Explain Floyd-Warshall Algorithm (All Pairs Shortest Path).

Difficulty: 6/10

all-pairs shortest path, dynamic programming, graph algorithms

Floyd-Warshall

Floyd-Warshall computes shortest paths between every pair of vertices using dynamic programming. It incrementally allows each vertex k to serve as an intermediate point and updates dist[i][j] using dist[i][k] + dist[k][j]. It supports negative edges but not negative cycles if meaningful shortest paths are required.

javascript

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Time: O(V³).
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Space: O(V²).
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Supports negative edges.
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dist[v][v] < 0 after processing indicates a negative cycle.
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Useful when all-pairs distances are required and V is moderate.

Scenario Questions

0-2 years experience

2-5 years experience

Follow-up Questions