Shortest path in an adjacency list in non-weighted graph

Question

First, I would like to make sure I got the structure correct. As far as I know, an adjacency list representing a graph looks like this:

AdjList is an ArrayList, where each element is an object. Each object contains an ArrayList inside to represent vertices connected. So for example, in the image above, Vertext 1 (first index in the AdjList) is connected to the vertex at index 2, 4, and 5 of the AdjList. Is this representation of an adjacency list correct? (ps: I know indices start at 0, i put 1 here for simplicity/ease).

If it is correct, which algorithm should I use to find the shortest path between two vertices?

Answer 1

There is no algorithm to give you just the shortest path between two vertices. You can use either:

1. Dijkstra's algorithm to find the shortest path between one vertex and all the others (and then choose the one you need).
2. Roy-Floyd algorithm to find the shortest path between all possible pairs of vertices.

The links also include pseudocode.

Answer 2

这是Dijkstra最短路径算法在Java中的示例及其解释

Answer 3

You can use Dijkstra's and Floyd Warshall. For unweighed graph assume weight of each edge to be 1 and apply the algorithm.

Answer 4

Previous answers mention disjktra and floyd algorithms to resolve the problem and are valid solutions, but where the graph is unweighted, the best solution is use a BFS technique, simpler and optimal.

BFS has a algorithm complexity of O(n), while disjktra O(n * log(n)) and Floyd O(n^2)