of resources at any given time, so parts of it can be downloaded or deleted as needed. Developers will be able to specify what code is needed at what times by tagging sections of code as ODRs. These portions will be automatically downloaded from the App Store when they are required and deleted when they won't be needed again.

Bitcode: It refers to an "intermediate representation" of an app that developers will upload to the App Store rather than a pre-compiled binary. This works hand-in-hand with App Slicing, allowing the bitcode to be compiled on demand as 32-bit or 64-bit, depending on the downloading device. This will also allow any compiler improvements made by Apple to be implemented automatically, rather than having developers resubmit their apps.

INTRODUCTION TO JAVA PROGRAMS

Block----> public class class_name
{
public static void main(string args[ ])
{
System.out.println (...);
}
}

Access specifier in JAVA language:
The major job of access specifier is to specify the scoop of the variable (data member), constructor out any class.
Access specifier---> variable, function, class, constructor.

JAVA folder-> package

Boundaries/scope:
• within the same class
• within the same package
• outside the package

Types of access specifier in JAVA: public, protected, default(no access specifier), private

Public: within the same class, within the same package, outside the package
Protected: within the same class, within the same package and outside the package (only in inheritance)
Default: within the same class, within the same package
Private : within the same class.

In JAVA, you can't declare a variable or function or any member as global.

Java doesn't support an global member like C or C++, bit if a member is declared as public , it behaves as a global member in JAVA.

Execute that class that only contains the main.
You can't execute more than one class simultaneously.

If the class is declared as public then the class name and file name should be the same.

Almost one public class can be declared and that would be the entry point.

Private and public keywords are not allowed for top level class but nested class can be declared as private or protected.

Class
Class is a collection of similar kind of objects, that is from one class we can create "n" number of objects, all with similar type.
Class is a blue print of the object, I.e skeleton.

Class is a logical container which never allocated any memory.
In JAVA , class is able to contain 4 types of members.
1. Data mamber
2. Method member
3. Block member
4. Constructor member

public class Test
{
  int x; // data member
  Test() // constructor member
  {
  }
  static // block member
  {
  }
  public static void main( string args[]) //method member
  {
  System.out.println("Hello");
}

Javac: to compile the JAVA program.
Javap: JAVA dessemble. It will display all the members present in all user defined or pre defined class.

Class name is the identifier which maybe same as the file name, but should satisfy the rules of the identifier ( data member, object/ reference name, method name, constructor name, class name, Package name )
Space is not allowed in identifier.
Identifier rules:
1. Space is not allowed in identifier.
2. Digits are allowed but the name can't start with digits.
3. Should not be a reserved word. (Keyword)
4. No special symbols are allowed except "_" or "$"

PUBLIC STATIC VOID MAIN
In JAVA, "main" is user defined function, but the signature is predefined.
Compiler never checks the "main" method existence.
But the execution is always started from the main method.

KERNEL calls the main method in C and C++
But JVM( JAVA Virtual Machine ) calls the main function in JAVA.
• JAVA Virtual Machine.
• System software
• Development in C language.
• Platform dependant ( but JAVA is platform independant)

JVM is a system software inbuilt to OS (I.e itbis present by default)
The main job of JVM is to execute the class file, and the execution always starts from the main method.l, as the main method is always called by JVM from the OS, which is outside the package. So main method should be declared as public, else it can't be called from outside.

WHY MAIN METHOD IS STATIC IN JAVA?
Main method is called by the JVM with the name of the class.
If a method is called by the class name, it should be declared as static in JAVA.

A curved iPhone is reportedly planned

Hold your breath!
Apple is planning to give an "Edge" to Samsung yet again.
Plus,
Sources claim that Apple is very interested in OLED display technology, and that is good news given how well these displays have evolved in color saturation and brightness.

T-Mobile's iPhones are getting the 'blue screen of death'

If you have the same problem, you are not alone!

From now, you don't need a Facebook account to log into the Facebook messenger

Facebook Messenger no longer requires a Facebook account. Starting today, new Messenger users in the US, Canada, Venezuela and Peru can sign up using a full name and phone number.

Seems like the messenger didn't get much of a success!

Color-changing condoms tell you what sort of VD you just got

A group of teenage inventors have struck upon a clever way to alert folks to the presence of various venereal diseases before the burning starts: fluorescing condoms that light up when they encounter dangerous bacteria or virii.

