I did a search on similar topics, but the answers are too vague for my level of understanding and comprehension, and I don't think they're specific enough to my question.
Similar threads:
Tree (directed acyclic graph) implementation
Representing a DAG (directed acyclic graph)
Question:
I have formatted a text file which contains data of the following format...
Example dataset:
GO:0000109#is_a: GO:0000110#is_a: GO:0000111#is_a: GO:0000112#is_a: GO:0000113#is_a: GO:0070312#is_a: GO:0070522#is_a: GO:0070912#is_a: GO:0070913#is_a: GO:0071942#part_of: GO:0008622
GO:0000112#part_of: GO:0000442
GO:0000118#is_a: GO:0016581#is_a: GO:0034967#is_a: GO:0070210#is_a: GO:0070211#is_a: GO:0070822#is_a: GO:0070823#is_a: GO:0070824
GO:0000120#is_a: GO:0000500#is_a: GO:0005668#is_a: GO:0070860
GO:0000123#is_a: GO:0005671#is_a: GO:0043189#is_a: GO:0070461#is_a: GO:0070775#is_a: GO:0072487
GO:0000126#is_a: GO:0034732#is_a: GO:0034733
GO:0000127#part_of: GO:0034734#part_of: GO:0034735
GO:0000133#is_a: GO:0031560#is_a: GO:0031561#is_a: GO:0031562#is_a: GO:0031563#part_of: GO:0031500
GO:0000137#part_of: GO:0000136
I'm looking to construct a weighted directed DAG from this data (the above is just a snippet). The whole dataset of 106kb is here: Source
--------------------------------------------------
Taking into consideration line-by-line, the data of each line is explained as follows...
First line as an example:
GO:0000109#is_a: GO:0000110#is_a: GO:0000111#is_a: GO:0000112#is_a: GO:0000113#is_a: GO:0070312#is_a: GO:0070522#is_a: GO:0070912#is_a: GO:0070913#is_a: GO:0071942#part_of: GO:0008622
'#' is the delimeter/tokenizer for the line data.
The First term, GO:0000109 is the node name.
The subsequent terms of is_a: GO:xxxxxxx OR part_of: GO:xxxxxxx are the nodes which are connected to GO:0000109.
Some of the subsequent terms have connections too, as depicted in the dataset.
When it is is_a, the weight of the edge is 0.8.
When it is part_of, the weight of the edge is 0.6.
--------------------------------------------------
I have Google-d on how DAGs are, and I understand the concept. However, I still have no idea how to put it into code. I'm using Java.
From my understanding, a graph generally consists of nodes and arcs. Does this graph require an adjacency list to determine the direction of the connection? If so, I'm not sure how to combine the graph and adjacency list to communicate with each other.
After constructing the graph, my secondary goal is to find out the degree of each node from the root node. There is a root node in the dataset.
For illustration, I have drawn out a sample of the connection of the first line of data below:
Image Link
I hope you guys understand what I'm trying to achieve here. Thanks for looking through my problem. :)
Because it's easier to think about, I'd prefer to represent it as a tree. (Also makes it easier to traverse the map and keep intermediate degrees.)
You could have a Node class, which would have a Collection of child Node objects. If you must, you could also represent the child relationships as a Relationship object, which would have both a weight and a Node pointer, and you could store a Collection of Relationship objects.
Then you could do a walk on the tree starting from the root, and mark each visited node with its degree.
class Node{
String name;
List<Relationship> children;
}
class Relationship{
Node child;
double weight;
}
class Tree{
Node root;
}
Here, Tree should probably have a method like this:
public Node findNodeByName(String name);
And Node should probably have a method like this:
public void addChild(Node n, double weight);
Then, as you parse each line, you call Tree.findNodeByName() to find the matching node (and create one if none exists... but that shouldn't happen, if your data is good), and append the subsequent items on the line to that node.
As you've pointed out, DAGs cannot really be converted to trees, especially because some nodes have multiple parents. What you can do is insert the same node as the child of multiple parents, perhaps using a hash table to decide if a particular node has been traversed or not.
Reading the comments, you seem confused by how a Node can contain Relationships which each in turn contains a Node. This is quite a common strategy, it is in general called the Composite pattern.
The idea in the case of trees is that the tree can be thought of as consisting of multiple subtrees - if you were to disconnect a node and all its ancestors from the tree, the disconnected nodes would still make a tree, though a smaller one. Thus, a natural way to represent a tree is to have each Node contain other Nodes as children. This approach lets you do many things recursively, which in the case of trees is often, again, natural.
Letting a Node keep track of its children and no other parts of the tree also emulates the mathematical directed graph - each vertex is "aware" only of its edges and nothing else.
