Permutations/Rank of a permutation: Difference between revisions

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;References:
# [http://webhome.cs.uvic.ca/~ruskey/Publications/RankPerm/RankPerm.html Ranking and Unranking Permutations in Linear Time] by MyrvomdMyrvold & Ruskey. (Also available via Google [https://docs.google.com/viewer?a=v&q=cache:t8G2xQ3-wlkJ:citeseerx.ist.psu.edu/viewdoc/download%3Fdoi%3D10.1.1.43.4521%26rep%3Drep1%26type%3Dpdf+&hl=en&gl=uk&pid=bl&srcid=ADGEESgDcCc4JVd_57ziRRFlhDFxpPxoy88eABf9UG_TLXMzfxiC8D__qx4xfY3JAhw_nuPDrZ9gSInX0MbpYjgh807ZfoNtLrl40wdNElw2JMdi94Znv1diM-XYo53D8uelCXnK053L&sig=AHIEtbQtx-sxcVzaZgy9uhniOmETuW4xKg here]).
# [http://www.davdata.nl/math/ranks.html Ranks] on the DevData site.
# [http://stackoverflow.com/a/1506337/10562 Another answer] on Stack Overflow to a different question that explains its algorithm in detail.
 
=={{header|Python}}==
This is based on the work shown in the paper by MyrvomdMyrvold & Ruskey and has algorithms for the two types of ordering of permutations that they show.<br>
Their algorithm is efficient and pythons transparent use of arbitrary precision integers allows the Stack Overflow questions limits to be used. (Chopped at four rather than a million random samples although function get_random_ranks(144, 1e6) doesn't take long).
 
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