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

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9
votes
2answers
324 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: ...
6
votes
1answer
196 views

How to efficiently find all combinations of the letters in an alphabet given a condition

Problem: I want to find all unique expressions with n number of terms that contain all the digits (or characters) in alphabet. ...
6
votes
2answers
141 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 ...
6
votes
1answer
798 views

Random number generation with specific distribution

I am writing a program for solving the shortest path in travelling salesman problem, with a twist that there are multiple salesmen who partition the cities among themselves, thus creating two part ...
1
vote
6answers
284 views

How to build a game board [duplicate]

I have - rather lazily - constructed a chessboard like this: ...
11
votes
2answers
420 views

How to fill a grid make its total be largest

I have a blank grid whose dimension is 5*5. I want to fill it with some number using 1, 2, 3 and 4. But in every blank space if you fill 2, its neighbor (include four direction, such as left, ...
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 ...
6
votes
1answer
316 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 ...
4
votes
2answers
478 views

Efficiently determining the largest minimum cost to travel from a fixed source to an arbitrary sink in a weighted graph

Let $v_i$ be a vertex in a graph $G$ with vertices $(v_1,...,v_N) \in V$ and edges $(e_1,...,e_M) \in E$ with associated weights $(w_1,...,w_M)$. Let $v_s \in V$ be specified vertex in the graph. In ...
3
votes
2answers
160 views

Replace missing data

I have vectors of equal lengths where I want to replace the zeroes (missing data) with their preceding values. So far I have written: ...
3
votes
2answers
2k views

How to linearize an expression automatically?

I would like to automatically linearize some long equations in the scope of variational calculus. Here follows an example of what I need to do : Given two variables $a_1 = q_1 + \delta q_1$ and $a_2 ...
9
votes
3answers
512 views

How do we solve N-Rooks variation using primes?

Using a $p_n $x $p_n$ matrix, how can we solve the N-Rooks problem to find a prime in every row and column? ...
7
votes
1answer
270 views

Making FindShortestPath a little bit sloppy [duplicate]

I have a dense graph, and I'd like to find multiple "almost shortest" paths from a source vertex, $v_s$, to a sink vertex, $v_s$, on an undirected graph $G$. How can I repeatedly run ...
6
votes
1answer
175 views

Why is FindInstance failing when I relax a set of constraints?

I'm attempting to use FindInstance to generate coordinate sets for plausible triangles with edge length distance constraints. E.g.: ...
5
votes
3answers
147 views

Unragging a matrix

Today I ran into matrices like this one: ...
4
votes
2answers
249 views

A problem about recursion formula of de Casteljau algorithm

I use Mathematica to implement the de Casteljau 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 de Casteljau algorithm generated as follows: ...
4
votes
1answer
145 views

Center of quadrangular

Having 4 points A (ax, ay), B (bx, by), C (cx, cy) and D ...
3
votes
2answers
197 views

Pollard's Rho algorithm

I'm working in Mathematica and I'm trying to implement the [Pollard's Rho Algorithm for the Discrete Logartihm Problem][1].
3
votes
0answers
630 views

Solving recursion relations using Mathematica

I want to solve the recursion relation given in equation 2.7(a/b) on page $6$ of this paper. (..the initial seed is $F_1 = G_1 = 1$ and the functions $\alpha$ and $\beta$ are defined on page $5$ in ...
2
votes
2answers
150 views

Refining subset relations

People who do combinatorics (like me) are often faced with the following problem: For a list of combinatorial objects (vectors, permutations graphs,etc.), we know what multi-set of values it ...
2
votes
2answers
55 views

Count elements between matching opening and closing parentheses?

Suppose I have a List of the form: lst={"(", "x1", "x2", "(", "(", "x3", ")", "x5", "(", "x6", ")", ")", ")"} For each pair ...
2
votes
2answers
174 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
1answer
141 views

Is it possible for me to explicitly specify a point list for SpatialGraphDistribution?

The function RandomGraph[SpatialGraphDistribution[n, r]] generates a random geometric graph over $[0,1]^2$ where vertices are connected if they are within a ...
1
vote
1answer
265 views

Efficient algorithm to generate a basis for exact diagonalization

The problem is described as follows: I need to generate a basis(matrix) in lexicographic order. For two different basis vector $\{n_1,n_2,\cdots,n_M\}$ and $\{t_1,t_2,\cdots,t_M\}$, there must exist ...
1
vote
1answer
164 views

How can I stop DiscreteMarkovProcess[] from relabeling vertices?

I'm attempting to calculate the mean first passage time between two vertices, $v_1$ and $v_2$, provided some undirected graph $G$. However, I noticed that running the following script: ...
0
votes
1answer
310 views

Generate encoding from nested list

Taking reference of Huffman code algorithm, ...