Question

I have a directed acyclic graph I’m trying to implement but I’m not sure what structure I can use. I keep believing that a tree or adjacency list would be viable but I am not given nodes to work with.

So in this case I tried to implement it using a 2d array, storing the priorities, in degrees and out degrees. However, I’m having problems figuring out how to insert an edge between two vertices and how I can check if a vertice is another vertice’s parent in this way.

Answer 1

When you say you’re “storing the priorities, in degrees and out degrees”, it suggests you don’t quite grok adjacency matrices. For an adjacency matrix M, vertices correspond to indices, and edges from v to u correspond to an entry in the matrix at M_vu (i.e. M_vu is the number of edges from v to u). The out-degree of a vertex v is ΣM_*v; the in-degree is ΣM_v*. If the matrix is in row-major order (M_{row, col}), these correspond to the column and row sums, respectively.

“Priority” isn’t a vertex property in plain DAGs. If you have priorities associated with the vertices, your graph class should contain another data structure mapping vertices to priorities (probably a vector, since vertices are usually numbered consecutively). Better still, have two graph classes: a DAG class, and a child PriorityDAG class that adds a priority property for nodes:

class DAG {
public:
    typedef int Vertex;
    ...
};

class PriorityDAG : public DAG {
public:
    using DAG::Vertex;
    typedef int Priority;

    Priority priority(Vertex vertex);

protected:
    std::vector<Priority> priorities;
    ...
};

If you’re ever going to have other types of graphs (undirected, cyclic), you can make a Graph class to be the parent of DAG.

Thus, to insert an edge, increment the value M_vu. If v is a parent of u, then there is an edge from v to u, so M_vu > 0.