Concatenate strings if they have an overlapping region

Question

I am trying to write a script that will find strings that share an overlapping region of 5 letters at the beginning or end of each string (shown in example below).

facgakfjeakfjekfzpgghi
                 pgghiaewkfjaekfjkjakjfkj
                                    kjfkjaejfaefkajewf

I am trying to create a new string which concatenates all three, so the output would be:

facgakfjeakfjekfzpgghiaewkfjaekfjkjakjfkjaejfaefkajewf

Edit:

This is the input:

x = ('facgakfjeakfjekfzpgghi', 'kjfkjaejfaefkajewf', 'pgghiaewkfjaekfjkjakjfkj')

**the list is not ordered

What I've written so far *but is not correct:

def findOverlap(seq)
    i = 0
    while i < len(seq): 
        for x[i]:
        #check if x[0:5] == [:5] elsewhere

 x = ('facgakfjeakfjekfzpgghi', 'kjfkjaejfaefkajewf', 'pgghiaewkfjaekfjkjakjfkj')
findOverlap(x)

Answer 1

Create a dictionary mapping the first 5 characters of each string to its tail

strings = {s[:5]: s[5:] for s in x}

and a set of all the suffixes:

suffixes = set(s[-5:] for s in x)

Now find the string whose prefix does not match any suffix:

prefix = next(p for p in strings if p not in suffixes)

Now we can follow the chain of strings:

result = [prefix]
while prefix in strings:
    result.append(strings[prefix])
    prefix = strings[prefix][-5:]
print "".join(result)

Answer 2

A brute-force approach - do all combinations and return the first that matches linking terms:

def solution(x):
    from itertools import permutations
    for perm in permutations(x):
        linked = [perm[i][:-5] for i in range(len(perm)-1) 
                               if perm[i][-5:]==perm[i+1][:5]]
        if len(perm)-1==len(linked):
            return "".join(linked)+perm[-1]
    return None

x = ('facgakfjeakfjekfzpgghi', 'kjfkjaejfaefkajewf', 'pgghiaewkfjaekfjkjakjfkj')
print solution(x)