7619: [CSES Problem Set] Tree Matching
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Description
You are given a tree consisting of $n$ nodes.
A matching is a set of edges where each node is an endpoint of at most one edge. What is the maximum number of edges in a matching?
A matching is a set of edges where each node is an endpoint of at most one edge. What is the maximum number of edges in a matching?
Input
The first input line contains an integer $n$: the number of nodes. The nodes are numbered $1,2,\ldots,n$.
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: the maximum number of pairs.
Constraints
$1≤n≤2⋅10^5$
$1 \le a,b \le n$
$1 \le a,b \le n$
Sample 1 Input
5
1 2
1 3
3 4
3 5
Sample 1 Output
2
One possible matching is (1,2) and (3,4).