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

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22
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7answers
731 views

Alternative ways to implement a triangular recursion

Triangular recursions are a class of algorithms that frequently turn up in computational mathematics. These recursions are expressible in the general form ...
3
votes
3answers
83 views

Generating increasingly longer lists from a single list

I start with an array such as {{1,1},{0,1},{-1,1}}. (1) I want to create an array from this which replaces each array inside the array with 3 new arrays, one ...
6
votes
2answers
373 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, ...
5
votes
1answer
239 views

How to create a Poincare disk type kaleidoscope in Mathematica?

Creating a Kaleidoscope in Mathematica is not a new topic at all, examples can be found from the links like: Wolfram reference and Wolfram demonstrations. My question is how to create Poincare disk ...
2
votes
1answer
137 views

Neighbourhood - Calculations

SeedRandom[0]; n = 5; (m = N @ RandomInteger[{1, 3}, {n, n}]) // MatrixForm result1 = MeanFilter[m, 1] // MatrixForm ...
51
votes
3answers
24k views

How to create a new “person curve”?

Wolfram|Alpha has a whole collection┬╣ of parametric curves that create images of famous people. To see them, enter WolframAlpha["person curve"] into a Mathematica ...
11
votes
5answers
808 views

How to deal with recursion formula in Mathematica?

In engineering problems, I am always seeing many recursion formula. For instance, In the book "The NURBS book", I discovered many recursion formula Fibonacci ...
11
votes
2answers
227 views

Temporal database reconstruction in mathematica

<EDIT> after some internet research I found the database domain that deals with this kind of thing: Temporal Databases. I think my question therefore becomes how to reconstruct a temporal ...
2
votes
3answers
64 views

Reconstructing an expression [duplicate]

I have a nested expression like this one expr = Tan[Sin[Cos[x]]]; I can deconstruct it with ...
3
votes
2answers
225 views

A problem about recursion formula of deCasteljau algorithm

I use mathematica to realize the deCasteljaul algorithm $$\vec{P}_{k,i}(u_0)=(1-u_0)\vec{P}_{k-1,i}(u_0)+u_0\vec{P}_{k-1,i+1}(u_0)$$ The graphics that deCasteljaul algorithm generated as below: ...
5
votes
2answers
182 views

Graph expansion on Mathematica

Is there a way by which Mathematica can be given a graph as an input and be asked to find its expansion? Note: By "expansion" I mean the quantity called "isoperimetric number" or "Cheeger constant", ...
8
votes
3answers
306 views

Random Integer Sequences

I want to construct a random square matrix in the following manner: a) Three states [0 | 1 | 2] are repeated ...
14
votes
2answers
462 views

Better way to test that a matrix is upper-triangular?

Today, I got to thinking about how to test that a matrix was upper-triangular. So I had a try at it. Algorithm $\quad \quad a_{ij}=0 $ Or $i \leq j$ $\Rightarrow$ $True$ My solution is ...
9
votes
3answers
918 views

An inverted pyramid

I want to draw a pyramid approximately like this ...
11
votes
7answers
673 views

Splitting strings into letter keys and integers

I have strings of the following form: string = "ABC123DEFG456HI89UZXX1"; Letter keys of variable lengths are followed by (positive) integers. I want to get this ...
9
votes
5answers
711 views

Coalition Games

Suppose an election produces the following result: result = {{"a", 120}, {"b", 80}, {"c", 50}, {"d", 30}}; Letters are parties and numbers seats. To form a ...
18
votes
3answers
470 views

How to generate a blank crossword sheet?

I attempted to generate a blank crossword sheet. My method is by combining the rows and columns as shown on the graph below. However, some of the across and ...
9
votes
4answers
315 views

Replacing matrix values

I want to find the n largest values in a matrix and replace all others with zero. The solution I found uses ReplaceAll and becomes very slow as the size of ...
9
votes
2answers
239 views

Extracting values with multiple keys

I want to extract sorted data from a huge database based upon two (or more) keys in a very timely manner. Here is a reproducible toy example for two keys only: ...
5
votes
1answer
137 views

How to make a case insensitive sorted list and rename the file names of a given folder?

Suppose I had about 500 .JPG and .jpg files in my folder "c:\images\". How to ask ...
1
vote
6answers
233 views

How to build a game board [duplicate]

I have - rather lazily - constructed a chessboard like this: ...
12
votes
2answers
504 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: ...
0
votes
1answer
58 views

Speeding up ReplaceRepeated while truncating to desired order

I need to program in an algorithm that recursively makes algebraic replacements which leads to an utterly complicated algebraic function of $x$, but whose final result is only needed at fixed order in ...
16
votes
4answers
2k 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, ...
14
votes
4answers
716 views

“Indexing” a vector

I need to "index" a vector according to the first occurence of its distinct elements. I have written ...
1
vote
2answers
578 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 ...
23
votes
5answers
2k views

Mathematica Implementations of the Random Forest algorithm

Is anyone aware of Mathematica use/implementation of Random Forest algorithm?
12
votes
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
votes
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
votes
3answers
519 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
votes
3answers
178 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
votes
2answers
267 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: ...
-1
votes
3answers
199 views
13
votes
6answers
453 views

Partitioning an integer into $k$ equal parts

Say I have an integer $M$. Is there a one-line command to create a partition of $M$ into $k$ integers s.t. the difference between any two integers is as small as possible? For example, with $M = ...
8
votes
8answers
741 views
16
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
279 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 ...
1
vote
0answers
125 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 ...
7
votes
2answers
279 views

What is the underlying algorithm for GroupElementToWord?

What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
22
votes
3answers
5k 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
152 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
221 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
141 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 ...
21
votes
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
votes
1answer
85 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
50 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
219 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 ...
5
votes
1answer
767 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. ...