444iq's blog

How to find kth largest element when array is modifiable and k always vary.

By 444iq, history, 5 years ago, In English

How to find kth largest element each time where k will vary and array is modifiable. That is you can add new elements to the array array can have duplicates.

for example say array is 10 , 20 , 15.

2nd largest = 15

add 17 to array

array becomes 10 15 17 20

3rd largest = 15

Q <= 10^5.

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5 years ago, # |
← Rev. 2   Vote: I like it +3 Vote: I do not like it

You can use PBDS

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    5 years ago, # ^ |
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    array can contain duplicates too, i tried it with pdbs but it work for unique elements.

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      5 years ago, # ^ |
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      use less_equal instead of less.

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        5 years ago, # ^ |
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        Thanks a lot. It worked.

        Suppose we also want to delete a single element which occurs more than 1 time.

        A.erase(x) will delete all x. how to erase just a single x value ?

        nilesh8757

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          5 years ago, # ^ |
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          You can keep pairs $$$(a_i, id)$$$ in the ordered set ($$$less$$$), where $$$id$$$ is unique for each pair.

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5 years ago, # |
← Rev. 5   Vote: I like it 0 Vote: I do not like it

Ordered_multiset

Just change less to less_equal

Like this:

#define ordered_set tree<int , null_type,less_equal<int >, rb_tree_tag,tree_order_statistics_node_update> 
#include <ext/pb_ds/assoc_container.hpp> 
#include <ext/pb_ds/tree_policy.hpp> 
using namespace __gnu_pbds;
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    5 years ago, # ^ |
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    But it is giving wrong answer after I perform delete, and I am not able to delete single element from it.

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      5 years ago, # ^ |
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      You can use find_by_order to find kth element and add is just insert

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      5 years ago, # ^ |
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      You need to write 

      while(a.find(k) != a.end()){
   a.erase(a.find(k));
}
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        5 years ago, # ^ |
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        Thanks.

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          5 years ago, # ^ |
          ← Rev. 4   Vote: I like it 0 Vote: I do not like it

          RetiredPlayer but there is one problem here.

          suppose 1 , 3 , 3 , 5 , 7 , 9 , 11

          3rd largest = 3

          less than 9 = 5 elements

          delete(3)

          it becomes 1 , 3 , 5 , 7 , 9 , 11

          3rd smallest = 5 , but it is showing 3. http://ideone.com/Oessur

          No of elements less than 9 are 5 , but it should be 4

          after deletion things are not working as it should be.

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            5 years ago, # ^ |
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            In the blog above you said about just adding and finding kth element, Ordered_set can't erase element x but it can erase k th element by doing A.erase(A.find_by_order(k))

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5 years ago, # |
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Try implementing it with fenwick tree. If all the values are less than 1e5 then it becomes relatively easy. If the values can go high then you need to store the queries and process the elements offline so that you can compress the higher values to smaller values.Every element will be compressed to some element <=1e5 as the no. of unique values <= 1e5. Now you can use binary search on fenwick tree !!

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