algorithm - How to optimally change item.OrderNum fields to match list order -

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i have list of objects ordernum fields.

the ordernum fields have match list order (but are not required continuous).

easy solution. reset every ordernum when list order changes:

for (int = 0; < list.length; i++) {     list[i].ordernum = i; }

but ordernum stored in sql, the smaller amount of ordernum reset, better. when ordernum have reset, changes can big. there 32 bits use. ordered list retrieved by:

select * orderable_items order order_num;

the actual programming language c#.

assuming numbers sparsely spaced, can following:

  • compute target index in every element in original list
  • compute longest increasing subsequence (o(nlogn)) on indices
    • leave ordernum unchanged on elements in computed subsequence
    • change ordernums on rest of elements fall appropriate gaps

this assumes there's enough space between original ordernums. after several such reorderings might need readjust numbers case.


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