How to split text without spaces into list of words

Using a trie data structure, which holds the list of possible words, it would not be too complicated to do the following:

1. Advance pointer (in the concatenated string)
2. Lookup and store the corresponding node in the trie
3. If the trie node has children (e.g. there are longer words), go to 1.
4. If the node reached has no children, a longest word match happened; add the word (stored in the node or just concatenated during trie traversal) to the result list, reset the pointer in the trie (or reset the reference), and start over

A naive algorithm won't give good results when applied to real-world data. Here is a 20-line algorithm that exploits relative word frequency to give accurate results for real-word text.

(If you want an answer to your original question which does not use word frequency, you need to refine what exactly is meant by "longest word": is it better to have a 20-letter word and ten 3-letter words, or is it better to have five 10-letter words? Once you settle on a precise definition, you just have to change the line defining wordcost to reflect the intended meaning.)

The idea

The best way to proceed is to model the distribution of the output. A good first approximation is to assume all words are independently distributed. Then you only need to know the relative frequency of all words. It is reasonable to assume that they follow Zipf's law, that is the word with rank n in the list of words has probability roughly 1/(n log N) where N is the number of words in the dictionary.

Once you have fixed the model, you can use dynamic programming to infer the position of the spaces. The most likely sentence is the one that maximizes the product of the probability of each individual word, and it's easy to compute it with dynamic programming. Instead of directly using the probability we use a cost defined as the logarithm of the inverse of the probability to avoid overflows.

The code

from math import log

# Build a cost dictionary, assuming Zipf's law and cost = -math.log(probability).
words = open("words-by-frequency.txt").read().split()
wordcost = dict((k, log((i+1)*log(len(words)))) for i,k in enumerate(words))
maxword = max(len(x) for x in words)

def infer_spaces(s):
    """Uses dynamic programming to infer the location of spaces in a string
    without spaces."""

    # Find the best match for the i first characters, assuming cost has
    # been built for the i-1 first characters.
    # Returns a pair (match_cost, match_length).
    def best_match(i):
        candidates = enumerate(reversed(cost[max(0, i-maxword):i]))
        return min((c + wordcost.get(s[i-k-1:i], 9e999), k+1) for k,c in candidates)

    # Build the cost array.
    cost = [0]
    for i in range(1,len(s)+1):
        c,k = best_match(i)
        cost.append(c)

    # Backtrack to recover the minimal-cost string.
    out = []
    i = len(s)
    while i>0:
        c,k = best_match(i)
        assert c == cost[i]
        out.append(s[i-k:i])
        i -= k

    return " ".join(reversed(out))

which you can use with

s = 'thumbgreenappleactiveassignmentweeklymetaphor'
print(infer_spaces(s))

---

The results

I am using this quick-and-dirty 125k-word dictionary I put together from a small subset of Wikipedia.

Before: thumbgreenappleactiveassignmentweeklymetaphor.
After: thumb green apple active assignment weekly metaphor.

Before: thereismassesoftextinformationofpeoplescommentswhichisparsedfromhtmlbuttherearen odelimitedcharactersinthemforexamplethumbgreenappleactiveassignmentweeklymetapho rapparentlytherearethumbgreenappleetcinthestringialsohavealargedictionarytoquery whetherthewordisreasonablesowhatsthefastestwayofextractionthxalot.

After: there is masses of text information of peoples comments which is parsed from html but there are no delimited characters in them for example thumb green apple active assignment weekly metaphor apparently there are thumb green apple etc in the string i also have a large dictionary to query whether the word is reasonable so what s the fastest way of extraction thx a lot.

Before: itwasadarkandstormynighttherainfellintorrentsexceptatoccasionalintervalswhenitwascheckedbyaviolentgustofwindwhichsweptupthestreetsforitisinlondonthatoursceneliesrattlingalongthehousetopsandfiercelyagitatingthescantyflameofthelampsthatstruggledagainstthedarkness.

After: it was a dark and stormy night the rain fell in torrents except at occasional intervals when it was checked by a violent gust of wind which swept up the streets for it is in london that our scene lies rattling along the housetops and fiercely agitating the scanty flame of the lamps that struggled against the darkness.

As you can see it is essentially flawless. The most important part is to make sure your word list was trained to a corpus similar to what you will actually encounter, otherwise the results will be very bad.

---

Optimization

The implementation consumes a linear amount of time and memory, so it is reasonably efficient. If you need further speedups, you can build a suffix tree from the word list to reduce the size of the set of candidates.

If you need to process a very large consecutive string it would be reasonable to split the string to avoid excessive memory usage. For example you could process the text in blocks of 10000 characters plus a margin of 1000 characters on either side to avoid boundary effects. This will keep memory usage to a minimum and will have almost certainly no effect on the quality.

Here is solution using recursive search:

def find_words(instring, prefix = '', words = None):
    if not instring:
        return []
    if words is None:
        words = set()
        with open('/usr/share/dict/words') as f:
            for line in f:
                words.add(line.strip())
    if (not prefix) and (instring in words):
        return [instring]
    prefix, suffix = prefix + instring[0], instring[1:]
    solutions = []
    # Case 1: prefix in solution
    if prefix in words:
        try:
            solutions.append([prefix] + find_words(suffix, '', words))
        except ValueError:
            pass
    # Case 2: prefix not in solution
    try:
        solutions.append(find_words(suffix, prefix, words))
    except ValueError:
        pass
    if solutions:
        return sorted(solutions,
                      key = lambda solution: [len(word) for word in solution],
                      reverse = True)[0]
    else:
        raise ValueError('no solution')

print(find_words('tableapplechairtablecupboard'))
print(find_words('tableprechaun', words = set(['tab', 'table', 'leprechaun'])))

yields

['table', 'apple', 'chair', 'table', 'cupboard']
['tab', 'leprechaun']

Based on the excellent work in the top answer, I've created a pip package for easy use.

>>> import wordninja
>>> wordninja.split('derekanderson')
['derek', 'anderson']

To install, run pip install wordninja.

The only differences are minor. This returns a list rather than a str, it works in python3, it includes the word list and properly splits even if there are non-alpha chars (like underscores, dashes, etc).

Thanks again to Generic Human!

https://github.com/keredson/wordninja