28
votes
Accepted
Faster derangements?
Chunks of derangements
Since I've already written library link code generating permutations, generating derangements requires just few tweaks:
...
- 15k
25
votes
Accepted
25
votes
23
votes
Accepted
How to generate all Feynman diagrams with Mathematica?
Here is a piece of code that is inspired by quantum field theory. The physics background can be found in this physics.SE post.
First, we define some auxiliary functions:
...
21
votes
Accepted
20
votes
House of Santa Claus
This is of course the Chinese postman problem, which is solved by the function FindPostmanTour[]. First, represent the edges of the directed graph:
...
- 124k
20
votes
Transform a number to a factorial
An example target, a bit over half-a-million digits:
x = 123456!;
IntegerLength@x
574965
Results for target, and a non-hit:
...
- 25.6k
19
votes
Accepted
Lazy form of Tuples/Outer to loop over list of lists
The implementation of lazy tuples here pretty much contains the solution to the lazy Outer problem. I will take the relevant parts from that code.
The following ...
- 114k
18
votes
Faster derangements?
Here is one way to generate them directly: it is based on a way to generate all permutations but discards invalid ones early:
...
- 8,744
17
votes
Accepted
Generating Tuples with restrictions
Select[
IntegerPartitions[24, {8}, Range[5]],
#.# == 86 &
]
...
Kuba♦
- 136k
17
votes
Accepted
How to generate all possible orderless partitions of a list according to another list?
A solution using Repeated, ReplaceList, and the Orderless attribute.
...
- 270k
17
votes
Permutations of nested parentheses (Dyck words)
StringReplaceList
I just realized that there is a comparatively clean though not highly efficient way to write this using ...
- 270k
16
votes
How to count all cliques (not just maximal ones) in graphs?
Mathematica only finds maximal cliques, i.e. cliques (complete subgraphs) that are not part of a larger clique.
Computing the number of all cliques given the maximal ones is not trivial because some ...
- 233k
16
votes
Accepted
16
votes
Accepted
Mathematica implementation of Zeilberger's algorithm (previously done in Maple)
There is also a newer package, HolonomicFunctions, that has an implementation of Chyzak's generalization of Zeilberger's algorithm. To perform the desired task, use the following commands:
...
15
votes
How to generate all possible orderless partitions of a list according to another list?
Permutations treats repeated elements as identical, so you can get a flattened version of the desired result with something like
...
- 84.7k
15
votes
Accepted
List all possible license plate numbers
I would use
a = Alphabet[]; (* letter *)
d = Range[0, 9]; (* digit *)
result = Tuples[{a, a, d, d, d, d}];
- 233k
15
votes
Transform a number to a factorial
Stirling's approximation, $n! \sim n^ne^{-n}$, is the Swiss army knife of factorial problems. If $x = n!$, this implies that $\ln x \sim n \ln n - n$; and surprisingly this can be solved with a ...
- 15k
15
votes
Can you give a faster implementation with Mathematica for these q-analog functions?
There are lots of QFunctions (see also wikipedia)
Some are the q(,t)-analog version of the original MATH objects. (orthogonal polynomials, special functions, etc. ) However, it seems to me that some ...
- 897
14
votes
Lazy form of Tuples/Outer to loop over list of lists
Overview
Here is a refinement of @Leonid's approach that is a bit faster. The basic idea is to create a TuplesFunction that encapsulates the tuples information, ...
- 130k
14
votes
Solving word search puzzles
Update
To allow string with multiple words separated by single space, and possible multiple instances of word and non empty intersection of positions:
...
- 58.8k
14
votes
Permutations of lists of fixed even numbers
The permutation you described is called "derangement". There is a function Derangement in Combinatoricapackage.
...
- 7,851
14
votes
Accepted
Permutations of lists of fixed even numbers
Permutations where no element remains in its original place are called derangements. Counting them is easy enough: the number of derangements of a set of size $n$ is $!n$, or the subfactorial of $n$. ...
- 8,744
14
votes
Accepted
Generating set partition diagrams
I need to reproduce this diagram ...
We can use the function blobF from this answer to generate blobs around subsets:
...
- 384k
14
votes
All possible combinations of ways to write an equation
Tuples + Dot:
Tuples[{1, -1}, 3].{q, p1, p2}
{p1 + p2 + q, p1 - p2 + q, -p1 + p2 + q, -...
- 384k
13
votes
Accepted
Tuples optimization challenge
Don't use brute force, instead compute probabilities for each amount of leading zero bits in OrderDistribution for the smallest entry of ...
- 18.7k
13
votes
Accepted
How can I correctly use LazySubsets from Wolfram's Lazy package?
The package doesn't seem to be well-documented, so I have to guess. If I guess it right, those Lazy* functions are supposed to work only on ...
- 63.9k
12
votes
Tuples with one "joker" digit?
Permutations can do this. You just need to give it enough copies of 1 and 2 such that they ...
- 8,744
12
votes
Accepted
Cyclic and Non-cyclic Permutations
Per the request, I post my comment as an answer:
First question
cy := Permute[#, CyclicGroup[Length@#]] &
cy[Range@5]
{{1, 2, 3, 4, 5}, {2, 3, 4, 5, 1}, {3, 4,...
- 26.4k
12
votes
Any alternative way to compute IntegerPartitions?
There are 190,569,292 unrestricted integer partitions of 100 (PartitionsP@100).
This will need >1gb of RAM just to keep the final result.
You can generate them in ...
- 25.6k
Only top scored, non community-wiki answers of a minimum length are eligible