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There's one question posted about Fibonacci Series, which I am much familiar with it. But there are multiple answers and linked questions to it. As I was digging through it with some interest, there's a solution which is linked to here
This algorithm solves the problem by O(log(n)) quite impressive. But I couldn't understand the logic and so called Matrix exponentiation [looked wiki, but unable to relate to it].
So kindly anyone can explain exactly how they achieved with more details and better explanation [if you can explain with code, prefer in Java, much helpful].
Thanks :)
What you need to understand is the algorithm, not the implementation.
The first thing you need to understand is that this algorithm will not give you all the fibonacci numbers, only those with with a n that is a power of 2.
The second thing is that a multiplication of constantly sized matrices of course takes constant ( O(1) ) time.
The trick now is to correctly note that the n'th fibonacci number can be formed by n-times multiplication of the matrix described in your link, which i will call M.
You get the log complexity by now "reordering" the matrix operations from, for example M*(M*(M*M)) to (M*M)*(M*M). With each matrix squaring, you go to M^2n instead of M^n+1.
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I'm having trouble understanding the concept of using FFT to calculate frequency changes. I've been scavenging through a ton of articles on this concept but it's still confusing me. I found a Stack Overflow article about the steps to take to calculate the frequency, but I'm still a little bit confused on exactly what to do in Java.
Sounds like you need to start way back with some general concepts. An FFT is just a fast DFT. A DFT uses Fourier decomposition on a set of sampled data. So first you need to understand what a waveform is, what a sinusoid is, what a frequency is (and is not the same as a musical pitch), and how Fourier's theorem works to relate the two. Then how to compute a DFT on a window of a sampled waveform, and how to interpret the complex result vector. Then how to do it fast in Java.
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I've been aksed to write a program that finds the largest area of equal neighbour elements in a rectangular matrix and prints its size. I tried to construct a 2d array with some numbers but I think that I should switch to using a tree or something in order to solve this problem. Chould somebody suggest a possible way of solving it?
For example:
"Hint: use the algorithm Depth-first search or Breadth-first search."
Sounds like a standard maze search problem. I suggest you use recursion to find all the elements which you haven't been to before which have the same number as the one you have found. You can either update the matrix as you go or create a copy to keep track of the cells you have visited. So you don't need a tree or even an additional complex data structure.
use the algorithm Depth-first search or Breadth-first search
These are two types of recursive searches. I suspect you could implement both of these to see how they behave.
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I have a program which involves with a bunch of huge numbers (I have to put them into bignumbers type). The time complexity is unexpectedly huhge too. So, I was wondering, do these two factors have a connections? Any comments are greatly appreciated.
Do they have a connection to each other? Probably not.
You can have a large complexity algorithm working on small numbers (such as calculating the set of all sets for ten thousand numbers all in the range 0..30000) and you can have very efficient algorithms working on large numbers (such as simply adding up ten thousand BigInteger variables).
However, they'll both probably have a cascading effect on the time it takes your program to run. Large numbers will add a bit, a high-complexity algorithm will add a bit more I say 'add' but the effect is likely to be multiplicative, much worse - for example, using an inefficient algorithm may may your code take 30% longer, and the use of BigInteger may add 30% to that, giving you a 69% overall hit:
t * 1.3 * 1.3 = 1.69t
Sorry for the general answer but, without more specifics in the question, a general answer is the best you'll probably get. In any case, I believe (or at least hope) it answers the question you asked.
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I need som help understanding how this works! how do I go about calculating the complexity of 'Computing the first half of an array of n items' or 'displaying the third element in a linked list' ? I need someone to explain how this works, theses are just examples, so be free to use your own if it helps explaining! thank you.
You should look at how the processing time of the algorithm grows as the size of the input grows. I'll take your two concrete examples:
Computing the first half of an array of n items
We need to process n/2 items. If n doubles, then the processing time should also double. Consequently, this is a linear operation (i.e. O(n)).
displaying the third element in a linked list
We always want to display the third element, so the size of the list doesn't actually matter. If it doubles, we don't care; the processing time is not affected. Consequently, this is a constant-time operation (i.e. O(1)), it doesn't depend on the size of the input.
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I am learning java on my own. I have books to read. but i feel i am not really coding anything significant . Can you guys give me any programming problem that would really help me get more practical experience rather than a theoretical experience with java ?
Appreciate it.
silverkid
Many people learn new languages by solving problems from Project Euler.
To give you some examples, here are the 10 first problems in the project:
Add all the natural numbers below one thousand that are multiples of 3 or 5.
Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed four million.
Find the largest prime factor of a composite number.
Find the largest palindrome made from the product of two 3-digit numbers.
What is the smallest number divisible by each of the numbers 1 to 20?
What is the difference between the sum of the squares and the square of the sums?
Find the 10001st prime.
Discover the largest product of five consecutive digits in the 1000-digit number.
Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.
Calculate the sum of all the primes below two million.
I just wanted to put an idea out here for you from my own experiences.
Whilst studying I was given the task of creating a Client/Sever chat application, I found it really interesting and there are plenty of obvious ways you can extend the program to better your ability.
For instance, start with a basic server and client simply sending text to one another. And then advance to having users (from a database perhaps) who have to log in to the application. You can make it as simple and as complicated as you wish.
Hope this helps.
Tony
Try this:
Martyr2’s Mega Project List
Java exercises:
http://www.google.com/search?aq=f&sourceid=chrome&ie=UTF-8&q=java+exercise
Java examples:
http://www.exampledepot.com/
What area of Java programming are you interested in? Web, device, desktop?
Sure Why Not, Here it is : http://download.oracle.com/javase/tutorial/