Function Repository Resource:

EquivalentOrderings

Generalize Ordering by giving alternative orderings if there are equal items

Contributed by: Andrew Read

ResourceFunction["EquivalentOrderings"][list]

return a list of all possible orderings of list considering the permutations of equal items.

ResourceFunction["EquivalentOrderings"][list,n]

return a list of all possible orderings of list considering the permutations of equal items, and limit each ordering to n items.

Details and Options

All elements in list must accept the default comparison operator

Find the two ways of ordering this list:

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If the orderings are limited to the first two elements, then there is only one way of ordering the list:

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EquivalentOrderings will work on the same non-numeric values as Ordering:

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Compare with Ordering:

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Finding all possible orderings of a list of probabilities is helpful for considering alternative Huffman codes:

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Uncomment the Print statements to watch the algorithm work!