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sort on x and y of 2d points


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#1 giugio   Members   -  Reputation: 209

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Posted 10 December 2012 - 05:36 AM

hello.
I would use a sort algorithm that works with multiple indices.
For example i would sort based on cx and cy a set of 2d point.
I think to x and y combined in a color and i wish extract the groups of 2d points that have a similar color.
Is the same thing as an ordering based on x and y?
thanks.

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#2 Álvaro   Crossbones+   -  Reputation: 11865

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Posted 10 December 2012 - 08:03 AM

It's unclear if you want sorting or clustering. For sorting, the algorithms don't change, but you have to provide a comparator function. The most common total order for 2D points is the lexicographical order: You first compare the x coordinates, and you only compare the y coordinates as a tiebreaker.

However, the result of sorting won't generally make a good clustering algorithm, which is what you seem to need.

#3 Bacterius   Crossbones+   -  Reputation: 8157

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Posted 11 December 2012 - 12:17 PM

As Alvaro says above, you'll need to define some form of metric to compare the distance between two (x, y) "colors". The closest thing I can think of to your request is a kd-tree, which is basically a multidimensional binary tree, which sorts a list of points in k dimensions, which supports efficient nearest-neighbor search (find the N closest colors in the tree to some color, according to your definition of "closest") and range search (find all the colors in the tree closer to some color than some distance X, again according to your definition of "distance").

But it depends on what you want to do, you haven't given enough information.

Edited by Bacterius, 11 December 2012 - 12:18 PM.

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

 

- Pessimal Algorithms and Simplexity Analysis





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