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Critical Connections in a Network

Difficulty: HARD
Contributed By

Problem Statement

There are ‘N’ servers numbered from ‘1’ to ‘N’ connected by undirected server-to-server connections forming a network.

You are given a matrix ‘EDGES’ storing the information about the connections, where each row, ‘EDGES[i]’ contains two integers ‘U’ and ‘V’, which implies that there is an undirected server-to-server connection between ‘U’ and ‘V’.

Any server can reach other servers directly or indirectly through the network.

A critical connection is a connection that, if removed, will make some servers unable to reach some other server.

Return all critical connections in the network in any order. If there are no critical connections return empty matrix.

For Example:
For the given graph

If we remove the connection between ‘2’ and ‘4’. Then ‘4’ will not be reachable from any other server.
Input Format :
The first line contains an integer 'T' which denotes the number of test cases.

The first line of each test case contains two integers ‘N’ and ‘M’, denoting the number of servers and number of connections respectively.

The following ‘M’ lines contain two integers ‘U’ and ‘V’ denoting there is an undirected server-to-server connection between server ‘U’ and server ‘V’.
Output Format :
For each test case, print all the critical connections in any order on separate lines.
Note :
You don't need to print anything, it has already been taken care of. Just implement the given function.
Constraints :
1 ≤ T ≤ 10
2 ≤ N ≤ 100
N - 1 ≤ M ≤ 100
1 ≤ U, V ≤ N

Time limit: 1 sec
Sample Input 1 :
2
4 4
1 2
1 3
2 3
2 4
3 2
1 2
2 3
Sample Output 1 :
2 4
1 2
2 3
Explanation of Sample Output 1 :
In test case 1, the graph is shown below.

If we remove the connection between ‘2’ and ‘4’. Then ‘4’ will not be reachable from any other server.


In test case 2, the graph is shown below.

If we remove the connection between ‘3’ and ‘2’. Then ‘3’ will not be reachable from any other server. Similarly, if we remove the connection between ‘1’ and ‘2’. Then ‘1’ will not be reachable from any other server.
Sample Input 2 :
2
2 1
1 2
4 4
1 2
1 3
3 4
2 4
Sample Output 2 :
1 2
Explanation of Sample Output 2 :
In test case 1, the graph is shown below.

If we remove the connection between ‘1’ and ‘2’. Then ‘1’ will not be reachable from any other server.

In test case 2, the graph is shown below.

No matter which connection we remove it is not possible to make some servers unable to reach some other server.
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