Python program to divide one group to sub-groups with exceptions

Question

I want to write a python code to divide a group consist of several rows to sub-groups depending on specific criteria to the effect that every row can join a group contain certain rows, but not permitted to join groups contain other rows. for example:

Group_A =[
[[2, 3, 5, 6, 8], [1, 4, 7, 9], 0],
[[3, 4, 7, 8, 9], [0, 2, 5, 6], 1],
[[0, 3, 7, 8, 9], [1, 4, 5, 6], 2],
[[0, 1, 4, 7, 9], [2, 5, 6, 8], 3],
[[1, 5, 6, 8, 9], [0, 2, 3, 7], 4],
[[0, 2, 4, 7, 9], [1, 3, 6, 8], 5],
[[0, 4, 7, 8, 9], [1, 2, 3, 5], 6],
[[2, 3, 5, 6, 8], [0, 1, 4, 9], 7],
[[0, 2, 4, 7, 9], [1, 3, 5, 6], 8],
[[2, 3, 4, 6, 8], [0, 1, 5, 7], 9]] 

Output:

Group_1 = [
[[2, 3, 5, 6, 8], [1, 4, 7, 9], 0]
[[1, 5, 6, 8, 9], [0, 2, 3, 7], 4]
[[2, 3, 5, 6, 8], [0, 1, 4, 9], 7]]

Group_2 = [
[[3, 4, 7, 8, 9], [0, 2, 5, 6], 1]
[[0, 3, 7, 8, 9], [1, 4, 5, 6], 2]
[[0, 4, 7, 8, 9], [1, 2, 3, 5], 6]]

Group_3 = [
[[0, 1, 4, 7, 9], [2, 5, 6, 8], 3]
[[0, 2, 4, 7, 9], [1, 3, 6, 8], 5]
[[0, 2, 4, 7, 9], [1, 3, 5, 6], 8]]

Group_4 = [[[2, 3, 4, 6, 8], [0, 1, 5, 7], 9]]

For more illustration: For the first row [[2, 3, 5, 6, 8], [1, 4, 7, 9], 0], 0 is the number of the row, [2, 3, 5, 6, 8] the group contains rows 2,3,5,6 and 8 that row number 0 not permitted to join, but can join a group contain most of these rows[1, 4, 7, 9].

Another example as follows:

Group_B = [
[[1, 3, 6, 7, 9], [2, 4, 5, 8], 0]
[[0, 2, 4, 5, 8], [3, 6, 7, 9], 1]
[[0, 1, 4, 7, 8], [3, 5, 6, 9], 2]
[[0, 1, 4, 5, 8], [2, 6, 7, 9], 3]
[[2, 3, 7, 8, 9], [0, 1, 5, 6], 4]
[[1, 3, 6, 7, 9], [0, 2, 4, 8], 5]
[[0, 1, 5, 7, 8], [2, 3, 4, 9], 6]
[[0, 4, 5, 6, 8], [1, 2, 3, 9], 7]
[[1, 4, 6, 7, 9], [0, 2, 3, 5], 8]
[[0, 4, 5, 7, 8], [1, 2, 3, 6], 9]]

Output:

Group_1 = [
[[0, 1, 4, 7, 8], [3, 5, 6, 9], 2]
[[0, 1, 4, 5, 8], [2, 6, 7, 9], 3]
[[0, 1, 5, 7, 8], [2, 3, 4, 9], 6]
[[0, 4, 5, 7, 8], [1, 2, 3, 6], 9]]

Group_2 = [
[[1, 3, 6, 7, 9], [2, 4, 5, 8], 0]
[[1, 3, 6, 7, 9], [0, 2, 4, 8], 5]
[[1, 4, 6, 7, 9], [0, 2, 3, 5], 8]]

Group_3 = [
[[0, 2, 4, 5, 8], [3, 6, 7, 9], 1]
[[0, 4, 5, 6, 8], [1, 2, 3, 9], 7]]

Group_4 = [[[2, 3, 7, 8, 9], [0, 1, 5, 6], 4]]

