C - Don’t be cycle
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C - Don’t be cycle
Score : $300$ points
Problem Statement
You are given a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the $i$-th edge connects vertex $A_i$ and vertex $B_i$. Let us delete zero or more edges to remove cycles from the graph. Find the minimum number of edges that must be deleted for this purpose.
What is a simple undirected graph?
A simple undirected graph is a graph without self-loops or multi-edges whose edges have no direction.
What is a cycle?
A cycle in a simple undirected graph is a sequence of vertices $(v_0, v_1, \ldots, v_{n-1})$ of length at least $3$ satisfying $v_i \neq v_j$ if $i \neq j$ such that for each $0 \leq i < n$, there is an edge between $v_i$ and $v_{i+1 \bmod n}$.
Constraints
- $1 \leq N \leq 2 \times 10^5$
- $0 \leq M \leq 2 \times 10^5$
- $1 \leq A_i, B_i \leq N$
- The given graph is simple.
- All values in the input are integers.
Input
The input is given from Standard Input in the following format:
Output
Print the answer.
6 7
1 2
1 3
2 3
4 2
6 5
4 6
4 5
2
One way to remove cycles from the graph is to delete the two edges between vertex $1$ and vertex $2$ and between vertex $4$ and vertex $5$.
There is no way to remove cycles from the graph by deleting one or fewer edges, so you should print $2$.
4 2
1 2
3 4
0
5 3
1 2
1 3
2 3
1