Question:
What is the purpose of Bellman-Ford algorithm?
What is the purpose of Bellman-Ford algorithm?
Show Hint
Bellman-Ford:
• Single Source Shortest Path
• Handles Negative Weights
• Detects Negative Cycles Dijkstra:
• Faster
• Does not handle negative edge weights
• Single Source Shortest Path
• Handles Negative Weights
• Detects Negative Cycles Dijkstra:
• Faster
• Does not handle negative edge weights
Updated On: Jun 25, 2026
- Detecting single source shortest paths in a weighted graph with negative weights
- Detecting all pairs shortest paths in a weighted graph with negative weights
- Detecting single source shortest paths in undirected graph without negative weights
- Detecting all pairs shortest paths in a weighted graph without negative weights
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The Correct Option is A
Solution and Explanation
Concept:
Bellman-Ford is a shortest path algorithm that computes the shortest distance from a single source vertex to all other vertices.
Unlike Dijkstra's algorithm, Bellman-Ford can handle graphs containing negative edge weights.
It can also detect negative weight cycles.
Step 1: Recall the purpose of Bellman-Ford.
Given a source vertex \(s\), Bellman-Ford computes: \[ d(s,v) \] for every vertex \(v\). Thus it is a single-source shortest path algorithm.
Step 2: Identify its major advantage.
Bellman-Ford works correctly even when some edge weights are negative. For example, \[ A \rightarrow B=-5 \] can be processed successfully.
Step 3: Compare with other algorithms.
Dijkstra's algorithm fails for graphs with negative edge weights. Floyd-Warshall computes all-pairs shortest paths. Therefore Bellman-Ford is uniquely associated with single-source shortest paths and negative weights.
Step 4: Write the answer.
Hence Bellman-Ford is used for \[ \boxed{\text{Single Source Shortest Paths with Negative Weights}}. \] Therefore option (A) is correct.
Step 1: Recall the purpose of Bellman-Ford.
Given a source vertex \(s\), Bellman-Ford computes: \[ d(s,v) \] for every vertex \(v\). Thus it is a single-source shortest path algorithm.
Step 2: Identify its major advantage.
Bellman-Ford works correctly even when some edge weights are negative. For example, \[ A \rightarrow B=-5 \] can be processed successfully.
Step 3: Compare with other algorithms.
Dijkstra's algorithm fails for graphs with negative edge weights. Floyd-Warshall computes all-pairs shortest paths. Therefore Bellman-Ford is uniquely associated with single-source shortest paths and negative weights.
Step 4: Write the answer.
Hence Bellman-Ford is used for \[ \boxed{\text{Single Source Shortest Paths with Negative Weights}}. \] Therefore option (A) is correct.
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