Garvit_2013's blog

Confusion about Time Complexity (help)
By Garvit_2013, history, 3 years ago, In English

Can anybody tell me Time complexity of my code? I am confused a lot about this . I think it should be 14! or 14^14 or something else. Please help me and tell me If I am wrong.

Code Link https://codeforces.me/contest/1646/submission/148429105

Thanks in advance

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3 years ago, # |
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The time complexity seems to be $$$O(2^f)$$$ where $$$f$$$ is the size of your factorial array.

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    3 years ago, # ^ |
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    Thanks

    Can you please explain how you arrive at this complexity?

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      3 years ago, # ^ |
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      Oh, I am sorry, I actually made a mistake and the time complexity is actually more like $$$O(f\cdot2^f)$$$.

      When I saw your code, I deduced that your recursive method is actually just recursing over all subsets(which is equal to $$$2^f$$$) and each recursive call also iterates from $$$i..f$$$ branching more recursive calls. Therefore, $$$2^f$$$ recursive calls, and for each call, we iterate at most $$$f$$$ times making our time complexity $$$O(f\cdot2^f)$$$

      If you want a bit more concrete explanation, I can try :), let's denote $$$T(f)$$$ to be the number of operations your recursive method performs for a size $$$f$$$ array. Note that, the $$$T(f)$$$ could be written as $$$T(f)=f+T(f-1)+T(f-2).......$$$.

      Can you see why?

      Now, working some math out $$$T(f)=f+T(f-1)+T(f-2).......\leq f\cdot 2^f$$$ which I will convinentiely skip ;). Hence, our time complexity is $$$O(f\cdot2^f)$$$

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