7631: [CSES Problem Set] Finding a Centroid
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Description
Given a tree of $n$ nodes, your task is to find a centroid, i.e., a node such that when it is appointed the root of the tree, each subtree has at most $\lfloor n/2 \rfloor$ nodes.
Input
The first input line contains an integer $n$: the number of nodes. The nodes are numbered $1,2,…,n$.
Then there are $n-1$ lines describing the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.
Then there are $n-1$ lines describing the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.
Output
Print one integer: a centroid node. If there are several possibilities, you can choose any of them.
Constraints
$1≤n≤2⋅10^5$
$1 \le a,b \le n$
$1 \le a,b \le n$
Sample 1 Input
5
1 2
2 3
3 4
3 5
Sample 1 Output
3