6279: ABC225 —— B - Star or Not
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Description
You are given a tree with $N$ vertices and $N-1$ edges.
The vertices are numbered $1,2,\ldots,N$. The $i$-th edge connects Vertex $a_i$ and Vertex $b_i$.
Determine whether this tree is a star.
Here, a star is a tree where there is a vertex directly connected to all other vertices.
The vertices are numbered $1,2,\ldots,N$. The $i$-th edge connects Vertex $a_i$ and Vertex $b_i$.
Determine whether this tree is a star.
Here, a star is a tree where there is a vertex directly connected to all other vertices.
Notes
For the definition of a tree, see Tree (graph theory) - Wikipedia.Input
Input is given from Standard Input in the following format:
$N$
$a_1\ b_1$
$\vdots$
$a_{N-1}\ b_{N-1}$
$N$
$a_1\ b_1$
$\vdots$
$a_{N-1}\ b_{N-1}$
Output
If the given graph is a star, print Yes; otherwise, print No.
Constraints
$3≤N≤10^5$
$1 \leq a_i \lt b_i \leq N$
The given graph is a tree.
$1 \leq a_i \lt b_i \leq N$
The given graph is a tree.
Sample 1 Input
5
1 4
2 4
3 4
4 5
Sample 1 Output
Yes
The given graph is a star.
Sample 2 Input
4
2 4
1 4
2 3
Sample 2 Output
No
The given graph is not a star.
Sample 3 Input
10
9 10
3 10
4 10
8 10
1 10
2 10
7 10
6 10
5 10
Sample 3 Output
Yes