Data Structure Chapter 1 & 2

Introduction to

Algorithm

What is an Algorithm? (1/2) 
• Definition

– A computable set of steps to achieve a desired result
What is an Algorithm? (2/2) 
• Properties

      –  Finiteness -> an algorithm terminates after a finite numbers of steps 


      –  Definiteness -> each step in algorithm is unambiguous. This means that the action specified by the step cannot be interpreted (explain the meaning of) in multiple ways & can be performed without any confusion 


      –  Input -> an algorithm accepts zero or more inputs 


      –  Output -> it produces at least one output 


      –  Effectiveness -> it consists of basic instructions that are realizable. This means that the instructions can be performed by using the given inputs in a finite amount of time 


Classes of Algorithm (1/4)

• There is no universally accepted breakdown for the various types of algorithms, but there are common classes that algorithms are frequently agreed to belong to e.g.

• Dynamic Programming Algorithms: This class remembers older results and attempts to use this to speed the process of finding new results.

Classes of Algorithm (2/4)

• Greedy Algorithms: Greedy algorithms attempt not only to find a solution, but to find the ideal solution to any given problem.

• Brute Force Algorithms: The brute force approach starts at some random point and iterates through every possibility until it finds the solution.

• Randomized Algorithms: This class includes

any algorithm that uses a random number at

any point during its process.

Classes of Algorithm (3/4)

• Branch and Bound Algorithms: Branch and bound algorithms form a tree of subproblems to the primary problem, following each branch until it is either solved or lumped in with another branch.

• Simple Recursive Algorithms: This type of algorithm goes for a direct solution immediately, then backtracks to find a simpler solution.

Classes of Algorithm (4/4)

• Backtracking Algorithms: Backtracking algorithms test for a solution, if one is found the algorithm has solved, if not it recurs once and tests again, continuing until a solution is found.

• Divide and Conquer Algorithms: A divide and conquer algorithm is similar to a branch and bound algorithm, except it uses the backtracking method of recurring in tandem with dividing a problem into subproblems.

Algorithm Analysis (1/15) • Why should we analyze algorithms?

– A problem may have numerous algorithmic solutions.

– In order to choose the best algorithm for a particular task, you need to be able to judge how long a particular solution will take to run.

– Or, more accurately, you need to be able to judge how long two solutions will take to run, and choose the better of the two.

– You don't need to know how many minutes and seconds they will take, but you do need some way to compare algorithms against one another.

Algorithm Analysis (2/15)

• Most algorithms transform input objects into output objects.

• The running time of an algorithm typically grows with the input size.

• Average case time is often difficult to determine.

• We focus on the worst case running time.

– Easier to analyze

– Crucial to applications such as games, finance and robotics

Algorithm Analysis (3/15)

• How to Calculate Running Time

– Write a program implementing the algorithm

– Run the program with inputs of varying size and composition

– Use a method like System.currentTimeMillis() to get an accurate measure of the actual running time

– Plot the results

Algorithm Analysis (4/15) 
• Limitations

– It is necessary to implement the algorithm, which may be difficult.

– Results may not be indicative of the running time on other inputs not included in the experiment.

– In order to compare two algorithms, the same hardware and software environments must be used.

Algorithm Analysis (5/15) 
• Theoretical Analysis

– Uses a high-level description of the algorithm instead of an implementation

– Characterizes running time as a function of the input size, n.

– Takes into account all possible inputs

– Allows us to evaluate the speed of an algorithm independent of the hardware/software environment

Algorithm Analysis (6/15)

• Primitive Operations

– Basic computations performed by an algorithm

– Identifiable in pseudocode

– Largely independent from the programming language

– Exact definition not important (we will see why later)

– Assumed to take a constant amount of time in the RAM model

Algorithm Analysis (7/15)

• Primitive Operations Examples: – Evaluating an expression
– Assigning a value to a variable
– Indexing into an array

– Calling a method
– Returning from a method

Algorithm Analysis (8/15) 
• Counting Primitive Operations

• By inspecting the pseudocode, we can

determine the maximum number of primitive

operations executed by an algorithm, as a

function of the input size

Algorithm arrayMax(A, n) currentMax ¬ A[0]
for i ¬ 1 to n - 1 do
if A[i] > currentMax then currentMax ¬ A[i]

{ increment counter i } return currentMax

# operations 1

n
(n - 1) (n - 1) (n - 1) 1
4n - 1

Total

Algorithm Analysis (9/15) 
• Estimating Running Time

– Algorithm arrayMax executes 4n - 1 primitive operations in the worst case.

