-is-this-fft-'s blog

By -is-this-fft-, history, 2 years ago, In English

Sometimes we see problems where a seemingly naive algorithm — for example simple brute force — is actually the correct solution. Mostly, I mean problems where, due to some clever observations, the complexity of the brute force algorithm is greatly reduced.

For example, in a recent contest we had 1168B - Good Triple. You can notice that any string of length at least 9 contains a "good triple", which means a brute force is sufficient here and runs in $$$O(n)$$$.

Or 1028F - Make Symmetrical where you can notice that on any given circle, there are not too many lattice points.

Randomized input is also a good source of these. In 896C - Willem, Chtholly and Seniorious you can observe that after a bit of time, most adjacent elements of the array are equal and write something seemingly naive based on that.

What are some other examples of problems where a stupid brute force is actually the correct solution?

 
 
 
 
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2 years ago, # |
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problem Ehab and Expected XOR Problem

my code complexity was $$$O(2^{2n})$$$ which passed fast because it finds next number with low number of iterations so actual runtime of the code wasn't slow

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    2 years ago, # ^ |
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    Can you prove even that this solution produces maximal length, without using ideas from real solution?

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2 years ago, # |
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1073D - Berland Fair brute force solution is correct because given cost reduces very fast on every iteration.

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2 years ago, # |
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It often happens in problems where you need to print the answer with some precision. If something is unlikely to happen, don't compute it.

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15 months ago, # |
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Intersting. For example any div2A problem.

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15 months ago, # |
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https://www.codechef.com/GW19MOS/problems/MEANPROB

This is from a ICPC regional. The bruteforce algorithm works

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15 months ago, # |
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  • Problems about merging small sets to large sets
  • Tree DP in $$$O(nk)$$$ time by iterating only until $$$min(subtreeSize[v], k)$$$.
  • $$$O(3^{n/3})$$$ clique: It looks like a simple branch-and-bound heuristic at first glance.
  • Problems with randomization: link. You can use similar tricks for smallest enclosing circles and Voronoi diagram.
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15 months ago, # |
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Maybe just for me but I came up with the solution of 1361F in half a minute.

PS: my real color is orange

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15 months ago, # |
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Because the problem setter is also stupid sometime.