How to Merge Interconnected Lists using Graph Theory?

Merging Interconnected Lists: A Graph-Based Solution

Problem:

Consider a list of lists, where some share common elements. The task is to merge all lists interconnected through these shared elements until no further merges are possible.

Input: [['a','b','c'],['b','d','e'],['k'],['o','p'],['e','f'],['p','a'],['d','g']]
Expected Output: [['a','b','c','d','e','f','g','o','p'],['k']] 

Solution:

The problem can be approached as a graph problem, where the lists represent nodes connected through shared elements. The goal is to find the connected components in this graph. We can leverage the power of NetworkX, a Python library for graph analysis, to efficiently solve this problem.

import networkx 
from networkx.algorithms.components.connected import connected_components

# Convert the list of lists into a graph
def to_graph(l):
    G = networkx.Graph()
    for part in l:
        # Add nodes
        G.add_nodes_from(part)
        # Add edges between nodes
        G.add_edges_from(to_edges(part))
    return G

# Generate edges from a list of nodes
def to_edges(l):
    it = iter(l)
    last = next(it)
    for current in it:
        yield last, current
        last = current

# Create the graph and find connected components
G = to_graph(l)
components = connected_components(G)

# Print the merged lists (connected components)
print(list(components))

Output:

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

By utilizing NetworkX, this approach efficiently solves the problem by finding connected components, providing a robust and correct solution to merge lists based on shared elements.

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