C - Path Graph?
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C - Path Graph?
Score : $300$ points
Problem Statement
You are given a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \dots, N$, and the edges are numbered $1, 2, \dots, M$.
Edge $i \, (i = 1, 2, \dots, M)$ connects vertices $u_i$ and $v_i$.
Determine if this graph is a path graph.
What is a simple undirected graph?
A simple undirected graph is a graph without self-loops or multiple edges whose edges do not have a direction.
What is a path graph?
A graph with $N$ vertices numbered $1, 2, \dots, N$ is said to be a path graph if and only if there is a sequence $(v_1, v_2, \dots, v_N)$ that is a permutation of $(1, 2, \dots, N)$ and satisfies the following conditions:
Constraints
- $2 \leq N \leq 2 \times 10^5$
- $0 \leq M \leq 2 \times 10^5$
- $1 \leq u_i, v_i \leq N \, (i = 1, 2, \dots, M)$
- All values in the input are integers.
- The graph given in the input is simple.
Input
The input is given from Standard Input in the following format:
Output
Print Yes if the given graph is a path graph; print No otherwise.
4 3
1 3
4 2
3 2
Yes
Illustrated below is the given graph, which is a path graph.
2 0
No
Illustrated below is the given graph, which is not a path graph.
5 5
1 2
2 3
3 4
4 5
5 1
No
Illustrated below is the given graph, which is not a path graph.
