Pinely Round 1 (Div. 1 + Div. 2) |
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Finished |
This in an interactive problem.
There is an unknown tree consisting of $$$n$$$ nodes, which has exactly one centroid. You only know $$$n$$$ at first, and your task is to find the centroid of the tree.
You can ask the distance between any two vertices for at most $$$2\cdot10^5$$$ times.
Note that the interactor is not adaptive. That is, the tree is fixed in each test beforehand and does not depend on your queries.
A vertex is called a centroid if its removal splits the tree into subtrees with at most $$$\lfloor\frac{n}{2}\rfloor$$$ vertices each.
The only line of the input contains an integer $$$n$$$ ($$$3\le n\le 7.5\cdot10^4$$$) — the number of nodes in the tree.
Start interaction by reading $$$n$$$.
To ask a query about the distance between two nodes $$$u, v$$$ ($$$1 \le u, v \le n$$$), output "? u v".
If you determine that the centroid of the tree is $$$x$$$, use "! x" to report.
After printing a query, do not forget to output the end of a line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:
Hacks are disabled in this problem.
It's guaranteed that there are at most $$$500$$$ tests in this problem.
5 2 1 2 3 1 1 1
? 1 2 ? 1 3 ? 1 4 ? 1 5 ? 2 3 ? 3 4 ? 4 5 ! 3
Here is an image of the tree from the sample.
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