34
votes
Accepted
Optimization of function taking a permutation
How about a Monte-Carlo-Metropolis search? I'll implement a simplistic version here. See complete universal code further down. Update: Cleaned-up code now available in the Wolfram Function Repository, ...
- 49.8k
28
votes
Accepted
Faster derangements?
Chunks of derangements
Since I've already written library link code generating permutations, generating derangements requires just few tweaks:
...
- 15.1k
26
votes
22
votes
Fastest way to generate {{a,a},{a,b},{a,c},{b,b},{b,c},{c,c}} from {a,b,c}
Select[Tuples[{a,b,c},2],OrderedQ]
- 34.1k
19
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:
...
- 8,804
19
votes
Accepted
Delete duplicates from list of lists as if on a necklace
A high-performance solution
Since you are planning to work with thousands of necklaces, it may be much faster to introduce a canonical form.
The main point is to write a necklace canonization ...
- 7,886
18
votes
Accepted
StringContainsQ, but anywhere in order
StringMatchQ["aabbc", "*a*c*"]
True
StringMatchQ["aabbc", "*b*a*"]
False
You can also use ...
- 401k
18
votes
Accepted
Fastest way to generate {{a,a},{a,b},{a,c},{b,b},{b,c},{c,c}} from {a,b,c}
GroupTheory`Tools`Multisets[{a, b, c}, 2]
{{a,a},{a,b},{a,c},{b,b},{b,c},{c,c}}
- 27.2k
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 ...
- 273k
17
votes
Terse Method to Swap Lowest for Highest?
How about:
Module[{tmp = test},
With[{ord=Ordering[tmp]},
tmp[[ord]] = Reverse @ tmp[[ord]]];
tmp
]
{56, 9, 4, 3, -5, -2, -3, 1, 2, 7, 60, 58, ...
- 132k
17
votes
Accepted
ls Ordering[Ordering[list]] optimal?
No, Ordering[Ordering[list]] not optimal. And yes, there is a faster method:
...
- 110k
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}];
- 236k
15
votes
StringContainsQ, but anywhere in order
Is this what you need?
StringContainsQ["aabbc","a" ~~ ___ ~~ "c"]
True
The following documentation pages should help you get going with string patterns in ...
- 24.8k
14
votes
Permutations of lists of fixed even numbers
The permutation you described is called "derangement". There is a function Derangement in Combinatoricapackage.
...
- 7,911
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 $n$. ...
- 8,804
13
votes
Delete duplicates from list of lists as if on a necklace
Preface
If one could create a function f that calculates a canonical form of a necklace that turns all equivalent necklaces ...
- 113k
13
votes
Accepted
13
votes
Accepted
Evaluating Pfaffian
In the answer to: "https://mathematica.stackexchange.com/questions/125794/compute-numeric-pfaffians-of-matrices-efficiently" there is a pointer to the code below. I hope this will be helpful....
- 56.4k
12
votes
Accepted
Connectivity in a molecule and permutations
Getting the graph from the XYZ file
You have only a set of coordinates and atom types in an XYZ file. When you import it in Mathematica you can import 3 elements: the 3D plot, the coordinates, and ...
- 70.2k
12
votes
Permutations[Range[12]] produces an error instead of a list
Chunks of permutations
Here is a LibraryFunction implementation of "CoolMulti" algorithm generating permutations of multisets. The algorithm is described in:
A. ...
- 15.1k
12
votes
Faster derangements?
Here is a straightforward compiled implementation of Knuth's "Algorithm X" for lexicographically generating restricted permutations, specialized to the derangement case:
...
12
votes
Accepted
How to generate all involutive permutations?
I wondered how well Involutions has been implemented, so I tried to reimplement it myself. The following implementation can be up to 15 times faster than ...
- 110k
12
votes
Accepted
Can we turn this for loop into a more elegant Mathematica code?
Apparently, you try to apply a permutation given by list indirection to a vector duplicate.
Here are several ways to do it, ...
- 110k
12
votes
Fastest way to generate {{a,a},{a,b},{a,c},{b,b},{b,c},{c,c}} from {a,b,c}
Another possibility is to use Pick:
...
- 132k
11
votes
11
votes
Accepted
How to represent a product of cycles in matrix form?
mat = {Sort @ #, #} & @ PermutationList[a];
MatrixForm @ mat // TeXForm
$ \left(
\begin{array}{ccccccccccc}
1 & 2 & 3 & 4 & 5 & 6 & ...
- 401k
11
votes
Accepted
How do I get a list of all possible sums in a list nested list?
Total[Tuples@rn, {2}]
should do.
For cases where a very large number of tuples would be generated,
...
- 26k
11
votes
Shuffling two lists into each other
s = {2, 3, 6};
a = {a1, a2, a3};
b = {b1, b2, b3, b4};
n = Length[a] + Length[b];
list = Range@n;
list[[s]] = a;
list[[Complement[Range[n], s]]] = b;
list
...
- 84.1k
10
votes
Faster derangements?
Recursive Derangements
Here is my approach at doing this recursively:
...
- 13.6k
10
votes
Delete duplicates from list of lists as if on a necklace
This problem is simple enough, that halirutan's brute force method is still $O(n)$ complexity for comparing two necklaces of length $n$ (which is optimal). But I would like to offer an intelligent ...
- 11.5k
Only top scored, non community-wiki answers of a minimum length are eligible