How to convert a list of edges to a tree in python?

Question

I am having a list of edges that has the following format:

edges=[[1,4],[1,3],[1,2],[3,5],[3,6],[3,7]]

Here in each edge the first element is the parent node and the second is a child node i.e, in

[1,4]—->(1 is the parent node and 4 is child node)

I have to create a function that returns the pointer to the root of the tree. At first I tried creating a dictionary but after creating I am unable to proceed.

Please provide any ideas of how to implement this?

Asked By: vamsi bharadwaj

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Source

Answer 1

Assuming it is always a tree (and thus we have no two separate graphs) the task is the as determining which number never appears in the second position.

So:

Get a list of all numbers (nodes) which we call possible_roots
Iterate the list of your edges and remove the child node from our above list possible_roots
If it is a tree, there must only be one element left in possible_roots. This is the root of your tree.

Answered By: Timothy L Gillespie

Answer 2

There are many ways to create a tree data structure… moreover Python does not have a pointer data type, so the root of a tree would be an object.

Here is one way to do it:

First define a Node class:

class Node():
    def __init__(self, data=None):
        self.data = data
        self.children = []

Then the main algorithm:

def create_tree(edges):
    # Get all the unique keys into a set
    node_keys = set(key for keys in edges for key in keys)
    # Create a Node instance for each of them, keyed by their key in a dict:
    nodes = { key: Node(key) for key in node_keys }
    # Populate the children attributes from the edges
    for parent, child in edges:
        nodes[parent].children.append(nodes[child])
        # Remove the child from the set, so we will be left over with the root
        node_keys.remove(child)
    # Get the root from the set, which at this point should only have one member
    for root_key in node_keys:  # Just need one
        return nodes[root_key]

Run it as follows:

# Example run
edges = [[1,4],[1,3],[1,2],[3,5],[3,6],[3,7]]
root = create_tree(edges)

If you want to quickly verify the tree’s shape, add this method to the Node class:

    def __repr__(self, indent=""):
        return (indent + repr(self.data) + "n"
                + "".join(child.__repr__(indent+"  ") 
                          for child in self.children))

And use it to print the tree:

print(root)

This print method is just a very simple way to visualise the tree. With a bit more code you can also draw the branches of the tree, but this is enough to debug the code.

Answered By: trincot

Answer 3

You need to find out which vertex has no parent. This can be done by building a set of all vertices, then discarding vertices that have a parent.

Alternatively, this can be done from building on the one hand, the set of all parent vertices, and on the other hand, the set of all child vertices; then taking the set different parents - children.

Then there are three possibilities:

There are no vertices left. This means that your directed graph contained a cycle, and there is no root. Example: [[0,1], [1,2], [2,0]].
There is more than one vertex left. This means that your directed graph contains more than one "root". Example: [[0,2], [1,2]].
There is exactly one vertex left. This must be the root.

# FIRST METHOD
def get_root(dag):
    candidates = set(parent for (parent,_) in dag)
    for _,child in dag:
        candidates.discard(child)
    assert(len(candidates) == 1) # or handle len(candidates) == 0 and len(candidates) > 1 with an if/elif/else
    return candidates.pop()

# SECOND METHOD
def get_root(dag):
    parents, children = map(frozenset, zip(*dag))
    candidates = parents - children
    root, = candidates  # will raise exception if len(candidates) != 1
    return root

Testing:

print( get_root([[1,4],[1,3],[1,2],[3,5],[3,6],[3,7]]) )
# 1

print( get_root([[0,2], [1,2]]) )
# ValueError: too many values to unpack (expected 1)

print( get_root([[0,1], [1,2], [2,0]]) )
# ValueError: not enough values to unpack (expected 1, got 0)

Answered By: Stef

How to convert a list of edges to a tree in python?

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