– Define:

• a = Time taken by the fastest primitive operation 
• b = Time taken by the slowest primitive operation

– Let T(n) be worst-case time of arrayMax. Then • a(4n-1)<=T(n)<=b(4n-1)

– Hence, the running time T(n) is bounded by two linear functions

Algorithm Analysis (10/15) 
• Growth Rate Vs Running Time

– Changing the hardware/ software environment 
• Affects T(n) by a constant factor, but
• Does not alter the growth rate of T(n)

– The linear growth rate of the running time T(n) is an intrinsic property of algorithm arrayMax

Algorithm Analysis (11/15)

•  Worst-case Complexity

            –  Maximum steps the algorithm takes for any possible input. 


            –  Most tractable measure. 


•  Average-case Complexity

            –  Average of the running times of all possible inputs. 


            –  Demands a definition of probability of each input, 
which is usually difficult to provide and to analyze. 


•  Best-case Complexity 
– Minimum number of steps for any possible input. – Not a useful measure. 


Algorithm Analysis: (12/15) 
Example

Alg.: MIN (a[1], ..., a[n]) m ← a[1];

for i ← 2 to n if a[i] < m

then m ← a[i]; Running time:

– the number of primitive operations (steps)

executed before termination
T(n) =1 [first step] + (n) [for loop] + (n-1) [if condition] + (n-1) [the assignment in then] = 3n - 1

Order (rate) of growth:

– The leading term of the formula

– Expressestheasymptoticbehaviorofthealgorithm


Algorithm Analysis: (13/15) • Typical Running Time Functions

– 1 (constant running time):
• Instructions are executed once or a few times

– logN (logarithmic)
• A big problem is solved by cutting the original problem in smaller

sizes, by a constant fraction at each step – N (linear)

• A small amount of processing is done on each input element – N logN

• A problem is solved by dividing it into smaller problems, solving them independently and combining the solution

Algorithm Analysis: (14/15) • Typical Running Time Functions

– N2 (quadratic)
• Typical for algorithms that process all pairs of data items (double

nested loops) – N3 (cubic)

• Processing of triples of data (triple nested loops)

– NK (polynomial)

– 2N (exponential)
• Few exponential algorithms are appropriate for practical use

Algorithm Analysis: (15/15)

•

Asymptotic Notations

A way to describe behavior of functions in the limit – Abstracts away low-order terms and constant factors
– How we indicate running times of algorithms
– Describe the running time of an algorithm as n grows to ¥

• • •

O notation: (Big Oh)
– asymptotic “less than”:

W notation: (Big Omega) – asymptotic “greater than”:

Q notation: (Big Theta) – asymptotic “equality”:

f(n) “≤” g(n) f(n) “≥” g(n) f(n) “=” g(n)

O(Big Oh) -Notation

O(Big Oh) - Example

•  2n2 = O(n3): 


•  1000n2+1000n = O(n2): 


2n2 ≤cn3Þ2≤cnÞc=1andn0=2 • n2 = O(n2): n2 ≤ cn2 Þ c ≥ 1 Þ c = 1 and n0= 1

1000n2+1000n ≤ 1000n2+ 1000n2 = 2000n2
Þ c=2000 and n0 = 1

•  n = O(n2): n ≤ cn2 Þ cn ≥ 1 Þ c = 1 and n0= 1 


•  2n + 10 = O(n) : 


•  n2¹O(n) 


•  7n -2 = O(n) 


•  3n3 + 20n2 + 5 = O(n3) 


•  3 logn + log log n = O(log n) 


W (Big Omega) - Notation

• Intuitively: W(g(n)) = the set of functions with a larger or same order of growth as g(n)

W (Big Omega) - Example – 5n2 = W(n)

$ c, n0 such that: 0 £ cn £ 5n2 Þ cn £ 5n2 – 100n + 5 ≠ W(n2)

$c,n0 suchthat:0£cn2 £100n+5 100n + 5 £ 100n + 5n (" n ³ 1) = 105n

cn2 £ 105n
Since n is positive Þ cn – 105 £ 0

Þ c = 1 and n0 = 1

Þ n(cn – 105) £ 0
Þ contradiction: n cannot be smaller than a constant

– n = W(2n), n3 = W(n2), n = W(logn)


Þ n £ 105/c

Q (Big Theta) - Notation

• Intuitively Q(g(n)) = the set of functions with the same order of growth as g(n)

Q (Big Theta) - Example • n2/2 –n/2 = Q(n2)

