striker_46's blog

Count of max element

By striker_46, history, 8 months ago, In English

How to find number of elements greater than that elements for all elements of the array on the right side.

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8 months ago, # |
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You can use policy based data structure ( Ordered set ) . Then you can traverse the array from the right and keep checking no. of elements using order_of_key(a[i]) . o(nlogn) tc

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    8 months ago, # ^ |
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    I guess ordered set not work in case of duplicate element.

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      8 months ago, # ^ |
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      It works

      4 types of modification you can do Greater Greater Equal Less Less Equal

      typedef tree<int, null_type, less_equal<int>, rb_tree_tag,
            tree_order_statistics_node_update>
    op_set;

It acts like ordered-multiset , if you remove equal it acts like normal set
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8 months ago, # |
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Also ig it can be done using Divide and conquer ( Merge sort )

Here similar problem on leetcode :

https://leetcode.com/problems/count-of-smaller-numbers-after-self/description/

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8 months ago, # |
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You can also use Segment Tree, if array value is large in that case you have to normalize it down to <=n range.

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    8 months ago, # ^ |
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    Can you explain more as I am not much familiar with segment tree.

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8 months ago, # |
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you can sort the array in decreasing order keeping their index then you build segment / fenwick tree ans for index i is i — sum(0..j) j denotes index of element in original array then update the value of segment / fenwick tree. sum(0..i) denotes cnt of elements having value less <= element at index i and index < j

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8 months ago, # |
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Caculate i < j and a_i < a_j. Enumerate from n to 1. For position i, you only need to caculate how many greater than a_i. Use BIT, query(n) — query(a[i]) is answer for position i.

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    8 months ago, # ^ |
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    Also, you should normalize a[i] to the range [1,n]

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    8 months ago, # ^ |
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    Can you please explain this in a bit more detail and with clarity? Also what is the time complexity of this approach?

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8 months ago, # |
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i guess find the next greater element for every element to its right and add 1 to the answer* of that element to get the answer for this element.

  • answer means-- number of elements to its right such that they are greater than this element
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8 months ago, # |
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I guess you are trying to find count of inversions in array which is

if i < j and a[i] > a[j]

This can be done using merge sort along with a simple modification.

Link to understand sol

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8 months ago, # |
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Statement's really unclear, can you clarify what the problem is?

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