What is the time complexity of adjacency list vs matrix?

Best case O(1) matrix edge test. Worst case O(V) matrix neighbours. Space complexity is O(V²) matrix, O(V + E) list.

Adjacency list vs matrix

easy

A matrix costs V² whatever the edge count. For a social graph with a million users and fifty friends each, lists win by four orders of magnitude - and nearly every algorithm here wants a list.

Best O(1) matrix edge testWorst O(V) matrix neighboursSpace O(V²) matrix, O(V + E) list

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Where to go next

Breadth-first search

easy

Expands in rings, so it finds shortest paths.

Depth-first search

easy

A stack instead of a queue - that is the only difference.

Floyd-Warshall

medium

All pairs, three nested loops, one line of logic.