S_PATH_4
Which of the following scenarios can Dijkstra’s Algorithm NOT handle?

Question

BlackTom AI · Accepted Answer

We start by restating the question and listing the options to ensure clarity about what is being evaluated.
Question: Which of the following scenarios can Dijkstra’s Algorithm NOT handle?
Options:
- A cycle in a directed graph
- Any edge weight that is negative
- An acyclic graph
- Dijkstra’s can handle all of the above

Now, we analyze each option one by one to determine its correctness.
Option 1: A cycle in a directed graph
This statement is misleading. Dijkstra’s algorithm can handle graphs that contain cycles, as long as all edge weights are non-negative. The presence of a cycle does not inherently prevent the algorithm from functioning correctly; it simply explores edges and relaxes them, potentially visiting nodes repeatedly through cycles, but it still computes shortest paths correctly when weights are non-negative.
Option 2: Any edge weight that is negative
This is the key limitation of Dijkstra’s algorithm. If there exists any edge with a negative weight, Dijkstra’s method may incorrectly relax paths and fail to maintain the correct shortest path distances because it assumes that once a node’s shortest distance is determined, it cannot be improved by future relaxations. Therefore, this option identifies a scenario Dijkstra’s cannot handle.
Option 3: An acyclic graph
Dijkstra’s algorithm works perfectly fine on acyclic graphs. An acyclic graph does not cause any special issues; the algorithm will still propagate through nodes and compute shortest paths correctly as it relaxes edges in non-decreasing distance order, provided weights are non-negative.
Option 4: Dijkstra’s can handle all of the above
Since we have identified a scenario (negative edge weights) that Dijkstra’s cannot handle, this option cannot be true. The statement that it can handle all of the above is incorrect if negative weights are present.

In summary, the core misconception to avoid is thinking cycles or the presence of a cycle affect Dijkstra’s ability; the real constraint is non-negative edge weights. The only option that captures the actual limitation is Option 2, while Options 1 and 3 describe scenarios the algorithm can handle, and Option 4 contradicts the known limitation.

S_PATH_4 Which of the following scenarios can Dijkstra’s Algorithm NOT handle? 单项选择题

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