Regards,

Answer 1

My approach uses itertools to iterate over possible combinations

import itertools

Group_A =[
[[2, 3, 5, 6, 8], [1, 4, 7, 9], 0],
[[3, 4, 7, 8, 9], [0, 2, 5, 6], 1],
[[0, 3, 7, 8, 9], [1, 4, 5, 6], 2],
[[0, 1, 4, 7, 9], [2, 5, 6, 8], 3],
[[1, 5, 6, 8, 9], [0, 2, 3, 7], 4],
[[0, 2, 4, 7, 9], [1, 3, 6, 8], 5],
[[0, 4, 7, 8, 9], [1, 2, 3, 5], 6],
[[2, 3, 5, 6, 8], [0, 1, 4, 9], 7],
[[0, 2, 4, 7, 9], [1, 3, 5, 6], 8],
[[2, 3, 4, 6, 8], [0, 1, 5, 7], 9]]


Group_B = [
[[1, 3, 6, 7, 9], [2, 4, 5, 8], 0],
[[0, 2, 4, 5, 8], [3, 6, 7, 9], 1],
[[0, 1, 4, 7, 8], [3, 5, 6, 9], 2],
[[0, 1, 4, 5, 8], [2, 6, 7, 9], 3],
[[2, 3, 7, 8, 9], [0, 1, 5, 6], 4],
[[1, 3, 6, 7, 9], [0, 2, 4, 8], 5],
[[0, 1, 5, 7, 8], [2, 3, 4, 9], 6],
[[0, 4, 5, 6, 8], [1, 2, 3, 9], 7],
[[1, 4, 6, 7, 9], [0, 2, 3, 5], 8],
[[0, 4, 5, 7, 8], [1, 2, 3, 6], 9]]


def getGroups(groups):
    used = []
    c = 3
    group_c = 0
    print()
    while len(used) < 10:
        for x in range(0,10):
            for combo in itertools.combinations(groups[x][1], c):
                result = []
                for group in groups:
                        if group[2] not in used and group[2] in combo and x not in group[0]:
                            if (all(elem not in group[0] for elem in combo)):
                                result.append(group)
                
                if len(result) == c:
                    group_c += 1
                    print("GROUP", group_c)
                    
                    if x not in used:
                        print(groups[x])
                    for treffer in result:
                        print(treffer)
                        used.append(treffer[2])
                    used.append(x)
        c = c-1

getGroups(Group_A)

getGroups(Group_B)

The output looks as hopefully expected:

GROUP 1
[[2, 3, 5, 6, 8], [1, 4, 7, 9], 0]
[[1, 5, 6, 8, 9], [0, 2, 3, 7], 4]
[[2, 3, 5, 6, 8], [0, 1, 4, 9], 7]
GROUP 2
[[3, 4, 7, 8, 9], [0, 2, 5, 6], 1]
[[0, 3, 7, 8, 9], [1, 4, 5, 6], 2]
[[0, 4, 7, 8, 9], [1, 2, 3, 5], 6]
GROUP 3
[[0, 1, 4, 7, 9], [2, 5, 6, 8], 3]
[[0, 2, 4, 7, 9], [1, 3, 6, 8], 5]
[[0, 2, 4, 7, 9], [1, 3, 5, 6], 8]
GROUP 4
[[2, 3, 4, 6, 8], [0, 1, 5, 7], 9]

GROUP 1
[[0, 1, 4, 7, 8], [3, 5, 6, 9], 2]
[[0, 1, 4, 5, 8], [2, 6, 7, 9], 3]
[[0, 1, 5, 7, 8], [2, 3, 4, 9], 6]
[[0, 4, 5, 7, 8], [1, 2, 3, 6], 9]
GROUP 2
[[1, 3, 6, 7, 9], [2, 4, 5, 8], 0]
[[2, 3, 7, 8, 9], [0, 1, 5, 6], 4]
[[1, 3, 6, 7, 9], [0, 2, 4, 8], 5]
GROUP 3
[[1, 4, 6, 7, 9], [0, 2, 3, 5], 8]
GROUP 4
[[0, 2, 4, 5, 8], [3, 6, 7, 9], 1]
[[0, 4, 5, 6, 8], [1, 2, 3, 9], 7]