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

There was a discussion about this exact problem (though it was phrased in a different way) at http://www.perlmonks.org/?node_id=180276.

In the end the best solution was to do a binary search through all possible widths to find the smallest width that wound up with no more than the desired number of columns. If there are n items and the average width is m, then you'll need O(log(n) + log(m)) passes to find the right width, each of which takes O(n) time, for O(n * (log(n) + log(m))). This is probably fast enough with no more need to be clever.

If you wish to be clever, you can create an array of word counts, and cumulative lengths of the words. Then use binary searches on this data structure to figure out where the line breaks are. Creating this data structure is O(n), and it makes all of the passes to figure out the right width be O(log(n) * (log(n) + log(m))) which for reasonable lengths of words is dominated by your first O(n) pass.

If the widths of words can be floating point, you'll need to do something more clever with the binary searches, but you are unlikely to need that particular optimization.