Balkan Olympiad

Balkan Olympiad

Balkan Olympiad

Halo Nation – Halo: Evolutions: 26 Draconis system, Allison Stark, Battle of Kholo, Battle of Psi Serpentis, Battle of Skopje, Battle of Theta Ursae … Callisto Incident, Captain Teach, Ceretus Reviews| Travel to Macedonia and the Balkans Cities Anonymous said...

A first guess about the first problem: By the geometry of the objective, observe that there is some 0 <= s <= 1 such that minimizing (total A-cost)*(total B-cost) is equivalent to minimizing s*(total A-cost) + (1-s)*(total B-cost). However, trying "all" s does not work, but we can iteratively increase s and update the spanning tree whenever necessary. Every time we update, we also compute (total A-cost)*(total B-cost). Its not clear that we only have to update a polynomial number of times. To see this, recall that a minimum spanning tree can be constructed via a simple greedy procedure (always add the smallest outgoing edge). On the other hand, for any pair of edges a and b, there is exactly one "breakpoint" s' such that we prefer edge a for s <= s' and b for s > s'. This gives that there are at most n^2 breakpoints. Eternal glory?

Mon Jul 25, 03:47:00 AM EDT

  • Balkan Olympiad

    Balkan Olympiad

    Balkan Olympiad

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