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So, this is a part of a function I'm trying to make.

I don't want the code to be too complicated.

I have a list of words, e.g.

words = ['giraffe', 'elephant', 'ant', 'tiger', 'racoon', 'cat', 'hedgehog', 'mouse']

The idea of the word chain sequence is for the next word to begin with the letter that the last word ended in.

(Edit: Each word cannot be used more than once. Other than that there are no other constraints.)

I want the output to give the longest word chain sequence, which in this case is:

['hedgehog', 'giraffe', 'elephant', 'tiger', 'racoon']

I'm not really sure how to do it, I had different attempts at trying this. One of them...

This code finds the word chain correctly if we start with a specific word from the list, e.g. words[0] (so 'giraffe'):

words = ['giraffe', 'elephant', 'ant', 'tiger', 'racoon', 'cat', 'hedgehog', 'mouse']



word_chain = 



word_chain.append(words[0])



for word in words:

    for char in word[0]:



       if char == word_chain[-1][-1]:

            word_chain.append(word)



print(word_chain)

Output:

['giraffe', 'elephant', 'tiger', 'racoon']

BUT, I want to find the longest possible chain of words (explained above).

My method: So, I tried to use the above working code that I wrote and loop through, using each word from the list as the starting point and finding the word chain for each word[0], word[1], word[2] etc. Then I tried to find the longest word chain by using an if statement and compare the length to the previous longest chain, but I can't get it done properly and I don't really know where this is going.

words = ['giraffe', 'elephant', 'ant', 'tiger', 'racoon', 'cat', 'hedgehog', 'mouse']



word_chain = 

max_length = 0

for starting_word_index in range(len(words) - 1):



    word_chain.append(words[starting_word_index])



    for word in words:

        for char in word[0]:



            if char == word_chain[-1][-1]:

                word_chain.append(word)



    # Not sure



    if len(word_chain) > max_length:

        final_word_chain = word_chain

        longest = len(word_chain)

        word_chain.clear()



print(final_word_chain)

This is my nth attempt, I think this one prints an empty list, I had different attempts before this that failed to clear the word_chain list properly and ended up repeating words over again.

Any help much appreciated. Hopefully I didn't make this too teedious or confusing... Thanks!

You can use recursion to explore every "branch" that emerges when every possible letter containing the proper initial character is added to a running list:

words = ['giraffe', 'elephant', 'ant', 'tiger', 'racoon', 'cat', 'hedgehog', 'mouse']

def get_results(_start, _current, _seen):

  if all(c in _seen for c in words if c[0] == _start[-1]):

    yield _current

  else:

      for i in words:

        if i[0] == _start[-1]:

          yield from get_results(i, _current+[i], _seen+[i])





new_d = [list(get_results(i, [i], ))[0] for i in words]

final_d = max([i for i in new_d if len(i) == len(set(i))], key=len)

Output:

['hedgehog', 'giraffe', 'elephant', 'tiger', 'racoon']

This solution works similar to the breadth-first search, as the function get_resuls will continue to iterate over the entire list as long as the current value has not been called on before. Values that have been seen by the function are added to the _seen list, ultimately ceasing the stream of recursive calls.

This solution will also ignore results with duplicates:

words = ['giraffe', 'elephant', 'ant', 'ning', 'tiger', 'racoon', 'cat', 'hedgehog', 'mouse',]

new_d = [list(get_results(i, [i], ))[0] for i in words]

final_d = max([i for i in new_d if len(i) == len(set(i))], key=len)

Output:

['ant', 'tiger', 'racoon', 'ning', 'giraffe', 'elephant']

Here is a working recursive brute-force approach:

def brute_force(pool, last=None, so_far=None):

    so_far = so_far or 

    if not pool:

        return so_far

    candidates = 

    for w in pool:

        if not last or w.startswith(last):

            c_so_far, c_pool = list(so_far) + [w], set(pool) - set([w])

            candidates.append(brute_force(c_pool, w[-1], c_so_far))

    return max(candidates, key=len, default=so_far)



>>> brute_force(words)

['hedgehog', 'giraffe', 'elephant', 'tiger', 'racoon']

At every recursive call, this tries to continue the chain with every eligible word form the remaining pool. It then chooses the longest such continuation.

