Merging Linked Lists: A Graph-Theoretic Approach

Consider a list of lists, where certain lists share common elements. The task at hand is to merge all lists that contain at least one shared element, iteratively combining them until no more lists can be combined.

The solution lies in utilizing graph theory, viewing the list as a graph where each sublist represents a set of vertices, and shared elements denote edges between vertices. This transforms the problem into finding connected components within the graph.

NetworkX, a robust Python library, offers an efficient solution for this task. The code snippet below outlines the merging process:

import networkx as nx

# Convert the list of lists into a graph
G = nx.Graph()
for sublist in L:
    G.add_nodes_from(sublist)
    for v, w in to_edges(sublist):
        G.add_edge(v, w)

# Find the connected components of the graph
components = list(nx.connected_components(G))

# Merge the lists corresponding to each connected component
merged_lists = []
for component in components:
    merged_lists.append([node for node in component])

NetworkX's efficient algorithms make this approach both accurate and computationally efficient. Alternatively, custom graph data structures can be employed to achieve the same result.