Dynamic Programming or Memoization : Simple optimizing Concept yet Effective

Dynamic Programming or Memoization is a well known technique for optimization.  It is just a method that remembers your previously calculated results and stores it somewhere so that when time comes you can use it again.

Just to begin with, a straightforward example of Memoization is calculation of Factorials. When we calculate Factorial of 5, i.e.

5! = 1*2*3*4*5 = 120

Now when you're asked to calculate Factorial of 6, a normal human being wouldn't go on like 1*2*3*4*5*6 rather he would think that "Well, I just calculated upto 5! why not simply multiply 6 to the answer of 5! " This is exactly what we are going to make our computers to do.

So, How do I make computer to remember pre-calculated results?
Answer is as simple as the question, just store them at a particular location in any array/list/vector.

Have a look at this simple Python implementation for memoized Factorial.

C/C++ and Python Program to find GCD of a list of numbers

A very easy question though, yet thought posting about it thinking it may improve my explanation prowess.

Lets get back to old school math, how did we find Greatest Common Divisor (GCD) or you may call it Highest Common Factor(HCF) of two numbers?

Assuming you know primary Maths, I'd proceed further.

Lets take an example before we go ahead.

Find GCD of 54 and 24.

Divisors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54.

Divisors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.

Common divisors of 54 and 24: 1, 2, 3, 6

The greatest of these is 6.

Hence gcd(54,24) = 6

Okay, lets write an algorithm for this. Well, one would say, there's nothing to think of any algorithm, things are crystal clear. Find out the factors of two numbers, then find common factors and then the largest of them.

But brother! There exists a better algorithm. Our Father of Geometry, Euclid, left us an algorithm already. We simply have to implement it.

Fast Power Algorithm: C/C++ and Python Code

In competitive programming, traditional way to finding power may not work sometimes.

By traditional way I mean if we have to find 2^10 (just as an example).

Or else simply by using library function after including math.h (in C) we can do it by pow(2,10)

Well, but this doesn't help us anymore when it comes to finding base to the power (base^power) where power could be anything in the range 0 to 1000000 or even greater value, same goes for base

Whilst you may think it impractical but in competitive programming questions ask us find Modulus of the answer by any prime number such as 1000000007, just to make sure answer remains in range of int data type.

i.e. pow(2,100)%1000000007 = 976371285

Lets come to the point and discuss what you have come for :)

Fast Algorithm:

result = 1
If power is odd:
    result = result*value
value = value*value
power = power/2

Yeah, I know, above algorithm more looks like a code & was nothing but a bouncer. ;)

New 2013 RSS Facebook Twitter Google+ Buttons with Hover Effect

A new share button widget for 2013 with RSS Facebook Twitter and Google+ buttons (YouTube too on request)

Tried to make as looks as simple as possible like Windows 8 :p

It'll consume a very little space of your blog & can even be placed in a size of search bar's area :)

Qualities of the gadget are same as we had in earlier versions v1, v2. These versions were colored. But this one is Black & White for education or decent tech blogs.

Sub-Domain/Custom Domain: Advantages of Custom Domain

Okay firstly I'll clear that What is a custom domain? and What is Subdomain?

Subdomain:

The free domain that blogspot provides you with the extension .blogspot.com is a subdomain.

Actually the blogspot.com itself is a domain and when you sign up to create a blog you'll be prompted for a subdomain like "SUB-DOMAIN".blogspot.com

Image Credit: joomla365.com

Got it? Proceeding further with a 'Yes' :-)

Custom Domain:

Its a Top Level Domain (TLD) with extension .com .org .net .biz  and many more like .in(regionally targeted for India) .us .me(for personal site) etc.


Now we'll discuss the Advantages of having a Custom Domain for your blog.

6.00x MITx Python: Final Exam Preparation

Just thought of creating an online journal to revise things on the go, cause when I was reviewing video lectures from the beginning it took a lot of time. Sometimes I've to fast forward, normal pace at confusing situations & again fast forward made me sick of revising videos.

I'm only considering the Python language and use of its objects in this section.
This is just an index of all the topics upto Mid Term 1: (Still revising Classes is left for me :( )

Lets begin: (All the links lead to quick overview of respective topic and below the Titles I've briefly written about the stuff that topic contains)