Permute[expr,perm]
An inversion of a permutation σ is a pair (i,j) of positions where the entries of a permutation are in the opposite order: i σj. So a descent is just an inversion at two adjacent positions. For example, the permutation σ = 23154 has three inversions: (1,3), (2,3), (4,5), for the pairs of entries (2,1), (3,1), (5,4). Sometimes an inversion is defined as the pair of values. In 28: arr = np.arange(16).reshape((2, 2, 4)) In 29: arr Out29: array( 0, 1, 2, 34, 5, 6, 78, 9, 10, 11, 12, 13, 14, 15) In 32: arr.tra.
permutes the positions of the elements of expr according to the permutation perm.
Permute[expr,gr]
returns the list of permuted forms of expr under the elements of the permutation group gr.
Cyclic permutation of three elements in a list: Dropdmg 3 4 1.
Take the lowercase alphabet:
Exchange the first and last character:
Permute several characters:
Permute an expression under all elements of a group:
Permute the parts of an expression:
Permute the parts of an expression under all elements of a group:
Give a permutation in list form. The length of the expression does not change:
The eight possible rotations and reflections of a square:
Permute never changes the number of parts of an expression. It simply reorders them:
However, Part can change the number of parts:
When applied to the identity permutation list, Permute is the inverse of PermutationReplace:
Permute can also be used as an alternative to PermutationList:
Another way of inverting the action of Permute is using FindPermutation:
When all parts of the expression are different, the permutation can be uniquely recovered:
Permute is a right action with respect to the product of permutations:
Algorithm::Permute - Handy and fast permutation with object oriented interface
This handy module makes performing permutation in Perl easy and fast, although perhaps its algorithm is not the fastest on the earth. It supports permutation r of n objects where 0 < r <= n.
Returns a permutor object for the given items.
Returns a list of the items in the next permutation. The order of the resulting permutation is the same as of the previous version of Algorithm::Permute.
Returns the list of items which will be returned by next(), but doesn't advance the sequence. Could be useful if you wished to skip over just a few unwanted permutations.
Resets the iterator to the start. May be used at any time, whether the entire set has been produced or not. Has no useful return value.
Starting with version 0.03, there is a function - not exported by default - which supports a callback style interface:
A block of code is passed, which will be executed for each permutation. The array will be changed in place, and then changed back again before permute returns. During the execution of the callback, the array is read-only and you'll get an error if you try to change its length. (You can change its elements, but the consequences are liable to confuse you and may change in future versions.) Talyvel 4 manual.
You have to pass an array, it can't just be a list. It does work with special arrays and tied arrays, though unless you're doing something particularly abstruse you'd be better off copying the elements into a normal array first. Example:
The code is run inside a pseudo block, rather than as a normal subroutine. That means you can't use return, and you can't jump out of it using goto and so on. Also, caller won't tell you anything helpful from inside the callback. Such is the price of speed.
The order in which the permutations are generated is not guaranteed, so don't rely on it.
The low-level hack behind this function makes it currently the fastest way of doing permutation among others.
I've collected some Perl routines and modules which implement permutation, and do some simple benchmark. The whole result is the following.
Permutation of eight scalars:
Permutation of nine scalars (the Abigail's routine is commented out, because it stores all of the result in memory, swallows all of my machine's memory):
The benchmark script is included in the bench directory. I understand that speed is not everything. So here is the list of URLs of the alternatives, in case you hate this module.
Memoization is discussed in chapter 4 Perl Cookbook, so you can get it from O'Reilly: ftp://ftp.oreilly.com/published/oreilly/perl/cookbook
Mediatrans 6 8 utility trailer. Abigail's: http://www.foad.org/~abigail/Perl
Butler 4 2 2 download free. List::Permutor: http://www.cpan.org/modules/by-module/List
Best free ip camera software mac. The classic way, usually used by Lisp hackers: perldoc perlfaq4
In Edwin's words: Yustina Sri Suharini - my ex-fiance-now-wife, for providing the permutation problem to me.
Data Structures, Algorithms, and Program Style Using C - Korsh and Garrett
Algorithms from P to NP, Vol. I - Moret and Shapiro
Edwin Pratomo <edpratomo@cpan.org> was the original author.
Stephan Loyd <sloyd@cpan.org> is co-maintainer after version 0.12.
The object oriented interface is taken from Tom Phoenix's List::Permutor. Robin Houston <robin@kitsite.com> invented and contributed the callback style interface.
This software is copyright (c) 1999 by Edwin Pratomo.
This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.
To install Algorithm::Permute, copy and paste the appropriate command in to your terminal.
For more information on module installation, please visit the detailed CPAN module installation guide.
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