I was searching google for something and saw the post that some one needed a piece of software in which he can take a sheet of material- and that he can maximize the cuts.
he needs to be able to enter the width and the length of the roll.
Then he would enter the sizes of cuts that he would need. After all the sizes are entered, the software would tell me how to cut the material so that he can achieve maximum efficiency.
Possible???
is there some AI involved?
This is referred to as a packing problem and is an important area of research in combinatorics, a field of mathematics. See http://en.wikipedia.org/wiki/Packing_problem
Yes it is possible and done in manufacturing. The simple way to think about it is you try any combination the computer can think of and take the one that is best (brute force). Basically it pretends to make a cut and then sees what is left, makes another pretend cut and sees what is left until the material is gone and then it tries them in a different location/order.
It is an optimization problem and there are many solutions out there.
http://en.wikipedia.org/wiki/Optimization_problem A wiki link that will lead you to many hours of reading.
This is entirely possible. It's just an optimization layout problem. I can't help you code it, but it's definitely possible and I suspect strongly that there are even efficient algorithms to do it.
I would imagine this problem has already solved a long time ago, when people did the calculations rather than software. I dont know the name of the problem, but i have seen that solving the optimal way to pack circlse in a box is a well known mathematical problem.
This is indeed 2D bin packing. As for software, take a look at Drools Planner (open source, java).
Related
Basically I need to find an algorithm that will search a circular area for multiple mines minimising looking in the same place twice. The robot can start anywhere on the edge of the circle. I've looked into things like A* but all of them require knowledge of each goal before hand. The whole point of a mine detection robot is that the goals are unknown.Any cheap sensors can be used. Any suggestions?
just run a spiral?
it is not optimized at 100%, as te external circle will overlap a bit at the end, but it is the best for easy to write/debug (even visually).
For sensor it all depends on with kind of mine you are loking for. There are a lot of trick, like "minimum metal mine" (no metal detector will work on them) and so on.
I suggest you to use the Ant Colony Optimization algorithm for this task, although I'm not agree with you about "all of them require knowledge of each goal before hand", cause you can use as much as domain knowledge that is provided for you.
Here is a good place to start getting some information about the ACO (if required).
The reason that I suggest you ACO is it's intrinsic analogy with the problem you got.
If you provide more details about the problem I can tell you more about how to apply ACO to solve it (if required).
at workplace, the work I do is hardly near to challenging and doing that I think I might be losing the skills to look at a completely new problem and think about different ideas to solve it.
A friend suggested TopCoder.com to me, but looking at the overwhelming number of problems I can not decide how to get started?
what I want is to sharpen my techniques ( not particular language or framework ).
The only way to get started would be to pick problems. Division I is the more difficult division, so you will probably find that the division I medium and hard problems will be somewhat interesting and challenging (unless you are quite clever.)
If you check the event calendar, you can see what algorithm competition rounds are coming up in your time zone. The competitions have the added virtue of forcing you to read and analyze other people's code in the challenge phase, so even if you would just as soon practice without a clock, you may find them interesting.
TopCoder algorithm contests are a way to develop your coding speed. Solving any of the problems in the practice arena is difficult unless you already have knowledge of various algorithms.
The problems on Project Euler suffer from the same flaw. You already have to know the algorithms to solve the problems in a reasonable time frame.
What I would suggest is to pick a project that you're interested in, and pursue it as you have time. As an example, I'm currently learning how to work with the open street map tiles in an Eclipse rich client platform.
Try whit http://projecteuler.net Problems difficulty can be assumed by number of solvers.
I prefer this page, because it is language invariant and problems are really challenging
You need the experience of solving 2 problems in any online judge (like http://www.spoj.com, http://www.lightoj.com, http://www.codeforces.com) in any programming language of your choice. That will give you an idea about how are your programs tested online.
Then you can follow this -> http://localboyfrommadurai.blogspot.in/2011/12/new-to-topcoder.html
I have a decent grasp of NP Complete problems; that's not the issue. What I don't have is a good sense of where they turn up in "real" programming. Some (like knapsack and traveling salesman) are obvious, but others don't seem obviously connected to "real" problems.
I've had the experience several times of struggling with a difficult problem only to realize it is a well known NP Complete problem that has been researched extensively. If I had recognized the connection more quickly I could have saved quite a bit of time researching existing solutions to my specific problem.
Are there any resources (online or print) that specifically connect NP Complete to real world instances?
