370. Is This Graph a Tree
Print Yes if the graph is a tree and No otherwise.
A tree is a graph that is connected and has no cycle. That is two conditions, and the entire difficulty of this problem is that students check one and stop.
There is a shortcut worth knowing, and it is exact: a graph on n vertices is
a tree exactly when it is connected AND has exactly n - 1 edges. Either
condition alone is not enough. Look at the second sample: three vertices in a
triangle plus one lone vertex is 3 edges on 4 vertices, so the edge count is
right and the graph is still not a tree.
So count components, using the traversal from problem 363, and compare m
against n - 1. Both must hold.
Constraints - `1 ≤ n ≤ 100000` - `0 ≤ m ≤ 200000` - There are no self-loops and no repeated edges.
Input
The first line contains two integers n and m, the number of vertices and
edges. Each of the next m lines contains two integers u and v, an
undirected edge between those vertices. Vertices are numbered 1 to n.
Output
Print Yes or No on one line.
Hints
Four rungs, in order. The last two open once you have submitted an attempt. A wrong one counts.