Jun 7, 2011 · If you have a complete binary tree, by which I mean all internal nodes have two children, and all leaves at same depth. And if you number them starting from 1 i.e. in your case a = 1; b = 2; c = 3 ....

That'll work for any tree of size 6 of course but I have to abstract this for a tree of any size. Problem is the only way I can think of initializing the adjacency matrix is how I did it in my main function, but for that every single row in the matrix seems to always turns out the same. So how can I perform this abstraction?

In some cases, the data in a graph or tree is so simple (say, sequential integers), that nodes can be completely eliminated in favor of a lone adjacency list or 2d array. A binary heap is a good example of tree data that works very nicely as a flat structure, reinforcing the idea of picking whatever representation makes the most sense.

Dec 29, 2016 · There's no reason the adjacency list for each vertex couldn't be stored as a binary tree, but there are tradoffs. As you say, this adjacency list representation is often used for sparse graphs. Often, "sparse graph" means that a particular vertex is adjacent to few others. So your "adjacency list" for a particular vertex would be very small.

Mar 27, 2013 · This matrix presents a graph where nodes 1 and 2 are connected, 1 and 3 are connected, 2 and 3 are connected. How to bruteforce all combinations of possible paths in such a graph using this kind of matrix? I mean that picking just node 1 is a separate combination. Then, say, 1-2 is a separate combination. 1-2-3; 3-1-2.

Sep 6, 2016 · Note that you may as well represent a binary tree with an adjacency matrix (if necessary, you can encode the "left" and "right" child information with different adjacency values, e.g., 1 and 2), and a graph with such a recursive tree-like structure (although for a general graph, you'll have to allow for more than two outgoing edges).

Jul 27, 2022 · The next step is to traverse the tree, e.g. in DFS order (BFS works too but DFS is easier to quickly prototype unless your tree is deeper than stack limits allow). In (e.g.) a std::map<size_t, std::set<size_t>> you record each node’s descendants. Finally, you iterate through the map and nested sets to generate matrix lines and columns.

Sep 22, 2020 · If you know the adjacency list correspond to a binary tree then search for the root (only node with zero indegree). Later, perform a DFS (Depth First Search) starting at the root to create the tree. And, that is.

Mar 20, 2020 · Any adjacency matrix representing a tree will have exactly 2(N-1) 1's, since each edge sets two bits in the matrix (with no 1's on the diagonal, since trees have no self-edges). Furthermore, since the tree must be connected, there must be at least one 1 per row and column.

Apr 13, 2021 · I was looking at an example of a binary tree in an adjacency list format and I couldn't figure out what the binary tree equivalent looks like. There was a representation but the ordering didn't make sense e.g. left/right/parent. Searching didn't yield any results of how to figure out a binary tree from an adjacency list.