# Tagged Questions

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

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### Spectral Clustering

I am interested in the following question: How is it possible to check whether an algorithm is working properly? However, this question is too general for the post and I'd like to restrict attention ...
11answers
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### 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 ...
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51 views

### What Algorithm Does Mathematica use to Calculate Betweenness Centrality for Unweighted Graphs?

Recently asked this question http://math.stackexchange.com/questions/888369/betweenness-centrality-how-long-does-mathematica-take on the Mathematics SE. Does anyone know, as a follow up, what ...
0answers
129 views

### Creating a simple interactive app with CDF [closed]

I would like to implement an algorithm I have created using a (free) CDF document as interface. The idea is: The user has to give some input values (maybe through a sort of text box, if possible —a ...
3answers
492 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. ...
3answers
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### 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 ...
2answers
261 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: ...
3answers
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### Optimization Algorithm: ideas wanted

EDIT: Lets assume a random matrix: ...
4answers
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8answers
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### Replace interior of matrix with zeros

I have f.e. the following square matrix: ...
5answers
257 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 ...
0answers
116 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 ...
11answers
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### 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 ...
1answer
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### 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 ...
3answers
211 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 $a>0$, $b>1$. ...
1answer
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### 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 ...
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 ...
1answer
84 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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### 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.
1answer
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### 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 ...
1answer
670 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. ...
0answers
142 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 ...
0answers
121 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: ...
1answer
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### 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. ...
0answers
321 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 ...
2answers
122 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 ...
1answer
167 views

### Generate encoding from nested list

Taking reference of Huffman code algorithm, ...
2answers
215 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 ...
3answers
260 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 ...
3answers
296 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 ...
1answer
508 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 ...
2answers
148 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 ...
0answers
151 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 ...
4answers
915 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 ...
1answer
242 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 ...
2answers
171 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 ...
2answers
285 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 ...
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 ...
2answers
202 views

### Parallelizing or optimizing a script for calculating the size of all pairwise intersections between collections of sets

I need to speed up or parallelize an operation that looks essentially like this: ...
1answer
235 views

### Behavior of GraphicsMeshInPolygonQ 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: GraphicsMeshInPolygonQ[poly,pt] Displays ...
4answers
239 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 ...
5answers
431 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: ...
2answers
552 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 ...
2answers
294 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 ...
1answer
182 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 ...
2answers
469 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: ...
3answers
258 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 ...
3answers
618 views

### How to partition a list to make each subset's size equal and mean as close as possible

Suppose we have 3 lists each with 18 numbers like this: ...
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1answer
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### 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 ...