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https://issues.apache.org/jira/browse/ARROW-14314?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17537728#comment-17537728
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Ariana Villegas commented on ARROW-14314:
-----------------------------------------

Ok, I got it.

In that case, I think we can do something like this:
 * Given the following dictionary:
{code:java}
values: ['c', 'a', 'b', 'b']
indices: [0, 1, 3, 2, 3, 0]
{code}

 * Get sort_idx from values and transform it to give the same idx to same values
{code:java}
values_sort_idx = [1, 2, 3, 0]
transformed_sort_idx = [3, 0, 1, 1]{code}

 * Get sort_idx from transformed indices
{code:java}
transformed_indices = [3, 0, 1, 1, 1, 3]
sort_indices = [1, 2, 3, 4, 0, 5]{code}

With nulls, it will work similarly:
 * Given the following dictionary:
{code:java}
values: ['a', null, 'b', 'c']
indices: [0, 1, null, 0, 2, 3]
{code}

 * Get sort_idx from values and transform it to give the same idx to same values
{code:java}
values_sort_idx = [0, 2, 3, 1]
transformed_sort_idx = [0, 3, 1, 2]
{code}

 * Get sort_idx from transformed indices
{code:java}
transformed_indices = [0, 3, null, 0, 1, 2]
sort_indices = [0, 3, 4, 5, 1, 2]{code}
 

> [C++] Sorting dictionary array not implemented
> ----------------------------------------------
>
>                 Key: ARROW-14314
>                 URL: https://issues.apache.org/jira/browse/ARROW-14314
>             Project: Apache Arrow
>          Issue Type: Improvement
>          Components: C++
>            Reporter: Neal Richardson
>            Priority: Major
>              Labels: kernel
>             Fix For: 9.0.0
>
>
> From R, taking the stock {{mtcars}} dataset and giving it a dictionary type 
> column:
> {code}
> mtcars %>% 
>   mutate(cyl = as.factor(cyl)) %>% 
>   Table$create() %>% 
>   arrange(cyl) %>% 
>   collect()
> Error: Type error: Sorting not supported for type dictionary<values=string, 
> indices=int8, ordered=0>
> ../src/arrow/compute/kernels/vector_array_sort.cc:427  VisitTypeInline(type, 
> this)
> ../src/arrow/compute/kernels/vector_sort.cc:148  
> GetArraySorter(*physical_type_)
> ../src/arrow/compute/kernels/vector_sort.cc:1206  sorter.Sort()
> ../src/arrow/compute/api_vector.cc:259  CallFunction("sort_indices", {datum}, 
> &options, ctx)
> ../src/arrow/compute/exec/order_by_impl.cc:53  SortIndices(table, options_, 
> ctx_)
> ../src/arrow/compute/exec/sink_node.cc:292  impl_->DoFinish()
> ../src/arrow/compute/exec/exec_plan.cc:297  iterator_.Next()
> ../src/arrow/record_batch.cc:318  ReadNext(&batch)
> ../src/arrow/record_batch.cc:329  ReadAll(&batches)
> {code}



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