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?

View Explanation

Log in for full answers

Similar Questions

What type of algorithm can be used to solve the basic network model for the critical path method?

Assume a weighted undirected graph on which we apply Dijkstra's algorithm to find the shortest path between two nodes. If we add 1 to all the edge weights, the shortest path between the two nodes remains the same.

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler