Java Program using 4D array [closed]_问答_开发者

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I'm a first year computer engineering student and I'm quite new here. I have been learning Java for the past three and a half months, and C++ for six months before that. My knowledge of Java is limited to defining and using own methods, absolute basics of object-oriented programming like use of static data members and member visibility.

This afternoon, my computer programming prof taught us about multi-dimensional arrays in Java. About multi-dimensional arrays being simply arrays of arrays and so on. He mentioned that in nominal, educational programming, arrays beyond 2 dimensions are almost never used. Even 3D arrays are used only where absolutely essential, like carrying out scientific functions. This leaves next to zero use for 4D arrays as using them shows that "you're using the wrong datatype" in my prof's words.

However, I'd like to write a program in which the use of a 4D array, of any data type, primitive or otherwise, is justifi开发者_如何转开发ed. The program must not be as trivial as printing the elements of the array.

I have no idea where to begin, this is why I am posting this here. I'd like your suggestions. Relevant problem statements, algorithms, and bits and pieces of code are also welcome.

Thank you.

Edit: Forgot to mention, I have absolutely no idea about working with GUIs in Java, so please do not post ideas that implement GUIs.

Ideas:

- Matrix multiplication and it's applications like finding shortest path in graphs - Solving of systems of equations - Cryptography -- many cryptoprotocols represent data or keys or theirs internal structures in a form of matrices. - Any algo on graphs represented as matrices

I must have been having some kind of fixation on matrices, sorry :)

For 4D arrays one obvious thing I can think of is the representation of 3D environment changing in time, so 4th dimension represents time scale. Or any representation of 3D which have additional associated property placed in 4th dimension of array.

You could create a Sodoku hypercube with 4 dimensions and stores the numbers the user enters into a 4dimensional int array.

One use could be applying dynamic programming to a function that takes 4 integer parameters f(int x,int y,int z,int w). To avoid calling this expensive function over and over again, you can cache the results in a 4D array, results[x][y][z][w]=f(x,y,z,w);.

Now you just have to find an expensive integer function with arity of 4, oh, and a need for calculating it often...

Just to back him up,..your prof is quite right. I'm afraid I might be physically violent to anyone using a 4D+ array in production code.

It's kinda cool to be able to go into greater than 3 dimensions as an educational exercise but for real work it makes things way too complicated because we don't really have much comprehension of structures with greater than 3 dimensions.

The reason it's difficult to come up with a practical use for 4D+ arrays is because there is (almost) nothing that complicated in the real world to model.

You could look into modelling something like a tesseract , which is (in layman's terms ) a 4D cube or as Victor suggests use the 4th dimension to model constant time.

HTH

There are many possible uses. As others have said, you can model a hypercube or something that makes use of a hypercube as well as modeling a change over time. However, there are many other possible uses.

For example, one of the theoretical simulation models of our universe uses 11th dimensional physics. You can write a program to model what these assumed physics would look like. The user would only be able to see a 3-dimensional space which definitely limits usability, but the 4th dimensional coordinate could act like the changing of a channel allowing the user to change their perspective. If a 4th dimensional explosion occurs, for example, you might even want a 5th dimensional array so that you can model what it looks like in each connected 3-dimensional space as well as how it looks in each frame of time.

To take a step away from the scientific, think about an MMORPG. Today many of those games uses "instanced" locations which means that a copy of a given zone is created exclusively for the use of a given group of players so to prevent lag. If this "instanced" concept was given a 4th dimensional coordinate and it allows players to shift their position across instances it could effectively allow all server worlds to be merged together while allowing the players a great deal of control over where they go while decreasing cost.

Of course, your question wants to know about ideas without using a GUI. That's a bit more difficult because you are working in a 2D environment. One real application would be Calculus. We have 3D graphing calculators, but for higher dimensions you pretty much have to do it by hand. A pogram that aims to solve these calculations for you might not be able to properly display the information, but you can certainly calculate it. Also, when hologaphic interfaces become a widespread reality it may be possible to represent a hypercube graph in 3D making such a program useful.

You might be able to write a text based board game where the position of pieces is represented with text. You can add dimensions and game rules to use them.

The simplest idea I could give you is a save state system. At each interval the program in memory is copied and stored into a file. It's coordinate is it's position in time. At face value you may not need a 4D array to handle this, but suppose the program you were saving states of used a 3D array. You could set it up to represent each saved state as a position in time that you can make use of and then view the change in time.

I'm not sure what specifically you could do with this, because I just started thinking about it. But you could possibly use a 4D array for some sort of basic physics simulation, like modeling a projectile flight involving some wind values and what not. That just came to mind because the term 4D always brings to mind that the "position" of any object is 4 values, with time as the 4th.

Being a physics student we have only 3 dimension of space but we have a 4th dimension which is time. So thinking in that way we can think of an array of any dimension(1D or 2D or 3D) whose values differ with time or an array which keeps the record of every array whose values changed with time. It seems to be quite known to us. For example the "ATTENDANCE REGISTER" which we usually have in our classroom.

This is my view to it.

That's it. Enjoy :-)

To give a concrete example for the Ishtar's answer: Four-string alignment. To compute optimal two-string alignment, you write one string along one (say, horizontal) axis of a 2D-array (a matrix!) and the other one along the other array. The array is filled with edit costs, and the optimal alignment of the two strings is the one which produces the lowest cost, associated with a path through the matrix. A common way of finding such a path is by the above mentioned dynamic programming. You can look up 'Levenshtein distance' or 'edit distance' for technical details.

The basic idea can be expanded to any number of strings. For four strings you'd need a four-dimensional array, to write each string along one of the dimensions.

In practice, however, multiple string alignment is not done this way, for at least two reasons:

Lack of flexibility: Why would you need to align exactly four strings??? In computational molecular biology, for example, you might wish to align many strings (think of DNA sequences), and their number is not known in advance, but it is seldom four. You program would be useful for a very limited class of problems.
Computational complexity, in space and time. The requirements are exponential in the number of dimensions, making the approach impractical for most real-world purposes. Besides, most of the entries in such multi-dimensional array would lie on such suboptimal paths, which are never even touched, so that storing them would be simply waste of space.

So, for all practical purposes, I believe your professor was right.