If a programmer uses dynamic programming to solve the all-pairs shortest path problem for a directed graph, what memory scaling behavior occurs relative to the number of vertices?

💡 Explanation

The Floyd-Warshall algorithm, a dynamic programming approach for the all-pairs shortest path, stores a distance matrix. Because the matrix requires space for each pair of vertices, the memory scales quadratically, O(V^2); therefore quadratic scaling is correct, rather than linear, logarithmic, or exponential scaling.

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