•  1⁄2 n2 - 1⁄2 n ≤ 1⁄2 n2 "n ≥ 0 Þ c2= 1⁄2 


•  1⁄2 n2 - 1⁄2 n ≥ 1⁄2 n2 - 1⁄2 n * 1⁄2 n ( "n ≥ 2 ) = 1⁄4 n2 Þ c1= 1⁄4 
– n≠Q(n2):c1 n2 ≤n≤c2 n2 Þ only holds for: n ≤ 1/c1 
6n3 ≠ Q(n2):c1 n2 ≤6n3 ≤c2 n2 Þ only holds for: n ≤ c2 /6 
n≠Q(logn):c1 logn≤n≤c2 logn
Þ c2 ≥ n/logn, " n≥ n0 – impossible 


Asymptotic Notations - Exercise

• For each of the following pairs of functions, either f(n) is O(g(n)), f(n) is Ω(g(n)), or f(n) is Θ(g(n)). Determine which relationship is correct.

      –  f(n) = log n2; g(n) = log n + 5 


      –  f(n) = n; g(n) = log n2 


      –  f(n) = log log n; g(n) = log n 


      –  f(n) = n; g(n) = log2 n 


      –  f(n) = n log n + n; g(n) = log n 


      –  f(n) = 10; g(n) = log 10 


      –  f(n) = 2n; g(n) = 10n2 


      –  f(n) = 2n; g(n) = 3n 


f(n) = Q (g(n)) f(n) = W(g(n)) f(n) = O(g(n)) f(n) = W(g(n)) f(n) = W(g(n)) f(n) = Q(g(n)) f(n) = W(g(n)) f(n) = O(g(n))

More on Asymptotic Notations

•  There is no unique set of values for n0 and c in proving the asymptotic bounds 


•  Prove that 100n + 5 = O(n2)
– 100n+5≤100n+n=101n≤101n2 
for all n ≥ 5
n0 =5andc=101isasolution 
– 100n+5≤100n+5n=105n≤105n2 for all n ≥ 1 


n0 = 1 and c = 105 is also a solution
Must find SOME constants c and n0 that satisfy the asymptotic notation relation

Comparisons of Functions

•  Theorem:
f(n) = Q(g(n)) Û f = O(g(n)) and f = W(g(n)) 


•  Transitivity:
– f(n) = Q(g(n)) and g(n) = Q(h(n)) Þ f(n) = Q(h(n)) 
– SameforOandW 


•  Reflexivity: 
– f(n) = Q(f(n)) 
– SameforOandW 


•  Symmetry: 
– f(n) = Q(g(n)) if and only if g(n) = Q(f(n)) 


•  Transpose symmetry: 
– f(n) = O(g(n)) if and only if g(n) = W(f(n))
 


•

Asymptotic Notations in Equations

On the right-hand side
– Q(n2) stands for some anonymous function in Q(n2) 2n2 + 3n + 1 = 2n2 + Q(n) means:
There exists a function f(n) Î Q(n) such that

2n2 + 3n + 1 = 2n2 + f(n)

On the left-hand side

2n2 + Q(n) = Q(n2)

No matter how the anonymous function is chosen on the left-hand side, there is a way to choose the anonymous function on the right-hand side to make the equation valid.

Sorting Algorithms

Name	Best	Average	Worst	Method
Quick	n log n	n log n	n2	Partitioning
Merge	n log n	n log n	n log n	Merging
Heap	n log n	n log n	n log n	Selection
Insertion	n	n2	n2	Insertion
Selection	n2	n2	n2	Selection
Bubble	n2	n2	n2	Exchanging

Other Sorting Algorithms

• Introsort
• Timsort
• Shell sort
• Binary Tree sort • Cycle sort

• Library sort
• Patience sort • Smoothsort

• Strand sort • Tournament

sort
• Cocktail sort • Comb sort
• Gnome sort • Bogosort

Comparison Sort

Other Sorting Algorithms

• Pigeonhole sort • Bucket sort
• Counting sort
• LSD Radix sort
• MSD Radix sort • Spreadsort

Non Comparison Sort

______________________________________________________________________________________

Introduction to Data Structures 

• Problem solving =

– Understanding the problem – Designing a solution

– Implementing the solution 

• What exactly is a solution? – A solution = a program 

An Algorithm 

• An algorithm is a sequence of steps that take us from the input to the output.

