kien_coi_1997's blog

How to solve this hard problem about set?
By kien_coi_1997, 10 years ago, In English

There is n integer elements. Choose k elements then calculate their GCD, call result X.

What is maximal value of X?

k<=n<=3000, k<=100, elements in range 1..10^10.

Example:

3 2
120
36
100

Sample output

20
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10 years ago, # |
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These constraints are in a very gray area, it really depends on the time limit. So depending on the limit you may or may not be able to:

Factor each number: Sieve of Eratosthenes + 3000 * (primes below 10 ^ 5) = 3000 * 10000; Generate divisors of each number in O(divisor_count). Divisor_count is at most 2300. Keep a frequency table for the divisors and just select the biggest one that's over k.

Just a first thought. It's a fragile solution, but it may very well work. Again, the constraints are too fuzzy. Will look for something cleaner and smarter though :).

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    10 years ago, # ^ |
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    If I correctly understood your solution it wouldn't work because the gcd can be a composite number instead of a prime.

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      10 years ago, # ^ |
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      I take in account all divisors, composite or not. The factoring into primes part is only so you can generate the divisors of a number quickly, instead of trying each number up to 10 ^ 5.

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    10 years ago, # ^ |
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    Thank you, I understood.

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10 years ago, # |
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ez

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