Word wrap to X lines instead of maximum width (Least raggedness)

Question

Does anyone know a good algorithm to word wrap an input string to a specified number of lines rather than a set width. Basically to achieve the minimum width for X lines.

Answer 1

I'll assume you're trying to minimize the maximum width of a string with n breaks. This can be done in O(words(str)*n) time and space using dynamic programming or recursion with memoziation.

The recurrence would look like this where the word has been split in to words

def wordwrap(remaining_words, n):
    if n > 0 and len(remaining_words)==0:
        return INFINITY  #we havent chopped enough lines

    if n == 0:
        return len(remaining_words.join(' ')) # rest of the string

    best = INFINITY
    for i in range remaining_words:
        # split here 
        best = min( max(wordwrap( remaining_words[i+1:], n-1),remaining_words[:i].join(' ')), best  )  

    return best