ghoshsai5000's blog

How can I make this program faster — K Interesting Pairs ?
By ghoshsai5000, history, 8 years ago, In English

I have tried to solve the problem of finding k-interesting pairs [here].(http://mirror.codeforces.com/contest/769/submission/26220768)

My solution is quadratic O(n^2). If it is run on the sequence of numbers given, then n = 10^5 at most. I have followed the trick of the editorial and built an array of the frequencies of each element. This happens in O(n) time, with n = 10^5, at most

And have then applied the quadratic time algorithm on the frequency array so now n = 10^4. However, this isn't enough to get past the time limit.

What are further optimizations I can perform ?

Edit — I have performed some optimizations and managed to get an acceptance. Please tell me how I can make this faster ? I am not able to understand the algorithm some other people who got faster solution used. Some stored only those values of x, for which Population Count[x] is k and then did something I am unable to understand. For example, programs like this one.

Here's my code. Please help me.

Also, one more question — The same program seems to be performing at 78 ms here and at 93 ms here. What is the reason for the difference ? This may help me understand and speeden things up.

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8 years ago, # |
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Since Xor operation is fast, you probably can get accept by optimizing your code a little.

But if you're looking for a better time complexity to solve this, you can use the solution of this similar problem : 662C - Binary Table.

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    8 years ago, # ^ |
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    The problem you recommended is a bit too hard for me right now. I couldn't get any idea how to approach it and the editorial was a bit hard as well. Could you suggest some ways for me to optimize the accepted code that I have posted ?

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    8 years ago, # ^ |
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    Do you have any feedback ?

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      8 years ago, # ^ |
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      Your code runs in 78ms now, Why you wanna make it faster?

      What is the reason for the difference ?

      20ms is not that important, It's about the power of the judge and these things.

      I am not able to understand the algorithm some other people who got faster solution used

      Put their code here so we can tell you.

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        8 years ago, # ^ |
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        But, the same program shouldn't be running at two speeds, right ?

        I have noticed some people got it in even quicker time. I want to understand what they did that I didn't do.

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          8 years ago, # ^ |
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          Even to 100ms could be judge error. You're not dealing with a perfect judge, it's a common thing and it's not even a problem.

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            8 years ago, # ^ |
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            I have posted the other program you asked for.

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              8 years ago, # ^ |
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              That code's time complexity is O(N*C(14,K)). Instead of checking for all pairs if their xor has k bits, that code pre-processed something and now is only processing pairs that their xor has exactly k bits.

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                8 years ago, # ^ |
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                What is C(14, K) ? Can you calculate my code's time complexity ? It looks O(N) to me but I'm not sure.

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                  8 years ago, # ^ |
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                  14!/(K!*(14-K)!)

                  Your code runs in O(N^2).(RANGE^2 actually)

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                  8 years ago, # ^ |
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                  Can you provide some feedback on improving ?

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                  8 years ago, # ^ |
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                  You can use the problem that I gave you. It's O(N*lg(N)^2). Or you can use the code you linked in the blog that is O(N*C(14,K)).

                  You should change your algorithm for better time complexity, What do you expect?

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8 years ago, # |
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Auto comment: topic has been updated by ghoshsai5000 (previous revision, new revision, compare).

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8 years ago, # |
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Auto comment: topic has been updated by ghoshsai5000 (previous revision, new revision, compare).

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