SupaHotFire's blog

Find kth element in a multiset
By SupaHotFire, history, 9 months ago, In English,

I did solve this problem for a set with binary searching in a BIT but for multiset I don't know how to solve it for example if the multiset elements are 3 3 3 my solution will only see the last element because BIT is a prefix sum and BIT array would be BIT[3]=3 so binary searching with query is not giving a correct answer because I'm looking for a certain value not a range using binarysearch

any advice would be appreciated

 
 
 
 
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9 months ago, # |
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I think we can easily use pdbs in this case. link

ordered_set can be converted to ordered_multiset by converting less to less_equal in its declaration

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    9 months ago, # ^ |
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    Having the comparator as less_equal will only work for insert queries. While erasing, it will give unexpected results. The correct way is to keep a ordered_set of pairs as {$$$val, id$$$}.

    See this discussion for more details.

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    9 months ago, # ^ |
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    You can't do that. STL and pb_ds requires the comparator to be partial order. It will cause undefined behavior to violate the rule.

    We can make the set element pair<int, int> and put an unique ID in the second field. Then it's exactly a multiset of the first field.

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9 months ago, # |
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You can still solve it using BIT by changing what you binary search for. In the case of sets, you binary search for smallest index with prefix sum=k. For multiset binary for smallest index with prefix sum>=k.

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9 months ago, # |
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Binary searching the BIT works in $$$O(\log^2 n)$$$. If you're ready to go deeper, there is an $$$O(\log n)$$$ solution called "binary lifting" (basically stepping through the internal structure of the BIT), explained in this blog entry.

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