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

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3
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2answers
226 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: ...
11
votes
2answers
243 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 ...
8
votes
3answers
311 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
468 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 ...
5
votes
2answers
187 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", ...
9
votes
3answers
922 views

An inverted pyramid

I want to draw a pyramid approximately like this ...
9
votes
5answers
712 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 ...
11
votes
7answers
678 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
4answers
319 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 ...
18
votes
3answers
471 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
2answers
248 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
138 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
235 views

How to build a game board [duplicate]

I have - rather lazily - constructed a chessboard like this: ...
0
votes
1answer
59 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 ...
14
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4answers
723 views

“Indexing” a vector

I need to "index" a vector according to the first occurence of its distinct elements. I have written ...
3
votes
1answer
221 views

Spectral Clustering

I am attempting to implement a spectral clustering routine using Mathematica, but I am encountering difficulties. Using the standard Gaussian similarity function found in section 2.2 of this paper ...
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
525 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
180 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
270 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
200 views

Optimization Algorithm: ideas wanted

EDIT: Lets assume a random matrix: ...
3
votes
4answers
154 views
8
votes
8answers
743 views

Replace interior of matrix with zeros

I have f.e. the following square matrix: ...
1
vote
5answers
285 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
127 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 ...
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 ...
2
votes
1answer
162 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
224 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
149 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
239 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
786 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
votes
0answers
164 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 ...
1
vote
0answers
146 views

How to write my own interpolation method [duplicate]

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use ...
0
votes
1answer
75 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
368 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
133 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 ...
0
votes
1answer
187 views

Generate encoding from nested list

Taking reference of Huffman code algorithm, ...
6
votes
2answers
241 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 ...
3
votes
3answers
286 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 ...
4
votes
3answers
307 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
2answers
152 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 ...
4
votes
0answers
153 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 ...
7
votes
5answers
1k 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 ...
5
votes
1answer
262 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 ...
2
votes
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 ...
2
votes
2answers
306 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 ...
19
votes
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 ...