ORIGINAL CODING QUESTION
Critical network vertices
Count vertices whose removal, including incident edges, increases the number of connected components of the UNDIRECTED graph. Compare with the original component count.
Original exercise · hard. Editorial role relevance does not imply a company has asked this question.
Input and output
n m, then m vertex pairs (u,v). Vertices are zero-based.
Constraints
1 ≤ n ≤ 30; 0 ≤ m ≤ 100; vertex IDs in [0,n).
Example 1
Input
3 2 0 1 1 2
Output
1
Only the middle vertex is critical.
Example 2
Input
3 3 0 1 1 2 2 0
Output
0
The triangle has no critical vertex.
Explain your approach
Explain your time and auxiliary space complexity. Which input makes your algorithm work hardest?
Private grading inputs, expected outputs and canonical reference implementations are withheld. Authored expected outputs were cross-checked with independent reference oracles; compiler/runtime behavior still needs a verified execution provider.
Hint 1
Removal can split only the removed vertex’s original component.
Hint 2
A repeated traversal gives a useful baseline.
Hint 3
Discovery times and low-link values support a linear approach.
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