Prove Bellman-Ford detects negative cycles from source

Analyze the prove bellman-ford detects negative cycles from source.

Difficulty

medium

Companies

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Topic

Graphbellmanford negcycle proof

Examples

Input: "proof_case_1"

Output: true

Input: "proof_case_2"

Output: true

Hints

Recall that Bellman-Ford relaxes all edges |V|-1 times to guarantee shortest paths in graphs without negative cycles.

After |V|-1 relaxations, if any edge can still be relaxed, what does that imply about the graph's structure?

Prove that such a relaxation in the |V|th iteration must create a negative cycle reachable from the source, and explain why this cycle must be part of a path from the source.

Prove Bellman-Ford detects negative cycles from source

Analyze the prove bellman-ford detects negative cycles from source.