在Java中将有向无环图表示为二维数组

Question

How can I represent a directed acyclic graph as a 2-dimensional array if each row contains the immediate out-neighbours of a particular node. For example, if I have an array int [] [] edges, edges[0] = {1,2,3} means there are edges from node 0 to nodes 1, 2 and 3.

Answer 1

int n;
List<Integer>[] adj;
AdjacencyLists(int n) {
    adj = (List<Integer>[])new List[n];
    for (int i = 0; i < n; i++) 
        adj[i] = new ArrayList<Integer>(Integer.class);
}

.....

adj[a].add(b); // a -> b edge

Answer 2

If you have to use a 2D array - given that a 2D array at least in Java can't be sparse - then you need to allocate an NxN array: boolean[][] edges = new boolean[n][n];

1. You need to allow for the degenerate case where all the nodes are in a single chain, hence you need n-1 rows.
2. You need to allow for a star rooted on any node, hence n-1 columns.
3. It's vastly more complicated to store addresses in an array - given that the size has to be so large anyway - than to simple store "yes" at row j , position k for an edge from j -> k . And it's a lot faster to update the latter.

Obviously the sensible approach would be a HashMap from source node to a HashSet of target nodes, but that's apparently not what you're looking for.