Edit:
For example, I was working on a program that tried to divide students into groups based on age, grade, and school of origin, which is essentially a graph partitioning problem. It took me a while to realize the connection.
I have found that Computers and Intractability is the definitive reference on this topic.
Usually the connection you are talking about must be extracted with a so-called reduction, for example you reduce 3-SAT to the problem you are working with and then you can conclude that your problem has the same complexity of it.
This passage is not trivial, since you have to prove that you can turn every problem instance l of a known NP-Hard problem L into an instance c of your problem C using a deterministic polinomyal algorithms.
So, except from learning basical correlations of common NP-Hard problems using your memory, there's no way to be sure if a problem is similar to another NP-Hard without first trying to guessing and then proving it, you have to be smart.
here is a wiki link:
http://wapedia.mobi/en/List_of_NP-complete_problems
Notice it says
This list is in no way comprehensive (there are more than 3000 known NP-complete problems)
probably it would be a great task if anyone could compile such list.
A theorist should try to understand/proof an NP-Complete/Hard problem. But, a programmer doesn't have that time to. He needs a list.
Am I correct?
I think you should google it. And, read through all the links. Add any new problem found in the link to your list.
Hope it helps
PS : Don't forget to post the list when you're finished :P
For developing better intuition the book "The Algorithm Design Manual, Second Edition" by Skiena (excerpts on google books) is simply great.
List in the back with problems
(including hard problems), that
include an illustration and a
discussion (often) with a real world
example.
Covers both the theoretical
and practical side of things, often
talking about actual code.
Read excepts online here (see some examples in chapters 14):
http://books.google.dk/books?id=7XUSn0IKQEgC&printsec=frontcover#v=onepage&q&f=false
Chapter 16 (not online) discusses some hard problems, including graph partition.
In another question, I asked something similar but I ended up just posting my algorithm there and invalidating several answers. I re-ask it here:
If I "invented" an algorithm, what's the best way for me to figure out if it's already been published about/patented?
You would need to do some searching. Starting with Google search, generically, will often be sufficient to reassure you that your algorithm is not novel. If that is not conclusive, then you need to search harder, perhaps looking at searching various patent sites (Google, USPTO, other places too). If you still don't find anything, then maybe your algorithm is novel.
Next questions: is it worth it to you to try and patent it, or get someone else to patent it for you (a company, for example)? Indeed, can you patent it or does your employer already own it? This will depend in part on how likely it is that everyone else will want to use the same algorithm. The chances are, they won't. If you patent it, they will ignore it until the patent expires.
If you do find a way to afford getting the patent filed - and issued (which is not automatic just because you filed) - then you face enforcing your patent. Will you be able to identify and prosecute those who abuse your patent? If not, was it worth chasing it? Maybe, maybe not; but probably not.
Finally, note that you cannot actually patent a pure algorithm. You would have to reduce it to practice. That isn't as hard as it seems, but just be aware that pure mathematical algorithms are inherently non-patentable.
In summary:
You will probably find someone else already thought of it.
If you decide to patent it because it is novel, you need money.
You need money to file for the patent.
You need money to pursue those who abuse your patent.
You would probably be better off just publishing it.
Most often you basically just have to do back ground research in the given area. This is why when academics do research projects they start of by learning about the history (back ground) of the area all the way up to the current methods or theories being used. It also helps to ask someone who knows the area and has worked in it for many years.
Well, if it's in a textbook like your algorithm seems to have been (Dijkstra), then it definitely already exists in the public domain and cannot be patented. How you use the algorithm in your application as a whole might be, but most abstract ideas or implementations thereof (such as "finding the shortest path between two nodes") cannot be patented.
Or, you could waste a bunch of money and submit a patent and see what happens :)
In all seriousness though, you might start by searching for existing patents, or read up on some articles like this one to get a better feel for the patent process.
Tracking down every algorithm for a particular problem would be quite daunting. A better process might be to track down the best solutions known for the problem and compare them with yours.
I would start with Wikipedia. I know people say "don't use wiki for research", but it's pretty good at computer science (all those geeks contributing), and it will tell you pretty quickly what the best widely-known algorithms are. If you've got something strictly better than the algorithms you can find in Wikipedia, then it might be worth looking further. If Wikipedia's got something strictly better than your algorithm, then you've invented a curiosity at best and probably won't get rich or famous from it.
