Floyd–Warshall: When to Use It

Start with the idea

A problem is a good match for Floyd–Warshall when it asks for all-pairs shortest paths on small dense graphs. Here the concrete task is: Return shortest distance from 0 to 2. The visible input matrix=[[0,3,10],[inf,0,2],[inf,inf,0]] is an example, not a definition of the whole problem. Ask what operations the solution must support and what the input guarantees. Inspect weight signs and graph direction: non-negative shortest paths, negative edges, and zero-one weights support different algorithms. The right choice follows from those guarantees, not from a familiar noun in the prompt.

The decisive invariant is: Allow intermediate vertices one by one and combine paths through the newly allowed vertex. Try to say why it applies to the task without quoting the implementation. Which fact becomes known after one update, and which possible answers remain? Edge weights change what a path means. State whether the objective is minimum distance, a spanning structure, or feasible flow before choosing state. If that claim cannot be maintained on a legal input, the pattern is wrong or one of its preconditions is missing. A counterexample is more useful than a vague warning: change one property of the sample, trace the first two steps, and identify the exact claim that fails.

Compare costs before committing. The advertised bound is O(V^3) time · O(V^2) space; identify the operation responsible for it and the extra memory it needs.