Example recursive tree implementation
For instance, to search for an element in a binary search tree, you would call the root's search method. The root then checks whether the sought element is equal, less or greater than itself. If it is equal, the search exits with an appropriate return value. If it is less or greater, the root would instead call search on the left or right child, respectively, and they would do exactly the same thing.
Analogously, to add a new Node to the tree, you would call the root's add method with the new node as a parameter. The root decides whether it should adopt the new node or pass it on to one of its children. In the latter case, it would select a child and call its add method with the new Node as a parameter.
Related
I'm learning about search algorithms BFS and DFS. I plan to implement both but before I do that, I need to implement my graph structure. Here's my idea:
A graph of connecting cities: Each city is represented by a Node.
Our graph will simply be an ArrayList of Nodes added as they're created, and each Node will have a list of it's neighbors, and a parent which will let us know where we came from (for path retrieval). I haven't coded anything up yet, I wanted to get some feedback on my ideas before spending the time writing up something that won't work. Here's some pseudocode-ish, code. One potential problem I can see is how we're going to deal with Nodes that we can get to from multiple places (multiple parents). If anyone has any suggestions on dealing with that, feel free to share.
public class Node{
String name;
Node parent;
ArrayList<Node> neighbors;
public addNeighbor(Node n);
public setParent(Node n);
public getNeighbors()
...
}
public static void main(String[] args){
ArrayList<Node> graph = new ArrayList<Node>();
//build node
Node node = new Node(String name);
//add neighbors
node.addNeighbor(neighbor1);
node.addNeighbor(neighbor2);
//set parent
node.setParent(parent1);
//add to graph
graph.add(node);
path = dfs(graph, startNode, goalNode);
System.out.print(path);
}
Edit: I know I could look online and find implementations of this pretty easily, but I'd prefer to come up with my own solutions.
Your implementation look good. It's the classic implentation of a graph structure (a node with a list of neighbors). Some points:
You can use backtracking to deal with multiples paths that reach the same node. If the dfs method have a recursive implementation, you need to avoid the recursive call if the Node has already a parent. But if the new path is better that the old one, then you discard the old parent, and set the new one.
Your implementation is a directional graph. In other words, you can build a graph that has a path from A to B, but has no path from B to A. I don't know if this is ok for you.
I recommend you encapsulate the building of the graph inside a wrapper, that build both paths automatically, whith a unique call to a method. That way, always you build bidirectional paths.
You can use a Set to store the neighbors. That way, there is no duplicates. Of course, you need to implements the "equals" method in the Node class.
This may be a too-specific question, but I'm hoping there's a more general solution to my problem.
I have a class. In this class is a tree-type structure with many parent/child nodes. Also in this class is an Array filled with references to each node in this tree-type structure.
The tree's purpose is for each node to know where to draw itself on screen (every node has relative positional information based on its parent's location).
The Array's purpose is the draw order, I simply draw whatever node is referenced at Array[0] first and so on. (So, the nodes aren't being drawn in the order they appear in the tree necessarily).
My problem is this. I want to clone this overall class that contains these two objects (tree with nodes and an Array that references said nodes). This seems simple.
I create a deep copy of the tree structure and the nodes it contains. Cool.
However, I don't know how to repopulate a new Array with references to these new nodes in this new tree. It seems like it would be simple but I can't figure out how to do it.
I tried to be specific enough to give enough information without being too confusing, hope you understand.
Thanks.
If you're able to change the node data structure, you could add a field for the node's array index. That way, once you've rebuilt your tree you can just walk through it and use the index field to repopulate the array. Not super elegant, but it gets the job done...
Or, to avoid adding a field to your node class, I suppose you could use a temporary hashtable that maps nodes to array indices. Walk through your source array to populate the hashtable, then once you've cloned the tree, walk through the tree, looking up the new nodes in the hashtable (which will work fine assuming you've implemented equals and hashCode properly) and populating the array from those.
Problem is I don't understand how to create a tree. I have gone through many code examples on trees but I don't even know how to work with/handle a node and hence I don't understand how the node class works(that was present in all the program examples ). When i try to use methods such as appendChild(as mentioned in java docs),I get an error,and I am asked to create one such appendChild method inside that node class within the main program. Couldn't understand why that happened.
I am given integer pairs((u,v) meaning there is an edge between u & v) of nodes and I also need to know if any Element-to-node conversion is required for using u and v(of type integer) as nodes.
Please bear with me since my basics are weak. Little explanation on how the entire thing works/functions would be very helpful.
Thank you.
EDIT 1: I went through the following links:(hardly found anything on just unordered trees) http://www.cs.cmu.edu/~adamchik/15-121/lectures/Trees/code/BST.java http://www.newthinktank.com/2013/03/binary-tree-in-java/ . Tried to modify these codes to meet my own purpose but failed.
