An algorithm is a sequence of well-defined steps that defines in abstract the solution to a problem.

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636 views

Faster way to test if an expression equals zero

I want to test if expressions (mix of variables, functions and numbers) are zero valued, as fast as possible, and PossibleZeroQ is sometimes very slow. One solution ...
24
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5answers
2k views

Mathematica Implementations of the Random Forest algorithm

Is anyone aware of Mathematica use/implementation of Random Forest algorithm?
12
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2answers
3k views

Machine learning. SVM algorithm

I want to work with machine learning in Mathematica. Are there any SVM algorithms implemented in Mathematica anywhere? Or any other algorithms for machine learning? With positive and negative database ...
8
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11answers
1k views

Ragged Diamonds

diamond[n_Integer] := Table[1, {#}] & /@ (Range[n]~ Join~Range[n - 1, 1, -1]) diamond[5] // MatrixForm How could a more functional, "tablefree", solution ...
10
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3answers
561 views

Find intersection points with V10

My question departs from this one: Find intersection of pairs of straight lines but now I want to find the points with the new V10 Region-functions. ...
3
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3answers
197 views

Multivariate Polynomial Manipulation

I have a large homogenous multivariate polynomial in, say, 5 variables $a,b,c,d,e$. As an example take the polynomial $$a^4+2abcd+a^2 b^2+e^4+cde^2.$$ Now I would like to replace $k$-th power of any ...
4
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2answers
283 views

All possible pairs of two items

I have 4 different items {1, 2, 3, 4}. I want to obtain all possible pairs of two of the items. I have written: ...
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3answers
205 views
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8answers
756 views
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5answers
328 views

Write a number as the product of its two largest divisors

For even n >= 10 && n <= 98 I want to write n as the product of its two largest divisors (excluding ...
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0answers
144 views

What's a non-trivial Mathematica program involving conscious choice of stack vs. queue data structure?

In a typical computer science algorithms course, much attention is given to the discussion of queues vs. stacks as a data structure programmers need to consciously choose from to achieve algorithmic ...
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2answers
290 views

What is the underlying algorithm for GroupElementToWord?

What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
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3answers
6k views

Plotting a set of trajectories (not a vector field) in 3D

Consider a set of trajectories in 3D space, that possibly converge. By visualizing trajectories as arrows the result will look crowded as each arrowhead will be placed where the attractor is. In 2D, ...
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1answer
183 views

Implementing Kane's Subset Sum Algorithm

In the following paper, D. Kane describes an algorithm for subset sum that runs in logspace: http://arxiv.org/pdf/1012.1336v2.pdf. I am trying to implement it ...
3
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3answers
231 views

Can Mathematica solve $x^{b^2} + ax^b -1 = 0$ for $x$ with $a>0$, $b>1$?

I have a problem that I can't seem to solve neither analytically nor with Mathematica. Namely, I have the expression $$x^{b^2} + ax^b - 1= 0,$$ which I want to solve for $x$ with $a>0$, $b>1$. ...
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1answer
179 views

How do I find the all valid pairings between two sets?

I have a pretty hard problem to solve here, and I have no idea how to start. I have X kind of fruits and 5 colors (let's say Red, Green, Yellow, Blue and Purple). Each fruit can be available in ...
22
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4answers
1k views

Detecting patterns of black and white stones on a 2D board

I'm writing a program to play a game of Pente, and I'm struggling with the following question: What's the best way to detect patterns on a two-dimensional board? For example, in Pente a pair of ...
0
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1answer
90 views

How write this Function with many arguments? [duplicate]

F[x1_,x2_,...,x99_]:=expr How to write this Function in mathematica whithout complete write it?
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0answers
51 views

How to determine three last bindings made to a variable when evaluating an expression?

How can I create a list of bindings made to a certain variable when evaluating an expression? I want to determine three bindings made.
2
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1answer
311 views

Generating the set of all strings within a fixed edit distance of a initial string?

Provided a starting string initialString, and a particular alphabet of allowed characters {"A","B","C","D","E",...}, how can I ...
8
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1answer
949 views

Bresenham's line algorithm

Bresenham's line algorithm is producing discretized line for given two points for purpose of plotting for example. Like that: I have to stress that I'm interested in positions, not a plot. ...
5
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0answers
186 views

Challenge: Speeding up MaxDetect for application in 3D blob detection

In image segmentation it is a common problem that objects appear clustered and are therefore undistinguishable from each other when using simple algorithms. Based on this post I obtained efficient ...
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1answer
78 views

Implementation of a Hanning filter

I'm implementing a package for in-house signal processing. I wrote here a quite trivial function implementing a Hanning windowing of the signal. ...
3
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0answers
481 views

A* algorithm for finding shortest path in a graph

FindShortestPath finds the shortest path between two vertices in an edge-weighted graph, allowing a choice between the Dijkstra and Bellman-Ford algorithms. In my (limited) understanding, both of ...
6
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2answers
137 views

Algorithm in RandomChoice[{w1,w2,…}->{e1,e2,…},n]?

