30
votes
Accepted
Efficient lazy weak compositions
Chunks of weak compositions
Here is slightly modified version of algorithm used in Combinatorica`NextComposition converted to a ...
- 14.7k
28
votes
Accepted
Faster derangements?
Chunks of derangements
Since I've already written library link code generating permutations, generating derangements requires just few tweaks:
...
- 14.7k
25
votes
Permutations[Range[12]] produces an error instead of a list
Since Mathematica 8 it is possible generate the elements of any group one by one with GroupElements. Here's for example a randomly chosen element of the permutation ...
- 5,921
25
votes
Accepted
25
votes
21
votes
Accepted
20
votes
Alternative to Subsets to generate k-combinations
Subsets function takes optional third argument with standard sequence specification. Using this third argument you can take subsets "in chunks".
For example, ...
- 14.7k
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:
...
20
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:
...
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:
...
- 25.1k
18
votes
Improving speed of code computing number of nonrepeating partitions
Here is a summary of comments (before @ciao's best answer above), with a change in notation. These functions calculate the number of partitions of n into exactly <...
- 14.9k
18
votes
Accepted
Improving speed of code computing number of nonrepeating partitions
This seems pretty quick, particularly on larger cases / larger k, e.g.
451, 29, 101 finishes in a few seconds on the loungebook.
N.B. - I have not tested this ...
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:
...
- 8,564
17
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 ...
- 112k
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.
...
- 264k
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 ...
- 264k
16
votes
Improving speed of code computing number of nonrepeating partitions
Here is a totally different approach based on the fact that successive products forming the generating function are due to multiplication by a binomial $1+t*z^j$. Form a matrix $v$ of zeros with $n+1$ ...
- 14.9k
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 ...
- 225k
16
votes
Accepted
16
votes
Accepted
Generating Tuples with restrictions
Select[
IntegerPartitions[24, {8}, Range[5]],
#.# == 86 &
]
...
Kuba♦
- 132k
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
...
- 83.4k
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}];
- 225k
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 ...
- 13.6k
14
votes
Accepted
Finding all sublists or substrings of a given list/string
TMTOWTDI applies to both of these problems. Below I present an overview of various approaches I've come across, followed by timing data obtained in 10.4 on Windows 10 (the timing code is available as ...
- 8,564
14
votes
generating integer partitions
I needed to do this sometime ago while investigating Bell polynomial analogs. Normally, you'd do
FrobeniusSolve[Range[n], n]
but the fastest variation (and quite ...
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:
...
- 55.1k
14
votes
Permutations of lists of fixed even numbers
The permutation you described is called "derangement". There is a function Derangement in Combinatoricapackage.
...
- 7,661
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 $n$. ...
- 8,564
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:
...
- 349k
Only top scored, non community-wiki answers of a minimum length are eligible