I only got a blurry idea and that is not enough for implementation. I am trying to make a simple unordered tree,for which i am given u v pairs like:
(4,5) (5,7) (5,6). I just need to join (4<--5),(5<--7) and (5<--6). So how do I write a node class that only joins one node to the prev node? Besides,to do only this,do I need to bother myself with leftchild,rightchild? If not,how will I be able to traverse the tree and do similar operations such as height diameter calculation etc later?
Thank you for your patience.
Well Its not entirely clear whether you want an explanation on tree creation in general, on some tree implementation you have found, or you have a basic code already that you cannot get working. You might want to clarify that :).
Also tree creation in general:
Most explanation and implementation you will find might be "overly" elegant :). So try to imagine a simple linked list first. In that list you have nodes(the elements of the list). A node contains some valuable data and a reference to an other node object. A very simple tree is different only in that a node have more than one reference to other nodes. For example it has a Set of references, its "children".
Here is a VERY crude code only as an example for addChild() or appendChild in your case:
public class Node {
private String valueableData;
private Set<Node> children;
public Node(){
this.children=new HashSet<Node>();
}
public Node (String valueableData){
this.valueableData=valueableData;
this.children=new HashSet<Node>();
}
public void addChild(Node node){
children.add(node);
}
}
Now this implementation would be quite horrible (I even deleted the setter/getters), also it would be wise to keep the root nodes reference in some cases, and so on. But you might get the basic idea.
You might wanna create a cycle or recursion to go over the (u,v) integer pairs. You create the root node first then you just addChild() all the other nodes recursively, or create every node first then setChild() them according to your rules.
I have a large number of objects arranged in a tree-like structure (each node on the tree has parents and children, starting with one master node, and ending in many child nodes). Each object has it's own ID in the form of a string, and there are many duplicate IDs, but no duplicates sunder the same parent. Example:
ParentA:
childA
childB
childD
ParentB:
childA
childC
childD
The tree is also many layers deep.
I need a method of finding objects that will work like this (example is based on the previous list):
Example 1:
an ArrayList with the string {"childB"} is passed to the algorithm
there are no duplicate nodes with an ID of "childB", so a refrence to childB is returned
Example 2:
an ArrayList with the strings {"parentA", "childD"} is passed to the algorithm
there are no duplicate nodes with an ID of "childD" AND a parent with an ID of "parentA", so a reference to the given node is returned
Example 3:
an ArrayList with the string {"childD"} is passed to the algorithm
there are duplicate nodes with an ID of "childD" so the algorithm requests for more information (the name of the parent(s))
Keep in mind that there may be many levels of specificity, like {"nodeA", "nodeD", "nodeX", "nodeD"} so some kind of loop, or maybe a recursive method would be needed.
So, any ideas?
Update:
I created a depth-first-search algorithm to go through each node on the tree, and it works very well. The algorithm returns all nodes in the form of one ArrayList All I need now is a way to select one based on varying degrees of specificity. Can anyone help with that?
The above three examples show what I need.
depth-first search algorithm may be helpful for you!!!
I've got a set of TreeNodes, each of which has an id, a Collection of parent nodes, and a collection of child nodes.
For a given node Id, I'm looking for an efficient way to generate all the links that pass through that node. So in short, start at the node, and iterate through all its children. If a node has more than one child, create a link for each child. The traverse the children etc..
I'd also like to be able to do this in an 'upward' direction, through the parent nodes.
Is there a simple algorithm to do this?
EDIT: Oh, and I'd like to be able to output the id's of all the nodes in a given chain...
You are looking for a Breadth First or Depth First Search. At first it is not more than the following (this is depth first search).
Visit(Node node)
{
foreach (Node childNode in node.Children)
{
Visit(childNode);
}
DoStuff(node);
}
The problem is that the graph may contain cycles, hence the algorithm will enter infinite loops. To get around this you must remember visited nodes by flaging them or storing them in a collection. If the graph has no cycles - for example if it is a tree - this short algorithm will already work.
And by the way, if a TreeNode has multiple parents, it's not a tree but a graph node.
Well, if the nodes have a reference to the parent, it's simple as getting the parent recursively (once in a tree, each node has only one (or none at all, if it is a root) parent.
If there's no such reference, than you could use a breadth-first search, for instance, having as initial set your collection of parent nodes.
-- EDIT --
Once a node may have more than one parent, then you're dealing with a graph. There are also graph traversal algorithms (see table at the side).
Make sure that, if your graph has a cycle, you won't end up having a infinite loop
You might want to check out depthFirstEnumeration() and breadthFirstEnumeration() on DefaultMutableTreeNode. However, this doesn't solve your problem of wanting to navigate the tree in a bottom-up fashion.