Permutations by swapping: Difference between revisions

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{{draft task}}
Generate permutations of n items usingin algorithmswhich basedsuccessive onpermutations differ from each other by the swapping of any two items. Also generate the sign of the permutation which is +1 when the permutation is generated from an even number of swaps from the initial state, and -1 for odd. Show the permutations and signs of three items, in order of generation ''here''.
 
Such data are of use in generating the [[Matrix arithmetic|determinant]] of a square matrix and any functions created should bear this in mind.
 
Note: The Steinhaus–Johnson–Trotter algorithm generates successive permutations where ''adjacent'' items are swapped, but from [[wp:Parity_of_a_permutation#Example|this]] discussion adjacency is not a requirement.
 
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