• Properties of Algorithm 

–  Input: may or may not some input data

–  Output: at least one output

–  Definiteness: every step must be clear and unambiguous

–  Finiteness: It must terminate after a finite number of steps

–  Effectiveness: the steps must be basic steps so that dry-run will be possible

Data Organization 

• Any algorithm we come up with will have to manipulate data in some way 

– The way we choose to organize our data directly affects the efficiency of our algorithm 

• Solution = algorithm + data organization

– Both components are strongly interconnected. 

Data structures 

• Data structure: An arrangement of data in a computer’s memory (or sometimes on a disk).

• conceptual and concrete ways to organize data for efficient storage and efficient manipulation 

– Arrays, linked lists, stacks, trees, hash tables. 

• Algorithms manipulate the data in these 

structures in order to accomplish some task. – Inserting an item, search for an item, sorting. 

How are Data structures used • As an actual way to store real-world data 

– e.g., lists, trees

• As a tool to be used only within a program 

(not visible to the user)

– E.g., stacks, queues, priority queues 

• As a model of real-world situations – e.g., graphs 

Why different data structures 

• Each data structure has different advantages and disadvantages, and will be useful for different types of applications. 

– Example: arrays

• Fast access: if we know the index of the item we are looking for • Insertion and Deletion is slow

• size is fixed 

– Maintain a Job Queue • Queuecanbeused 

– Hierarchy of employees of an organization • Tree can be used  

Stack 

Types of data structures 

Data Structure 

Linear Non Linear 

Queue Tree Graph 

ADT 

• A primitive data type holds a single piece of data – e.g. in Java: int, long, char, boolean etc.

– Legal operations on integers: + - * / ... 

• Adatastructurestructuresdata! 

–  Usually more than one piece of data

–  Should provide legal operations on the data

–  The data might be joined together (e.g. in an array): a 

collection 

• An Abstract Data Type (ADT) is a data type together with the operations, whose properties are specified independently of any particular implementation.

Principles of ADT 

• Encapsulation:Providingdataandoperationsonthe data 

• Abstraction:hidingthedetails. 

– e.g. A class exhibits what it does through its methods; however, the details of how the methods work is hidden from the user 

• Modularity: Splitting a program into pieces.

– An object-oriented program is a set of classes (data structures) which work together.

– There is usually more than one way to split up a program .

__________________________________________________________________________________________________________________________________________________________________

A	R	R	A	Y	\0
327	328	329	330	331	332

• An array is an indexed sequence of components

– The array occupies sequential storage locations

– The length of the array is determined when the array is created, and cannot be changed

– Each component of the array has a fixed, unique index • Indices range from a lower bound to an upper bound

– Any component of the array can be inspected or updated by using its index

• This is an efficient operation: O(1) = constant time

Array Dimensions

• The simplest form of array is a ‘one- dimensional’ array

• The dimension of an array can be 1 or more than 1

• 1-D array – int A[10];

• 2-D array
– int A[3][5];

General Info

•   The two basic operations that access an array are 
– Extraction x = A[i]; – Storing A[i] = x; 


•   The smallest index of the array is called ‘lower bound’ (0 always in ‘C’) and highest index is ‘upper bound’ 
• The number of elements in an array is – upper - lower + 1 


General Info

•   Neither the upper nor the lower bound of an array can be changed during program execution (Static) 


•   One very useful technique is to declare a bound as a constant identifier (MACRO) 


1-D Array • Declaration

– int A[100];

•   The address of first element (A[0]) is called the 
‘base address’ let it be denoted by base(A) 


•   Suppose the size of each individual element of 
the array is esize 


Then the reference to the A[i] is to the 
element at location base(A) + i * esize

• int a[5]; • int *p;
• p = a;

‘a’ is a constant pointer pointing to the first

1-D Array & Pointer 

• Array of pointers – int *a[10]; 

– Array a can store 10 addresses – Ex. a[0] = &p, a[1] = &q like that 

• Pointer to an array

– int (*a)[10];

– a is a pointer pointing to an array of 10 integers 

Declaration 

– int A[3][5];
• This defines a new array containing 3 

elements 

• Each of these elements is itself an array containing 5 integers 

2-D Array • A 2-D array actually stored as a linear array 

– int numbers[3][4];

2-D Array & Pointer 

• int A [3][4]; 
• • int (*p)[4]; 

Array Operations 

• Traversal 

• Searching 

• Sorting 

• Insertion
– At begin, end, specific position, after element, before 

element 

• Deletion 

– From begin, end, specific position, after element, before element, element 

• Merging 

• Reversing 

Inserting an Element 

1. If array is full then print “overflow”

2. Else shift the elements to right from the position where you want to insert

3. Insert the new element at that position