My first instinct was DFS and I had to walk it back, which cost me time.
Clarify the problem constraints (e.g., graph size, edge weights, whether the cycle can repeat nodes) and then propose an efficient algorithm. A common approach is to run BFS from the target node to find the shortest path back to itself, or to use Dijkstra if weights are non-negative. Discuss time and space complexity and edge cases.
Pro tip: Mention that the shortest cycle through a node can be found by removing the target node, finding the shortest path from each neighbor to the target, and taking the minimum sum plus the edge back. This shows deep understanding and avoids pitfalls with self-loops.
Ask about graph size, whether edges have weights, if negative weights exist, and if the cycle can repeat vertices. This determines the appropriate algorithm and complexity.
For unweighted graphs, BFS from the target is optimal. For weighted graphs with non-negative weights, Dijkstra from the target works. If negative weights are possible, discuss Bellman-Ford or Floyd-Warshall.
Explain how to find the shortest cycle: e.g., run BFS/Dijkstra from the target, and when you encounter an edge back to the target, that forms a cycle. Keep track of the minimum distance.
State time and space complexity (e.g., O(V+E) for BFS, O(E log V) for Dijkstra). Discuss edge cases: no cycle, self-loop, multiple edges, disconnected graph.
Walk through a small example to verify the algorithm and demonstrate correctness. Mention potential optimizations or alternative approaches.
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