algorithm - Order statistic on intervals -

Looking at an array of numbers, a [0], a [1], ..., a [ N-1] , we get this type of query:

output k - the largest number in the range a [i], a [i] + 1], ..., a [J]

Can these questions be answered in the polygarydiumic time ( n ) in the query? If not, is it possible for the average result and still can get a good refined complexity?

Edit : This can be solved using a continuous tree tree O (n log n) < / Code> space is available, then

Yes, these questions can be answered in polylog timings.

Segment tree is deeply prefixed array by forming it with log (n) Therefore, the leaf nodes are similar to the source array, in the next-depth nodes, the 2-element sub-array is sorted In the next level, there are 4-element arrays created by mixing those two-element aerozes, in other words, sort the merge, but each merge phase has the result of a different array. Here is an example:

  Route: | 1 2 3 5 5 7 8 9 1 2 5 8 3 5 7 9 | 1 5 | 2 8 | 7 9. 3 5 Source: | 5 | 1 | 2 | 8 | 7 | 9 | 5 | 3 |   
 To answer a query, the split category is given (maximum 2 * in log (n) suburals) For example, Category  [0, 4]  should be divided into  [0, 3]  and  [4] , which gives two sorted arrays  [1 2 5 8]  And  [7] . Now the problem has been simplified to find the K-element in many ranks arrays. The easiest way to solve this is by binary search nested: first select binary search to select some candidate elements from each array starting from the first; Then use the binary search in other (small) arrays to determine the rank of this candidate element. It allows to get the key elements in time (log (n) ^ 4)  possibly some optimization (such as frictional cascading) or some other algorithm can do it faster ...