Rating changes for the last round are temporarily rolled back. They will be returned soon. ×

VietCT's blog

By VietCT, history, 7 months ago,

Hi guys.

I have a problem want to ask you guys.

Problem: Given a tree with n nodes, m segments in a tree with 2 endpoints. Find the maximum number of segments satisfy that not exist two segments with the edge intersect. (n < 1e3, m < 1e5);

My solution (WA passed 4/5) is: Sort m segments by the depth of their LCA. If two segments have the same LCA, if one of them have the endpoint equal to their LCA i choose it ,else i choose the one have shorter length. After sorted, i pick it one by one.

My sub For example:

n = 6, m = 4;

edges:

1 2

2 3

3 4

3 5

3 6

segments:

1 3

4 5

5 6

6 4

So the answer is 2 because we can choose segment (1, 3) and segment (4, 5) as path 1 -> 3 = 1 -> 2 -> 3, path 4 — > 5 = 4 — > 3 -> 5.

You also can choose (1, 3), (5, 6) or (1, 3), (6, 4)

• 0

 » 7 months ago, # |   -7 Can you give link or something? Or at least explain better. Please don't expect people to understand what you mean by "Find the maximum number of segments satisfy that not exist two segments with the paths intersect."
•  » » 7 months ago, # ^ |   0 Sorry for my bad english i will add an example to make it more clear
•  » » 7 months ago, # ^ |   0 It is clear enough bro?
•  » » » 7 months ago, # ^ |   0 Ok, now I understand. Do you have any proof/intuition why your greedy algorithm should always produce the optimal solution? To me it is not at all clear why it should work — seems like unproven greedy.
•  » » » » 7 months ago, # ^ |   0 My greedy algorithm is completely wrong. You have any ideas?
•  » » » » » 7 months ago, # ^ |   +1 How about something like: let $\mathrm{dp}[u]$ be the most segments that can be fit completely in the subtree of $u$.
 » 4 months ago, # |   -14 YOU GAY LOL
•  » » 4 months ago, # ^ |   0 won't be surprising if this is another "social experiment"
 » 4 months ago, # |   0 you miss one important detail that degree of each node is less than 10
•  » » 4 months ago, # ^ |   0 do you have problem link?
•  » » » 4 months ago, # ^ |   0 No it's a problem given by my teacher