How can I merge a chain of intersecting 2-D lists (list of of lists) into a single 2-D list of lists

Question

I have had to edit this question for the third time and present the data as simply as possible. I suppose the last one seemed very complex to recognize the pattern. Here is what I have now which looks more like the first one, for which @Andrej provided a solution, but I was unable to adapt to my scenario. I suppose that would go down to his conditions for merging. The original data is 3-D and is given below.`

original = [
            [[0,1],[2,3],[4,5]], 
            [[0,1],[4,5]], 
            [[2,3]], 
            [[6,7],[8,9],[10,11]], 
            [[8,9],[6,7]], 
            [[6,7],[10,11]], 
            [[16,17],[12,13],[14,15]], 
            [[12,13]], 
            [[14,15],[16,17],[18,19]]
            [[12,13],[16,17],[20,21]]
           ]   
`

From the given data, I want to obtain another 3-D merged data`

merged = [
          [[0,1],[2,3],[4,5]], 
          [[6,7],[8,9],[10,11]], 
          [[12,13],[14,15],[16,17],[18,19],[20,21]]
         ]

. I need to loop over all the 2-D list and merge all 2-D lists with common 1-D inner lists, while removing any duplicate 1-D lists. More like finding 2-D lists that have intersecting lists, and then merging all such 2-D lists. From the given original data, the first 2-D list intersects with the second through the list [0,1],[4,5] while the third 2-D list intersects with the first via [2,3] . Together, all three 2-D lists form a connected chain via their intersecting 1-D lists. This chain should be merged into a union of all three 2-D lists ie [[0,1],[2,3],[4,5]] . I have tried the sample code below:

import numpy as np
        
original = [
        [[0, 1], [2, 3], [4, 5]], 
        [[0, 1], [4, 5]], 
        [[2, 3]], 
        [[6, 7], [8, 9], [10, 11]], 
        [[8, 9], [6, 7]], 
        [[6, 7], [10, 11]], 
        [[16, 17], [12, 13], [14, 15]], 
        [[12, 13]], 
        [[14, 15], [16, 17], [18, 19]],
        [[12, 13], [16, 17], [20, 21]]
       ] 
    
        
    tmp = {}
    for subl in original:
        for a, b in subl:
            tmp.setdefault(a, set()).add(b)
    
    merged = []
    for k, v in tmp.items():
        out.append([[k, i] for i in v])
    
    print(merged)

But this is not giving the expected merged data as given above but this: [[[0, 0], [0, 1], [0, 2], [0, 3], [0, 4]], [[1, 0], [1, 1], [1, 2]], [[2, 0], [2, 1], [2, 2], [2, 3], [2, 4]]] . Any help would be hugely appreciated, please.

Answer 1

Try:

original = [
    [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4]],
    [[0, 1], [0, 2], [0, 3], [0, 4], [0, 5]],
    [[0, 2], [0, 3], [0, 5]],
    [[1, 0], [1, 2], [1, 4]],
    [[1, 2], [1, 3], [1, 4]],
    [[1, 0], [1, 2], [1, 3], [1, 4]],
    [[1, 0]],
    [[1, 0], [1, 3]],
    [[2, 0], [2, 1], [2, 2], [2, 3]],
    [[2, 1], [2, 2], [2, 3], [2, 4]],
    [[2, 2], [2, 3], [2, 4]],
    [[2, 3], [2, 4]],
    [[2, 4]],
]


tmp = {}
for subl in original:
    for a, b in subl:
        tmp.setdefault(a, set()).add(b)

out = []
for k, v in tmp.items():
    out.append([[k, i] for i in v])

print(out)

Prints:

[
    [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5]],
    [[1, 0], [1, 2], [1, 3], [1, 4]],
    [[2, 0], [2, 1], [2, 2], [2, 3], [2, 4]],
]