I wonder if someone happens to know the actual algorithm implemented in the particular overload of RandomChoice that handles explicitly presented discrete ...
9
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1answer
1k views

Efficient backtracking with Mathematica

Backtracking is a general algorithm for finding all (or some) solutions to some computational problem, that incrementally builds candidates to the solutions, and abandons each partial candidate c ...
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1answer
225 views

Generate encoding from nested list

Taking reference of Huffman code algorithm, ...
6
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2answers
278 views

Generated Numbers under a constraint?

Let's say I have five four dimensional vectors $p_i^\mu=(p_i^1,p_i^2,p_i^3,p_i^4)$ with $i=1,2,3,4,5$. Now, I want to fill the entries of these vectors ($4\cdot5=20$ in total) with some numbers, but ...
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3answers
335 views

Creating a function with integral zeroes of the 0th, 1st, and 2nd derivatives

I would like to be able to randomly generate functions, each of which satisfies $f : [-10, 10] \rightarrow [-10, 10]$ All the zeroes, critical points, and inflection points have an integral ...
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3answers
316 views

Fastest way to check if an expression contains all symbols from a list

I need to execute this function thousands of times, and the faster, the better. I came up with two versions, but wanted to see if you can come up with an even faster way. Is there a better way? I use ...
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1answer
169 views

Returning lists of pixels connected through their Moore neighborhoods

I have a binarized image in Mathematica 9, and I would like to generate a list of coordinates for clusters of pixels connected through their Moore neighborhoods, e.g. ...
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2answers
154 views

Checking whether a number can be composed from the cube of its digit

How to check whether or not the sum of the cube of each digit of a number is equal to the number itself? In the following code, I tried to return the number in question whenever it matches the ...
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2answers
360 views

Is there a way to parallelize the convolution component of EdgeDetect?

Provided an image like - test = Import["http://upload.wikimedia.org/wikipedia/commons/d/d5/Sunflowers.jpg"] We can run ...
5
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1answer
279 views

What algorithm and tools should I use to search a data set for the point nearest to a given point?

I have about 1,000,000,000 points, which are the longitudes and latitudes of some places in a city, formatted like this: $(106.1231233,41.43234234)$. I also have about 20,000 points which are the ...
14
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2answers
1k views

Higher order SVD

Does anyone know how to do a higher order SVD in Mathematica ? A good reference seems to be here http://www.sandia.gov/~tgkolda/pubs/pubfiles/SAND2007-6702.pdf but I don't understand their formalism ...
2
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2answers
172 views

Write 199319989756262759279209 = 5x + y, where x and y are integers

$\frac{199319989756262759279209}{5} $ = $ 3.9864\times 10^{22}$ according to Mathematica, but I would like to see this number exactly in decimal form (not in scientific notation). I'm attempting to ...
19
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1answer
519 views

Simulating Theatre puzzle

I have been trying to simulate the process of the theatre puzzle from the Joy of X (Strogatz). The puzzle, and some relevant material are here. My simplistic coding for this process follows: ...
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2answers
213 views
21
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3answers
1k views

Generate a Random Polygon

Does some package exist with a function that takes a parameter $n$ and generates a random 2D $n$-sided simple polygon (convex or non-convex), possibly within a certain bounding box? It does not ...
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4answers
288 views

Calculating the median difference between elements with a (particular pair) of consecutive integer indices residing in the same sublist

NOTE: I formally made a serious mistake in the first example provided. pointLists[[1]] had an extra element, and we should have a guarantee that ...
6
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1answer
292 views

Behavior of Graphics`Mesh`InPolygonQ with self-intersecting polygons

Playing around with some of the answers in the question How to check if a 2D point is in a polygon? I noticed that: Graphics`Mesh`InPolygonQ[poly,pt] Displays ...
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5answers
536 views

A fast way to calculate the median difference between pairs of elements

I have a list of coordinate pairs, take for example the following list of three pairs: ...
15
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3answers
696 views
1
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1answer
193 views

Efficiently determining if a morphological component overlaps a polygon with vertices at real number coordinates

I have a list of morphological components $m$, a set of vertices for a polytope $P$ (at real number coordinates), and I'd like to be able to calculate a list of morphological components $m'$ that ...
4
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3answers
348 views

Computing the mean difference between elements in a list with index $i$ and the closest elements with index $(i+1)$

I have a list that looks like this: preprocessedList = {{1,5.3},{1,5.566},{1,1.4322},{2,3.443543},{2,3.444},{3,0.1223},{4,1.3243},{4,1.554343}} Each element in ...
12
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4answers
2k views

Finding elementary cycles of (directed) graphs

I need to enumerate all the simple cycles (i.e. elementary cycles where no vertex is repeated other than the starting) of a graph which has both directed and undirected edges, where we can treat the ...
20
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1answer
475 views

Underlying Algorithms for List Manipulation Functions

Does anyone know, or know of a link for the underlying algorithms used for list manipulation functions? Specifically: Union with and without the ...
9
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2answers
269 views

Partitioning a superset of coordinates into subsets that generate continuous curves

Consider the data set corresponding to recorded trajectories for a particle: ...
2
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3answers
111 views

Reversibly merging sets of $k$ adjacent elements in an array

Say I have an array of the form: ExampleArray = {{1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {10}, {11}, {12}}; I'd like to be able to reversibly merge sets of ...