greedyman's blog

Find minimum sum of A and B using given operations
By greedyman, 9 years ago, In English

You have positive numbers A and B (1 <= A,B <= 10^18) and following operations:
  1) If P is prime number and divides A and B, then A/=P and B/=P.
  2) If P is prime number and divides A and P^2 divides B, then A/=P and B/=P^2.
Find minimum sum of A and B using operations 1 and 2 (no matter how many times).

Do you have any ideas?
It seems to have quite easy solution, and should work in something like O(lg max(A,B)).

  • Vote: I like it
  • +1
  • Vote: I do not like it

»
9 years ago, # |
  Vote: I like it +5 Vote: I do not like it

I think that this problem can be solved next way:

  1. g1 = gcd(A, B), B /= g1 — remove common prime divisors
  2. g2 = gcd(A, B), A /= g1, B /= g2 — remove common prime divisors, that were twice at B
  3. res = A + B
→ Reply
  • »
    »
    9 years ago, # ^ |
      Vote: I like it 0 Vote: I do not like it

    Yes, you are right :)
    This problem has me completely stuck.

    Finally AC, thank you very much.

    → Reply