zscoder's blog

Time complexity
By zscoder, 10 years ago, In English

I'm just wondering, how fast should my algorithm be in order to avoid TLE (Time Limit Exceeded)?

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10 years ago, # |
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Difficult to tell, around 10^8

for N=20, O(2^N) is nice

for N=30, O(N^5)

for N=100, O(N^3)

for N=1000, O(N^2)

for N=100000, O(N lg N)

for N>10^12, you may need to consider O(1)/O(lg N)

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    10 years ago, # ^ |
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    Exactly, it depends highly on basic operations you use. for example % (mod) is worth nearly dozens of if operations...

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      10 years ago, # ^ |
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      That's not true — integer modulo is fast (exactly as fast as division, to be exact, and integer division is fast nowadays) and floating point modulo is not used that much.

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        10 years ago, # ^ |
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        Well, I had a case where I multiplied 100x100 matrices and in the innermost loop I used integer modulo (long long to be precise) and when I put it in the second loop (from the 3rd one) the time decreased by 1 sec

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    10 years ago, # ^ |
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    Almost everything you mentioned should run longer than 10s, especially for N > 1012. Just the O(N3) and O(N5) are possible, if those are dynamics with low constants.

    For O(2N), anything above N = 20 requires optimization. If N > 108, you should probably try , but there are still peculiar complexities like .

    It's hard to say anything in general, because there are many subtle differences. You really find out what you can afford by experience.

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      10 years ago, # ^ |
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      Actually, CF's comment system messed it up. He didn't separate the list with commas rather he split it with newlines which are unfortunately not seen unless you type <br>

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        10 years ago, # ^ |
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        Ow... I thought it was separated by commas. That's why I always use Preview before posting.

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        10 years ago, # ^ |
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        that means i need to type two new lines to see the actual new line? orz

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10 years ago, # |
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Thanks!

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