With respect to data structures, Chris Okasaki has done substantial research into adopting classic data structures into a purely functional setting, as many of the standard data structures no longer work when using destructive updates. His book “Purely Functional Data Structures” shows how some structures, like binomial heaps and red/black trees, can be implemented quite … Read more
As you said some-word -> [doc385, doc211, doc39977, …] (sorted by rank, descending), I think the search engine may not do this, the doc list should be sorted by doc ID, each doc has a rank according to the word. When a query comes, it contains several keywords. For each word, you can find a … Read more
I believe the approach is to actually use a 3 dimensional noise field (every point in a 3D space has a scalar noise value) as opposed to a 2 dimensional field (every point on a 2D plane has a noise value). When using a 2D noise function to generate a height map, you offset the … Read more
Not being a regex expert, but finding the problem interesting, I looked around and found this interesting blog entry. Especially the syntax used there for defining the 2D regex looks appealing. The paper linked there might tell you more than me. Update from comment: Here is the link to the primary author’s page where you … Read more
TSP is a difficult problem. Multi-TSP is probably much worse. I’m not sure you can find good solutions with ad-hoc methods like this. Have you tried meta-heuristic methods ? I’d try using the Cross Entropy method first : it shouldn’t be too hard to use it for your problem. Otherwise look for Generic Algorithms, Ant … Read more
The easiest way is to start from the entry node of the graph, as if you were writing the code by hand. In order to solve the join problem, you can not use a recursive solution, you need to have a topological ordering of your graph, and then build the graph according to the ordering. … Read more
O( n log n ) solution
Pedro Moreno and others at Google/Youtube work on it. They use finite-state transducers to recognize sequences of music phone units, similar to phonemes in automatic speech recognition. Check out this article: Eugene Weinstein, Pedro J. Moreno; Music Identification with Weighted Finite-State Transducers, Proceedings of the International Conference in Acoustics, Speech and Signal Processing (ICASSP), 2007. … Read more
Are you constrained to a flat plane? If you can move to 3D, then you can use the Fibonacci Spiral to generate an arbitrary number of equidistant points on a sphere. There’s a really nice processing sketch of this at work at http://www.openprocessing.org/sketch/41142 (with the code to go with it). The image below shows what … Read more
There exists a solution, which involves dynamic programming, that runs in O(n*TotalSum), where n is the number of elements in the array and TotalSum is their total sum. The first part consists in calculating the set of all numbers that can be created by adding elements to the array. For an array of size n, … Read more