Question
A vertex v in a directed graph G is called a sink if: all other vertices of G have an edge that points to v,
A vertex v in a directed graph G is called a sink if:
all other vertices of G have an edge that points to v, and
no vertex in G, including v itself, has an edge that points from v.
Given the (partial) definition of an adjacency matrix below, complete the C# method Sink which returns true if the given vertex v (name) is both found and a sink; false otherwise. Note that E[i,j] = -1 when the edge from i to j does not exist. State the worst-case time complexity of your Sink method using the big-Oh notation where n is the number of vertices.
class DirectedGraph
{
public string[ ] V { set; get; } // Vertex list
public int[,] E { set; get; } // Adjacency matrix
public int NumVertices { set; get; }
public int MaxNumVertices { set; get; }
...
// FindVertex
// Returns the index of the given vertex (if found); otherwise returns -1
private int FindVertex (string name) { ... }
...
public bool Sink (string name) { ... }
}
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