Graphs

Adjacency list uses O(V + E) space; adjacency matrix uses O(V^2) regardless of edge count.

When the graph is dense (E close to V^2) or you need O(1) edge-existence checks, as in Floyd-Warshall; for sparse graphs a list is smaller and faster to iterate.

A flat list of (u, v, weight) triples; Kruskal's MST sorts it directly and Bellman-Ford iterates over it each round.

Build an adjacency list (hash map or array of lists from node to neighbors), plus in-degree counts if a topological order is needed.

O(V + E): each vertex is enqueued or visited once and each edge is examined a constant number of times.

It explores vertices in nondecreasing order of edge count from the source, so the first time a vertex is discovered is via a fewest-edge path.