Блог пользователя AshrafSustS19

Автор AshrafSustS19, история, 23 месяца назад, По-английски

I wasn't happy with the time complexity of my solution. So, I was looking for a solution with improved time complexity. And I found this. This guy solved this problem by only checking the first 200 elements after each index and comparing GCD of each pair . He won with the power of probability!

His submission: 184781213

Test Case

Test Case result should be Yes. His solution prints No

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23 месяца назад, # |
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What about picking $$$\min(n, 100)$$$ numbers randomly and then trying all possible pairs of them? Will it work?

How to calculate the probability of getting it right?

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    23 месяца назад, # ^ |
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    No, would have worked during the contest, but further test cases have been added. 184857290

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    23 месяца назад, # ^ |
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    It doesn't work because you can construct an array with only one pair such that $$$\gcd(a_i, a_j) = 1$$$. In that case, the probability of both $$$i, j$$$ being chosen randomly is $$$(100 \cdot 99) / (n \cdot (n-1))$$$, too low.

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23 месяца назад, # |
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Why does this work? I see it's AC and he got points for problem C