Question

I have a list of tuples. [ (1, 2), (2, 3), (4, 3), (5, 6), (6, 7), (8, 2) ]

I want to group them into lists based on which tuples are connected (have related values).

So the end result is two lists of related tuple values =
[ [1, 2, 3, 4, 8], [5, 6, 7] ]

How can I write a function to do this? This was a job interview question. I was trying to do it in Python, but I’m frustrated and just want to see the logic behind the answer, so even psuedo code would help me, so I can see what I did wrong.

I only had a few minutes to do this on the spot, but here is what I tried:

def find_partitions(connections):
 theBigList = []     # List of Lists
 list1 = []          # The initial list to store lists
 theBigList.append(list1)

 for list in theBigList:
 list.append(connection[1[0], 1[1]])
     for i in connections:
         if i[0] in list or i[1] in list:
             list.append(i[0], i[1])

         else:
             newList = []
             theBigList.append(newList)

Essentially, the guy wanted an list of lists of values that were related.
I tried to use a for loop, but realized that it wouldn’t work, and then time ran out.

Answer 1

As we fill in the components, at each stage there are three cases to consider (as you will have to match up overlapping groups):

1. Neither x or y are in any component already found.
2. Both are already in different sets, x in set_i and y in set_j.
3. Either one or both are in one component, x in set_i or y in a set_i.

We can use the built-in set to help. (see @jwpat’s and @DSM’s trickier examples):

def connected_components(lst):
    components = [] # list of sets
    for (x,y) in lst:
        i = j = set_i = set_j = None
        for k, c in enumerate(components):
            if x in c:
                i, set_i = k, c
            if y in c:
                j, set_j = k, c

        #case1 (or already in same set)
        if i == j:
             if i == None:
                 components.append(set([x,y]))
             continue

        #case2
        if i != None and j != None:
            components = [components[k] for k in range(len(components)) if k!=i and k!=j]
            components.append(set_i | set_j)
            continue

        #case3
        if j != None:
            components[j].add(x)
        if i != None:
            components[i].add(y)

    return components               

lst = [(1, 2), (2, 3), (4, 3), (5, 6), (6, 7), (8, 2)]
connected_components(lst)
# [set([8, 1, 2, 3, 4]), set([5, 6, 7])]
map(list, connected_components(lst))
# [[8, 1, 2, 3, 4], [5, 6, 7]]

connected_components([(1, 2), (4, 3), (2, 3), (5, 6), (6, 7), (8, 2)])
# [set([8, 1, 2, 3, 4]), set([5, 6, 7])] # @jwpat's example

connected_components([[1, 3], [2, 4], [3, 4]]
# [set([1, 2, 3, 4])] # @DSM's example

This certainly won’t be the most efficient method, but is perhaps one similar to what they would expect. As Jon Clements points out there is a library for these type of calculations: networkx, where they will be much more efficent.