How should I find the shortest path in the graph using linked list

Question

There are n nodes and there are edges between the nodes if they are connected directly. Each edge does not have weight and direction (If node a and b are connected, it means connected both way not one way).

Based on the graph, we can draw adjacency matrix which is two-dimensional array, A[0][0]...A[n-1][n-1]. So, the question is how to return the shortest path. If there is no path, should return empty path. And the path should return using linked list.

 |A B C D E
A|0 1 0 1 0
B|1 0 1 0 0 
C|0 1 0 1 0
D|1 0 1 0 1
E|0 0 0 1 0

So, based on the Matrix above, the shortest path from C to E is [C,D,E]. And the shortest path from A to C is [A,B,C].

We should use pseudo code with O(n^2) time complexity. And I briefly guess BFS approach would be great.

Answer 1

I believe this article answers your question. This problem can be solved with Dijkstra's algorithm. In your case the weight of each edge is equal to 1 so just make the dist_between(u,v) = 1 in the pseudo code. Time complexity of the solution is O(V^2). Note that, previous[v] = the node previous to the vth node in the shortest path to node v from the starting node . That means, in order to visit the vth node in the shortest possible way, you have to first come to the previous [v] node. So using this previous array, you can return the shortest path in any way you desire. If there is no path, the dist[v] in the pseudo code will be infinity.