How to Merge Lists with Overlapping Elements Using Graph Theory?

Merging Lists with Shared Elements: A Graph-Theoretic Approach

Given a collection of lists, some of which contain overlapping elements, the objective is to consolidate them into a set of lists comprising the full set of unique elements across the original lists. For instance, consider the following input list of lists:

L = [['a', 'b', 'c'], ['b', 'd', 'e'], ['k'], ['o', 'p'], ['e', 'f'], ['p', 'a'], ['d', 'g']]

The task is to merge lists that share common elements until no more lists can be combined. The desired output would be:

L = [['a', 'b', 'c', 'd', 'e', 'f', 'g', 'o', 'p'], ['k']]

While boolean operations and while loops could be employed, a more efficient approach can be found by viewing the lists as a graph. In a graph representation, each list corresponds to a set of nodes connected by edges. Therefore, the problem translates to finding the connected components within this graph.

One solution involves utilizing NetworkX, a robust library for graph analysis, as demonstrated below:

<code class="python">import networkx 
from networkx.algorithms.components.connected import connected_components

def to_graph(l):
    G = networkx.Graph()
    for part in l:
        # each sublist is a bunch of nodes
        G.add_nodes_from(part)
        # it also imlies a number of edges:
        G.add_edges_from(to_edges(part))
    return G

def to_edges(l):
    """ 
        treat `l` as a Graph and returns it's edges 
        to_edges(['a','b','c','d']) -> [(a,b), (b,c),(c,d)]
    """
    it = iter(l)
    last = next(it)

    for current in it:
        yield last, current
        last = current    

G = to_graph(l)
print(connected_components(G))
# prints [['a', 'c', 'b', 'e', 'd', 'g', 'f', 'o', 'p'], ['k']]</code>

By leveraging the power of graph theory, NetworkX effectively handles the task, ensuring correctness and efficiency.

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