AP CSP Day 49: Conditionals Advanced
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Practice Question
A network connects 5 devices with these links: A-B, A-C, B-C, B-D, C-D, C-E, D-E. What is the minimum number of connections that must fail before device A can no longer communicate with device E?
Device A connects to B and C. If both A-B and A-C fail, device A is completely isolated and cannot reach any other device, including E. Alternatively, if C-E and D-E both fail, device E becomes isolated. Either way, the minimum number of failures needed is 2.
A) Removing any single connection still leaves alternative paths between A and E (for example, if A-B fails, A-C-D-E still works). C) Two failures are sufficient to isolate either A or E. D) Four failures is more than the minimum needed.
Students test only one path and conclude that one failure is sufficient. To find the minimum, you must verify that ALL alternative paths are also broken.
To find minimum failures for disconnection, identify the node with the fewest connections — its degree equals the minimum cuts needed to isolate it. Check both endpoints.
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