Java Applet

What is Applet?
An applet is a Java program that can be embedded into a web page. It runs inside the web browser and works at client side. An applet is embedded in an HTML page using the APPLET or OBJECT tag and hosted on a web server.

Important points :

1. All applets are sub-classes (either directly or indirectly) of java.applet.Applet class.
2. Applets are not stand-alone programs. Instead, they run within either a web browser or an applet viewer. JDK provides a standard applet viewer tool called applet viewer.
3. In general, execution of an applet does not begin at main() method.
4. Output of an applet window is not performed by System.out.println(). Rather it is handled with various AWT methods, such as drawString().

Turtle Graphics

“Turtle” is a Python feature like a drawing board, which lets us command a turtle to draw all over it! We can use functions like turtle.forward(…) and turtle.right(…) which can move the turtle around.Commonly used turtle methods are :

Method	Parameter	Description
Turtle()	None	Creates and returns a new tutrle object
forward()	amount	Moves the turtle forward by the specified amount
backward()	amount	Moves the turtle backward by the specified amount
right()	angle	Turns the turtle clockwise
left()	angle	Turns the turtle counter clockwise
penup()	None	Picks up the turtle’s Pen
pendown()	None	Puts down the turtle’s Pen
up()	None	Picks up the turtle’s Pen
down()	None	Puts down the turtle’s Pen
color()	Color name	Changes the color of the turtle’s pen
fillcolor()	Color name	Changes the color of the turtle will use to fill a polygon
heading()	None	Returns the current heading
position()	None	Returns the current position
goto()	x, y	Move the turtle to position x,y
begin_fill()	None	Remember the starting point for a filled polygon
end_fill()	None	Close the polygon and fill with the current fill color
dot()	None	Leave the dot at the current position
stamp()	None	Leaves an impression of a turtle shape at the current location
shape()	shapename	Should be ‘arrow’, ‘classic’, ‘turtle’ or ‘circle’

Omega Notation

Ω Notation: Just as Big O notation provides an asymptotic upper bound on a function, Ω notation provides an asymptotic lower bound.

Ω Notation can be useful when we have lower bound on time complexity of an algorithm. As discussed in the previous post, the best case performance of an algorithm is generally not useful, the Omega notation is the least used notation among all three.

For a given function g(n), we denote by Ω(g(n)) the set of functions.

Ω (g(n)) = {f(n): there exist positive constants c and
                  n0 such that 0 <= c*g(n) <= f(n) for
                  all n >= n0}.

Let us consider the same Insertion sort example here. The time complexity of Insertion Sort can be written as Ω(n), but it is not a very useful information about insertion sort, as we are generally interested in worst case and sometimes in average case.

Reference: https://www.geeksforgeeks.org/analysis-of-algorithms-set-3asymptotic-notations/

Big O Notation

Big O Notation: The Big O notation defines an upper bound of an algorithm, it bounds a function only from above. For example, consider the case of Insertion Sort. It takes linear time in best case and quadratic time in worst case. We can safely say that the time complexity of Insertion sort is O(n^2). Note that O(n^2) also covers linear time.
If we use Θ notation to represent time complexity of Insertion sort, we have to use two statements for best and worst cases:
1. The worst case time complexity of Insertion Sort is Θ(n^2).
2. The best case time complexity of Insertion Sort is Θ(n).

The Big O notation is useful when we only have upper bound on time complexity of an algorithm. Many times we easily find an upper bound by simply looking at the algorithm.

O(g(n)) = { f(n): there exist positive constants c and 
                  n0 such that 0 <= f(n) <= c*g(n) for 
                  all n >= n0}

Reference:https://www.geeksforgeeks.org/analysis-of-algorithms-set-3asymptotic-notations/

Theta Notation

Θ Notation: The theta notation bounds a functions from above and below, so it defines exact asymptotic behavior.
A simple way to get Theta notation of an expression is to drop low order terms and ignore leading constants. For example, consider the following expression.
3n³ + 6n² + 6000 = Θ(n³)
Dropping lower order terms is always fine because there will always be a n0 after which Θ(n³) has higher values than Θn²) irrespective of the constants involved.
For a given function g(n), we denote Θ(g(n)) is following set of functions.

Θ(g(n)) = {f(n): there exist positive constants c1, c2 and n0 such 
                 that 0 <= c1*g(n) <= f(n) <= c2*g(n) for all n >= n0}

The above definition means, if f(n) is theta of g(n), then the value f(n) is always between c1*g(n) and c2*g(n) for large values of n (n >= n0). The definition of theta also requires that f(n) must be non-negative for values of n greater than n0.

Data Structure in a NutShell

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                      This blog focuses on discussing project works,assignments and computer science related subjects.Hope it will be useful.