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Permutations/Rank of a permutation: Difference between revisions
Permutations/Rank of a permutation (view source)
Revision as of 20:21, 25 October 2014
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A particular ranking of a permutation associates an integer with a particular ordering of all the permutations of a set of distinct items.
For our purposes the ranking will assign integers <math>0 .. (n! - 1)</math> to an ordering of all the permutations of the integers <math>0 .. (n - 1)</math>.
For example, the permutations of the digits zero to 3 arranged lexicographically have the following rank:
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</lang>
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<pre> 0: [ 1, 2, 3, 0 ] = 0
1: [ 3, 2, 0, 1 ] = 1
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}</lang>
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<pre>0 --> [0, 1, 2] --> 0
1 --> [0, 2, 1] --> 1
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test2('First ordering, large number of perms:', unranker1)</lang>
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<pre>First ordering:
From rank 0 to [1, 2, 0] back to 0
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(factorial (length xs))))]))
</lang>
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<
(for/list ([n 24])
(define p (perm '(0 1 2 3) n))
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(22 (3 2 0 1) 22)
(23 (3 2 1 0) 23))
</
=={{header|REXX}}==
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this modified version starts the permute numbers with 0 (zero) instead of 1.
Since this REXX program generates permutations without recursive calls,
testing for the limit for a ''stack overflow'' wouldn't be possible using this REXX program.
<lang rexx>/*REXX program shows permutations of N number of objects (1,2,3, ...).*/
parse arg N seed .; if N=='' then N=3 /*Not specified? Assume default*/
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do j=q+1 while @.j<@.q; end; parse value @.j @.q with @.q @.j
return 1</lang>
<pre style="overflow:auto;height:250px">
4 items, permute 0 = 0 1 2 3 rank= 0
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