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

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8
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8answers
643 views

Replace interior of matrix with zeros

I have f.e. the following square matrix: ...
15
votes
11answers
1k views

Efficient way to build a certain quadratic matrix

For odd n I'm looking for a short and swift way to construct with (f.e.) n = 3 n = 11 ...
1
vote
5answers
214 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 ...
15
votes
3answers
1k views

How to get actual triangles from DelaunayTriangulation[]?

The ComputationalGeometry package has a DelaunayTriangulation[] function. It returns a list of points connected to each point, ...
1
vote
0answers
78 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 ...
38
votes
1answer
1k views

How to construct a treemap using non-rectangles?

I've written the standard version of a tree map (a graphic that shows nested data) and I'm looking to improve on this layout by switching to different types of polygons or perhaps circles. Can anyone ...
1
vote
2answers
447 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 ...
6
votes
2answers
238 views

What is the underlying algorithm for GroupElementToWord?

What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
5
votes
2answers
283 views

Pruning elements in an array based on the existence of similar elements in adjacent arrays

Imagine I have a series of particles floating around in $\mathrm{R}^3$, where, at any given time, particles can pop into and out of existence. Here, for some number of time points, $(t_1, \dots, ...
20
votes
3answers
3k 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, ...
2
votes
1answer
95 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
votes
3answers
171 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 $a>0$, $b>1$. ...
0
votes
1answer
40 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 ...
20
votes
4answers
928 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
votes
1answer
73 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?
1
vote
0answers
45 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
votes
1answer
73 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 ...
4
votes
1answer
212 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. ...
3
votes
0answers
73 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 ...
0
votes
0answers
67 views

how to write my own interpolation method

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use: ...
0
votes
1answer
57 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
votes
0answers
190 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
votes
2answers
88 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 ...
7
votes
1answer
799 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 ...
0
votes
1answer
123 views

Generate encoding from nested list

Taking reference of Huffman code algorithm, ...
6
votes
2answers
155 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 ...
4
votes
3answers
244 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 ...
3
votes
3answers
187 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 ...
0
votes
0answers
41 views

Write nth line to file [duplicate]

I have a code that I am running on a supercomputer. Currently the algorithm must finish before I can export any results from the algorithm. What I would like to do is to have the algorithm write out ...
6
votes
4answers
455 views

Check if a matrix is Positive Semidefinite

I have a question concerning the check whether a given matrix is positive semidefinite or not. In mathematica the function PositiveDefiniteMatrixQ[m] tells me ...
0
votes
1answer
127 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. ...
3
votes
1answer
252 views

Specific Mathematica algorithms, for example LU Decomposition

Where I can find detailed information on algorithms used by Mathematica, especially for numerical methods. The Manual doesn't seem to iclude specifics in most cases. For example I get a different LU ...
3
votes
2answers
128 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 ...
2
votes
2answers
214 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 ...
3
votes
0answers
118 views

Using mathematica to discover algorithms?

In Steven Wolfram's blog entries, he discusses using mathematica to discover algorithms. I have tried several different google searches for papers on such topics, and have found none. I suspect this ...
51
votes
3answers
5k views

Programmatic approach to HDR photography with Mathematica image processing functions

The High dynamic range imaging (HDR or HDRI) direction in photography and image processing became very popular recently. Besides obvious photo art applications (see examples), there are many great ...
5
votes
1answer
200 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 ...
13
votes
2answers
752 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
votes
2answers
164 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 ...
2
votes
2answers
219 views

How does Accumulate work?

Accumulate can be used to compute the partial sums of a list. The partial sums can also be computed using a For loop but this ...
21
votes
2answers
874 views

How can I pack circles of different sizes into a spiral?

Given a list of circles of different areas, I need to arrange them tangentially in order of increasing area and spiraling outward. An example of the type of packing I'm attempting is shown by the ...
16
votes
1answer
402 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: ...
5
votes
2answers
190 views
14
votes
3answers
660 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 ...
1
vote
4answers
207 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 ...
5
votes
1answer
170 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 ...
6
votes
5answers
333 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: ...
7
votes
1answer
253 views

Implementing an algorithm for finding the largest circle that contains a single point in a set (and no other point)

This question concerns the implementation of an algorithm proposed by Rahul Narain on a former question of mine that was migrated to math.stackexchange: ...