This function creates an iterator (see: What does the "yield" keyword do?) which recursively calls the same iterator to create all possible tail sequences:

words = ['giraffe', 'elephant', 'ant', 'tiger', 'racoon', 'cat', 'hedgehog', 'mouse']



def chains(words, previous_word=None):

    # Consider an empty sequence to be valid (as a "tail" or on its own):

    yield 

    # Remove the previous word, if any, from consideration, both here and in any subcalls:

    words = [word for word in words if word != previous_word]

    # Take each remaining word...

    for each_word in words:

        # ...provided it obeys the chaining rule

        if not previous_word or each_word.startswith(previous_word[-1]):

            # and recurse to consider all possible tail sequences that can follow this particular word:

            for tail in chains(words, previous_word=each_word):

                # Concatenate the word we're considering with each possible tail:

                yield [each_word] + tail  



all_legal_sequences = list(chains(words))  # convert the output (an iterator) to a list

all_legal_sequences.sort(key=len) # sort the list of chains in increasing order of chain length

print(all_legal_sequences[-1]) # print the last (and therefore longest) chain

# Prints:  ['hedgehog', 'giraffe', 'elephant', 'tiger', 'racoon']

In the spirit of brute force solutions, you can check all permutations of the words list and choose the best continuous starting sequence:

from itertools import permutations



def continuous_starting_sequence(words):

    chain = [words[0]]

    for i in range(1, len(words)):

        if not words[i].startswith(words[i - 1][-1]):

            break

        chain.append(words[i])

    return chain



words = ['giraffe', 'elephant', 'ant', 'tiger', 'racoon', 'cat', 'hedgehog', 'mouse']

best = max((continuous_starting_sequence(seq) for seq in permutations(words)), key=len)



print(best)

# ['hedgehog', 'giraffe', 'elephant', 'tiger', 'racoon']

Since we're considering all permutations, we know that there must be a permutation that starts with the largest word chain.

This, of course, has O(n n!) time complexity :D

Another answer using a recursive approach:

def word_list(w_list, remaining_list):

    max_result_len=0

    res = w_list

    for word_index in range(len(remaining_list)):

        # if the last letter of the word list is equal to the first letter of the word

        if w_list[-1][-1] == remaining_list[word_index][0]:

            # make copies of the lists to not alter it in the caller function

            w_list_copy = w_list.copy()

            remaining_list_copy = remaining_list.copy()

            # removes the used word from the remaining list

            remaining_list_copy.pop(word_index)

            # append the matching word to the new word list

            w_list_copy.append(remaining_list[word_index])

            res_aux = word_list(w_list_copy, remaining_list_copy)

            # Keep only the longest list

            res = res_aux if len(res_aux) > max_result_len else res 

    return res



words = ['giraffe', 'elephant', 'ant', 'tiger', 'racoon', 'cat', 'hedgehog', 'mouse']

word_list(['dog'], words)

output:

['dog', 'giraffe', 'elephant', 'tiger', 'racoon']

Hopefully, a more intuitive way of doing it without recursion. Iterate through the list and let Python's sort and list comprehension do the work for you:

words = ['giraffe', 'elephant', 'ant', 'tiger', 'racoon', 'cat', 'hedgehog', 'mouse']



def chain_longest(pivot, words):

    new_words = 

    new_words.append(pivot)

    for word in words:

        potential_words = [i for i in words if i.startswith(pivot[-1]) and i not in new_words]

        if potential_words:

            next_word = sorted(potential_words, key = lambda x: len)[0]

            new_words.append(next_word)

            pivot = next_word

        else:

            pass

    return new_words



max([chain_longest(i, words) for i in words], key = len)

>>

['hedgehog', 'giraffe', 'elephant', 'tiger', 'racoon']

Set a pivot and check for potential_words if they start with your pivot word and do not appear in your new list of words. If found then just sort them by length and take the first element.

The list comprehension goes through every word as a pivot and returns you the longest chain.