Next, check the references at the bottom; they may lead you to papers (which will have more references that you can follow), or to academics' websites (which might have links). Also go to Citeseer and search for key words.
Unfortunately, there's no real replacement for having some basic knowledge. If you've invented (for instance) a graph-theoretic algorithm, but you don't know the language of graph-theory, then you'll struggle to find it because you won't know where to start looking. You might profitably spend your time reading an algorithms textbook -- that will give you an overview of good algorithms and how to speak about them.
If an algorithm or method can not be found right away (wikipedia/google), i find it rewarding to scan academic/engineering websites (web of science, ieee explore, acm etc.) for 'review' papers. If recent, they can give a solid overview over the field (e.g. graph search) mentioning books, papers and conferences. After that one can focus the search on particular methods.
When faced with a problem in software I usually see a solution right away. Of course, what I see is usually somewhat off, and I always need to sit down and design (admittedly, I usually don't design enough), but I get a certain intuition right away.
My problem is I don't get that same intuition when it comes to advanced algorithms. I feel much more up to the task of building another Facebook then building another Google search, or a Music Genom project. It's probably because I've been building software for quite some time, but I have little experience with composing algorithms.
I would like the community's advice on what to read and what projects to undertake to be better at composing algorithms.
(This question has nothing to do with Algorithmic composition. Well, almost nothing)
+1 To whoever said experience is the best teacher.
There are several online portals which have a lot of programming problems, that you can submit your own solutions to, and get an automated pass/fail indication.
http://www.spoj.pl/
http://uva.onlinejudge.org/
http://www.topcoder.com/tc
http://code.google.com/codejam/contests.html
http://projecteuler.net/
https://codeforces.com
https://leetcode.com
The USACO training site is the training program that all USA computing olympiad participants go through. It goes step by step, introducing more and more complex algorithms as you go.
You might find it helpful to perform algorithms physically. For example, when you're studying sorting algorithms, practice doing each one with a deck of cards. That will activate different parts of your brain than reading or programming alone will.
Steve Yegge referred to "The Algorithm Design Manual" in one of his rants. I haven't seen it myself, but it sounds like it's just the ticket from his description.
My absolute favorite for this kind of interview preparation is Steven Skiena's The Algorithm Design Manual. More than any other book it helped me understand just how astonishingly commonplace (and important) graph problems are – they should be part of every working programmer's toolkit. The book also covers basic data structures and sorting algorithms, which is a nice bonus. But the gold mine is the second half of the book, which is a sort of encyclopedia of 1-pagers on zillions of useful problems and various ways to solve them, without too much detail. Almost every 1-pager has a simple picture, making it easy to remember. This is a great way to learn how to identify hundreds of problem types.
problem domain
First you must understand the problem domain. An elegant solution to the wrong problem is no good, nor is an inefficient solution to the right problem in most cases. Solution quality, in other words, is often relative. A simple scheduling problem that has a deterministic solution that takes ten minutes to run may be fine if schedules are realculated once per week, but if schedules change several times a day then a genetic algorithm solution that converges in a few seconds may be required.
decomposition and mapping
Second, decompose the problem into sub-problems and known/unknown elements that correspond to elements of the solution. Sometimes this is obvious, e.g. to count widgets you need a way of identifying widgets, an incrementable counter, and a way of storing the count. Sometimes it is not so obvious. Sometimes you have to decompose the problem, the domain, and possible solutions at the same time and try several different mappings between them to find one that leads to the correct results [this is the general method].
model
Model the solution, in your head at least, and walk through it to see if it works correctly. Adjust as necessary (See decomposition and mapping, above).
composition/interfaces
Many times you can find elements of the problem and elements of the solution that map to each other and produce partial results that are useful. This composition and interface construction provides the kernal of the solution, and also serves to reduce the scope of the problem remaining. So then you just loop back to the top with a smaller initial problem, and go through it again.
experience
Experience is the best teacher, of course, but reading about different kinds of problems and solutions will also be helpful. Studying some of the well-known algorithms and their applications is likewise very helpful, e.g. Dijkstra, Bresenham, Unification, and of course, graph theory.
I am not sure intuition can be cultivated, but I think I know what you are asking. The more problems you solve, the more information and experience you have at your disposal for future problems. So, I say just practice. Practice programming real world applications and you run into plenty of problems. Sometimes, solving puzzles can be very educational as well.
I try to find physical analogues when I'm looking at a complex problem.