具有邻接矩阵的未加权图上的最长路径

Question

I first looked at other questions and did not find any proper answer. Suppose there is a 2 dimensional Array given where two nodes are saved and also as Input an Integer which has the total amount of all nodes. The task is now to find the longest path in a directed acyclic graph in Java.

I firstly had the Idea to run Bfs like:

long longestPath(long length, long Array[][])
{
int[] max = new int;
if( !visited(V)
    {dfs(v); maximum[] = max[dfs.distance};}
}

I stopped here then, because I think dfs does only work for trees. Then I had the idea to use topological sort.Indeed I dont know, how to implement that with the 2-dimensional array. does anyone have an idea?

Answer 1

Yes, you have to do topological sort. Longest path in a DAG can be found by doing a clever transformation ie use the negative of the current edge weights. In the newly transformed graph, you find the shortest path. And the negative of this value is the longest path.

For finding the shortest path in a DAG, you first do a top sort and then update in that order

// do this for all the valid adjacent edges according to your matrix
// u is the current vertex you are processing in the topological order
if(cost[u] + w < cost[v]) // assume the edge is from u to v 
{
    cost[v] = cost[u] + w;
}