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Find users with highest rating change in an interval
By aravind.nujella, history, 2 months ago, In English

Assume a codeforces like platform where there are $$$n$$$ users and their ratings vary over time $$$[0, T]$$$. Now given an interval $$$[l,r]$$$, we would like to find top k profiles which had highest delta in that interval.

Is it possible to answer this query without iterating over $$$n$$$ interval sums? For example we can get $$$O(n\log(n)\log(T))$$$ by maintaing fenwick tree per user and sorting the list of interval sums.

Edit: Added requirement to avoid looping over $$$n$$$ users..

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2 months ago, # |
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Cant you just use prefix sums of each profile. Then use PriorityQueue and in total you need to precompute in O(T*N) and each query works for O(N+K).

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    2 months ago, # ^ |
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    Thats true. What I should have asked for is to reduce $$$n$$$ factor in the query since I do not want to iterate over list of users.

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      2 months ago, # ^ |
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      You can store it in dp[l,r] and do query in O(K) but your space complexity will be very very large. I think there is more smart way, but its first what comes to mind.

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2 months ago, # |
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Auto comment: topic has been updated by aravind.nujella (previous revision, new revision, compare).

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2 months ago, # |
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I don't quite understand the problem, do you just want to find the k biggest values in a subarray?

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    2 months ago, # ^ |
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    No. More like TopK interval sums.

    Say you have user1 rating deltas [+10, -10, 20] and for user2 you have [+5, +10, -20] We can query like highest_delta in between time steps - For interval [1, 3] you get list of users [1, 2] - For interval [1, 2] and get list of users [2, 1]

    Found this on Stackoverflow, apparently called popularity algorithm — https://stackoverflow.com/questions/1025436/popularity-algorithm

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