How to Merge Lists with Shared Elements Using Graph Theory?

Merge Lists with Shared Elements: A Graph-Theoretic Approach

Consider the problem of merging lists that share common elements. Given a list of lists containing elements, the goal is to merge all lists that share an element and continually repeat this process until no more lists can be merged.

Initially, one may consider employing boolean operations and a while loop to achieve this. However, a more elegant solution lies in using graph theory.

Visualize the input list as a graph where each list represents a node, and shared elements are edges connecting them. The task becomes equivalent to finding connected components in this graph.

NetworkX provides a comprehensive solution for this task. It treats each list as a node and infers edges based on shared elements. By utilizing NetworkX's connected_components function, one can efficiently group lists that share elements into connected components.

Here's a Python implementation using NetworkX:

<code class="python">import networkx as nx

def merge_shared_lists(input_lists):
    # Convert lists to a graph
    G = nx.Graph()
    for part in input_lists:
        G.add_nodes_from(part)
        G.add_edges_from(to_edges(part))

    # Find connected components
    return [list(component) for component in nx.connected_components(G)]</code>

This approach offers several benefits:

• Correctness: NetworkX ensures the accuracy of the merge operation.
• Efficiency: NetworkX efficiently identifies connected components.
• Versatility: NetworkX supports a wide range of graph operations, allowing for further analysis or visualization.

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